Saturday, 24 June 2017

On This Day in Math - June 24

"For example" is not a proof.  
Jewish proverb

The 175th day of the year; 175 is the smallest number n greater than 1 such that n6
\(\pm 6\) are both prime.  *Prime Curios & Derek Orr

If S(n) = the sum of the proper divisors of n ( so S(8) = 1+2+4=7) then if S(n1) = n2 and s(n2)= n3... and s(n)=n1 we call the sequence a "sociable chain" of length n. There are, at this writing, 175 sociable chains with length greater than 2
(sociable chains of link two are called amicable numbers. The pair known to the ancients are 220 and 284 )

From Jim Wilder ‏@wilderlab : \( 175 = 1^1 + 7^2 + 5^3 \)


1497 The name America is first used for the newly discovered continent, or at least part of it. Named by John Cabot in honor of his Bristol sponsor, Welshman Robert Ameryk, a prosperous merchant. According to accounts from the period, a record for that year in the Bristol calendar stated, "... on Saint Johns Day, the land of America was found by merchants of Bristowe, in a ship of Bristowe called the Mathew."
 The first use of the name on a map was on the Waldseemuller map of 1507. As was common at the time, the map was accompanied by a cosmographia explaining the basics of cartography and how to use the map. In his  Cosmographiae Introductio  Waldseemuller makes clear that it is named for Vespucci.  Its full title translates to, "Introduction to Cosmography With Certain Necessary Principles of Geometry and Astronomy To which are added The Four Voyages of Amerigo Vespucci A Representation of the Entire World, both in the Solid and Projected on the Plane, Including also lands which were Unknown to Ptolemy, and have been Recently Discovered".
While Cabot certainly discovered the mainland of the Americas before Vespucci, it seems that the weight of evidence for why we use the name America is weighted heavily toward the Amerigo Vespucci theory.  An excellent analysis of the evidence on that side, and the lack of evidence in support of Ameryk, is given by The Renaissance Mathematicus here.  *PB combined notes from many sources.

1634 Gilles Personne de Roberval was proclaimed the winner of the triennial competition for the Ramus chair at the Coll`ege Royal in Paris. Thereafter, he kept his mathematical discoveries secret so that he could continue to win the competition and keep the chair. As a consequence he lost credit for many of his discoveries. *VFR
He worked on the quadrature of surfaces and the cubature of solids, which he accomplished, in some of the simpler cases, by an original method which he called the "Method of Indivisibles"; but he lost much of the credit of the discovery as he kept his method for his own use, while Bonaventura Cavalieri published a similar method which he independently invented. 
Another of Roberval’s discoveries was a very general method of drawing tangents, by considering a curve as described by a moving point whose motion is the resultant of several simpler motions. He also discovered a method of deriving one curve from another, by means of which finite areas can be obtained equal to the areas between certain curves and their asymptotes. To these curves, which were also applied to effect some quadratures, Evangelista Torricelli gave the name "Robervallian lines."

1644 In a letter to Torricelli, Fr. Marin Mersenne gives a method to find a number with any number of factors. He explained; since 60 = 2*2*3*5 subtract one from each factor (1,1,2, 4) and make them the exponents of any primes.. he used 24*32*5*7= 5040.. Of course Plato knew much earlier that 5040 had sixty factors.In Laws, Plato suggests that 5040 is the optimal number of citizens in a state because a) It is the product of 12, 20, and 21;  b) the 12th part of it can still be divided by 12; and c) it has 59 proper divisors, including all numbers for 1 to 12 except 11, and 5038--which is very close to 5040--is divisible by 11.

1687 In a letter to Huygens, Fatio de Dullier used an integrating factor to solve the differential equation 3x dy − 2y dx = 0. No earlier instance of an integrating factor is known. The fundamental conception of integrating factors was due to Euler (1734) and further developed by Clairaut (1739). *VFR

In 1778, David Rittenhouse observed a total solar eclipse in Philadelphia. In a letter to him, dated 17 Jul 1778, Thomas Jefferson wrote that "We were much disappointed in Virginia generally on the day of the great eclipse, which proved to be cloudy." Rittenhouse (1732-1796) was not only an American astronomer, but also a mathematician and public official. He is reputed to have built the first American-made telescope and was the first director of the U.S. Mint (1792-1795).*TIS  Jefferson was an excellent applied mathematician and had contacted Rittenhouse on another occasion.  Travelling through France ten years later, " in 1788, he noticed peasants near Nancy ploughing, and fell to wondering about the design of the moldboard, that is, the surface which turns the earth: he spent the next ten years working on this, on and off, wondering how to achieve the most efficient design, both offering least frictional resistance, and which also would be easy for farmers out in the frontiers to construct, far from technical help. He consulted the Pennsylvania mathematician Robert Patterson (born in Ireland in 1743), and consulted also another Philadelphia luminary, the self-taught astronomer and mathematical instrument-maker David Rittenhouse (1732-1796)."   Jefferson also communicated with Thomas Paine about bridge design, suggesting the use of catenary arches.  Jefferson is believed to be the first person ever to use the term "catenary" in English. 

1847 The first observation with the Great Refractor at Harvard was of the Moon on the afternoon of June 24, 1847. A number of significant achievements quickly followed. The eighth satellite of Saturn was discovered in 1848 by W.C. Bond and his son, George P. Bond, who was to succeed his father as Director in 1859. In 1850, Saturn's crape, or inner, ring was first observed, again by the Bonds. That same year, the first daguerreotype ever made of a star, the bright Vega, was taken by J.A. Whipple working under W.C. Bond, following several years of experiments using smaller telescopes. One of the earliest photographs of a double star, Mizar and Alcor in the handle of the Big Dipper, was achieved in 1857, using the wet-plate collodion process. *Observatory web page...  The 15 inch Great Refractor was "once the biggest and best telescope in the United States, perhaps the world."  *Frederik Pohl, Chasing Science, pg 42.

In 1898, a U.S. commemorative stamp was first used that carried the design of a major engineering construction project, the Mississippi River Bridge, a triple-arch steel bridge between East St. Louis, Illinois and St. Louis,
Missouri. Each span was roughly 500 feet and rested on piers resting on bedrock some 100 feet beneath the river bottom. Opened on 4 Jul 1874, the bridge was named after its designer, the self-trained engineer, James Eads. The upper level road also carried streetcars, which are seen in the stamp design along with steam ships on the river below. The trains that ran on its lower level are hidden from view at this angle. (Although still in use, the bridge no longer carries rail traffic.) The design was reissued in 1998.*TIS

In 1975, a moon tremour, caused by a strike of Taurid meteors, was detected by the seismometer network left on the Moon's surface by American astronauts. The major series of lunar impacts between 22 - 26 Jun 1975 represented 5% of the total number of impacts detected during the eight years of the network's operation, and included numerous 1-ton meteorites. The impacts were detected only when the nearside of the Moon (where the astronauts landed) was facing the Beta Taurid radiant. At the same time, there was a lot of activity detected in Earth's ionosphere, which has been linked with meteor activity. The Taurid meteor storm crosses the Earth orbit twice a year, during the period 24 Jun to 6 Jul and the period 3 Nov to 15 Nov.*TIS

1978 Charon first suggested for the name of Pluto's moon. Charon was originally known by the temporary designation S/1978 P 1, according to the then recently instituted convention. On June 24, 1978, U.S. Naval Observatory astronomer James Christy who had discovered the moon, first suggested the name Charon as a scientific-sounding version of his wife Charlene's nickname, "Char."
Although colleagues at the Naval Observatory proposed Persephone, Christy stuck with Charon after discovering it coincidentally refers to a Greek mythological figure: Charon is the ferryman of the dead, closely associated in myth with the god Hades, whom the Romans identified with their god Pluto. Official adoption of the name by the IAU waited until late 1985 and was announced on January 3, 1986.
There is minor debate over the preferred pronunciation of the name. The practice of following the classical pronunciation established for the mythological ferryman Charon is used by major English-language dictionaries such as the Merriam-Webster and Oxford English Dictionary.[19][20] These indicate only one pronunciation of "Charon" when referring specifically to Pluto's moon: with an initial "k" sound. Speakers of languages other than English, and many English-speaking astronomers as well, follow this pronunciation.
However, Christy himself pronounced the ch in the moon's name as sh, after his wife Charlene. *Wik

2012 Lonesome George, the last Pinta Island tortoise dies. Also known as the Pinta giant tortoise, Abingdon Island tortoise, or Abingdon Island giant tortoise, was a subspecies of Galápagos tortoise native to Ecuador's Pinta Island.
The subspecies was described by Albert Günther in 1877 after specimens arrived in London. By the end of the 19th century, most of the Pinta Island tortoises had been wiped out due to hunting. By the mid-20th century, it was assumed that the species was extinct until a single male was discovered on the island in 1971. Efforts were made to mate the male, named Lonesome George, with other subspecies, but no viable eggs were produced. Lonesome George died on June 24, 2012. The subspecies is believed to have become extinct; however, there has been at least one first-generation hybrid individual found outside Pinta Island *Wik


1880 Oswald Veblen, (June 24, 1880 – August 10, 1960) American mathematician, born in Decorah, Iowa, who made important contributions to differential geometry and early topology. Many of his contributions found application to atomic physics and relativity. Along with his interest in the foundations of geometry he developed an interest in algebraic topology, or analysis situs as it was then called and by 1912 was writing papers on this subject. Gradually he became more interested in differential geometry. From l922 onward most of his papers were in this area and in its connections with relativity. His work on axioms for differentiable manifolds and differential geometry contributed directly to the field.*TIS

1909 William Penney (24 Jun 1909, 3 Mar 1991 at age 81)(Baron Penney of East Hendred) British nuclear physicist who led Britain's development of the atomic bomb. Penney was to Britain as Robert Oppenheimer was to the U.S. He was a prominent part of the British Mission at Los Alamos during WW II, where his principal assignment was studying the damage effects from the blast wave of the atomic bomb, but he became involved in implosion studies as well. Penney's combination of expertise, analytical skill, effective communication, and the ability to translate them into practical application soon made him one of the five members of the Los Alamos “brain trust” that made key decisions. He was the only Briton to be part of the ten man Target Committee that drew up the list of targets for the atomic bombing of Japan. *TIS

1912 Wilhelm Cauer (June 24, 1900 – April 22, 1945) was a German mathematician and scientist. He is most noted for his work on the analysis and synthesis of electrical filters and his work marked the beginning of the field of network synthesis. Prior to his work, electronic filter design used techniques which accurately predicted filter behaviour only under unrealistic conditions. This required a certain amount of experience on the part of the designer to choose suitable sections to include in the design. Cauer placed the field on a firm mathematical footing, providing tools that could produce exact solutions to a given specification for the design of an electronic filter. *Wik
By the end of World War II, he was, like millions of less-distinguished countrymen and -women, merely a person in the way of a terrible conflagration.
Cauer succeeded in evacuating his family west, where the American and not the Soviet army would overtake it — but for reasons unclear he then returned himself to Berlin. His son Emil remembered the sad result.
The last time I saw my father was two days before the American Forces occupied the small town of Witzenhausen in Hesse, about 30 km from Gottingen. We children were staying there with relatives in order to protect us from air raids. Because rail travel was already impossible, my father was using a bicycle. Military Police was patrolling the streets stopping people and checking their documents. By that time, all men over 16 were forbidden to leave towns without a permit, and on the mere suspicion of being deserters, many were hung summarily in the market places. Given this atmosphere of terror and the terrible outrages which Germans had inflicted on the peoples of the Soviet Union, I passionately tried to persuade my father to hide rather than return to Berlin, since it was understandable that the Red Army would take its revenge. But he decided to go back, perhaps out of solidarity with his colleagues still in Berlin, or just due to his sense of duty, or out of sheer determination to carry out what he had decided to do.
Seven months after the ending of that war, my mother succeeded in reaching Berlin and found the ruins of our house in a southern suburb of the city. None of the neighbors knew about my father’s fate. But someone gave identification papers to my mother which were found in a garden of the neighborhood. The track led to a mass grave with eight bodies where my mother could identify her husband and another man who used to live in our house. By April 22, 1945, the Red Army had crossed the city limits of Berlin at several points. Although he was a civilian and not a member of the Nazi Party, my father and other civilians were executed by soldiers of the Red Army. The people who witnessed the executions were taken into Soviet captivity, and it was not possible to obtain details of the exact circumstances of my father’s death.

1915 Sir Fred Hoyle (24 June 1915 – 20 August 2001) English mathematician and astronomer, best known as the foremost proponent and defender of the steady-state theory of the universe. This theory holds both that the universe is expanding and that matter is being continuously created to keep the mean density of matter in space constant. He became Britain's best-known astronomer in 1950 with his broadcast lectures on The Nature of the Universe, and he recalled coining the term "Big Bang" in the last of those talks. Although over time, belief in a "steady state" universe as Hoyle had proposed was shared by fewer and fewer scientists because of new discoveries, Hoyle never accepted the now most popular "Big Bang" theory for the origin of the universe.

1927 Martin Lewis Perl (June 24, 1927 – September 30, 2014) was an American physicist who won the Nobel Prize in Physics in 1995 for his discovery of the tau lepton.
He received his Ph.D. from Columbia University in 1955, where his thesis advisor was I.I. Rabi. Perl's thesis described measurements of the nuclear quadrupole moment of sodium, using the atomic beam resonance method that Rabi had won the Nobel Prize in Phyics for in 1944.
Following his Ph.D., Perl spent 8 years at the University of Michigan, where he worked on the physics of strong interactions, using bubble chambers and spark chambers to study the scattering of pions and later neutrons on protons.[1] While at Michigan, Perl and Lawrence W. Jones served as co-advisors to Samuel C. C. Ting, who earned the Nobel Prize in Physics in 1976.
Seeking a simpler interaction mechanism to study, Perl started to consider electron and muon interactions. He had the opportunity to start planning experimental work in this area when he moved in 1963 to the Stanford Linear Accelerator Center (SLAC), then being built in California. He was particularly interested in understanding the muon: why it should interact almost exactly like the electron but be 206.8 times heavier, and why it should decay through the route that it does. Perl chose to look for answers to these questions in experiments on high-energy charged leptons. In addition, he considered the possibility of finding a third generation of lepton through electron-positron collisions. He died after a heart attack at Stanford University Hospital on September 30, 2014 at the age of 87. *Wik


1832 Timofei Fedorovic Osipovsky (February 2, 1766–June 24, 1832) was a Russian mathematician, physicist, astronomer, and philosopher. Timofei Osipovsky graduated from the St Petersburg Teachers Seminary.
He was to became a teacher at Kharkov University. Kharkov University was founded in 1805. The city of Kharkov, thanks to its educational establishments, became one of the most important cultural and educational centers of Ukraine. Osipovsky was appointed to Kharkov University in 1805, the year of the foundation of the University. In 1813 he became rector of the University. However in 1820 Osipovsky was suspended from his post on religious grounds.
His most famous work was the three volume book A Course of Mathematics (1801–1823). This soon became a standard university text and was used in universities for many years. *Wik

1880 Jules Lissajous (March 4, 1822, Versailles – June 24, 1880, Plombières-les-Bains) was a French mathematician best known for the Lissajous figures produced from a pair of sine waves. *SAU  The curves are also called Bowditch curves for the early American mathematician, Nathanial Bowditch,  who worked with them earlier.  In general, a parametric curve with equations x= A sin(k t ); y= B sin(m t), the curves can describe things as simple as a circle or ellipse to more complex open and closed curves.  If the ratio of k/m is rational, the curve will eventually close. 

*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Friday, 23 June 2017

On This Day in Math - June 23

We can only see a short distance ahead,
but we can see plenty there that needs to be done.

Alan Turing, From his paper on the Turing test

The 174th day of the year; there are 174 twin prime pairs among the first 1000 integers.

174 = 72 + 53 and is also the sum of four consecutive squares.

174 is the smallest number that begins a string of four numbers so that none of them is a palindrome in any base, b, \( 2 \leq b \leq 10 \)
From Jim Wilder ‏@wilderlab : \( 175 = 1^1 + 7^2 + 5^3 \)


1191 "In the month of June, the Vigil of the Nativity of St John the Baptist (June 23), the 9 th day before the Kalends of July, on the 27 th day of the Moon, at the 9 th hour of the day, the Sun was eclipsed and it lasted for three hours; the Sun was so obscured that the darkness arose over the Earth and stars appeared in the sky. And when the eclipse withdrew, the Sun returned to its
original beauty." This was an annular solar eclipse.

1585 Thomas Harriot arrived off the coast of Virginia (actually Cape Lookout, NC). He was the first substantial mathematician to visit North America. [John W. Shirley in Thomas Harriot: A Biography, 1983, p. 129; Thanks to Kullman] *VFR Thomas Harriot's name was once synonymous with a common method of solving quadratics taught in nearly every high school. Once commonly called Harriot's Method, today it is simply referred to as factoring.
And how did he come to be in the exploration of Virginia?? Here is the story from Encyclopedia Virginia, 2010:
Thomas Hariot (often spelled Harriot) was an English mathematician, astronomer, linguist, and experimental scientist. During the 1580s, he served as Sir Walter Raleigh's primary assistant in planning and attempting to establish the English colonies on Roanoke Island off the coast of present-day North Carolina. He taught Raleigh's sea captains to sail the Atlantic Ocean using sophisticated navigational methods not well understood in England at the time. He also learned the Algonquian language from two Virginia Indians, Wanchese and Manteo. In 1585, Hariot joined the expedition to Roanoke, which failed and returned to England the next year. During his stay in America, Hariot helped to explore the present-day Outer Banks region and, farther north, the Chesapeake Bay. He also collaborated with the artist John White in producing several maps notable at the time for their accuracy. Although Hariot left extensive papers, the only work published during his lifetime was "A Briefe and True Report of the New Found Land of Virginia", which evaluated the economic potential of Virginia. The report appeared most impressively in Theodor de Bry's 1590 edition that included etchings based on the White-Hariot maps and White's watercolors of Indian life. After a brief imprisonment in connection to the Gunpowder Plot (1605), Hariot calculated the orbit of Halley's Comet, sketched and mapped the moon, and observed sunspots. He died in 1621.

1676 Newton, via Oldenburg, sent his famous Epistola prior to Leibniz. It contained the first use of fractional exponents as well as the newly discovered binomial theorem.*VFR

In 1775, the first American-made book was advertised in Philadelphia, Penn. Titled Impenetrable Secret, the book was printed and sold by Story and Humphreys. Their advertisement in the Pennsylvania Mercury announced it was "printed with types, paper and ink manufactured in this Province."*TIS

1783 In June 1783, Charles Blagden, then assistant to Henry Cavendish, visited Antoine Lavoisier in Paris and described how Cavendish had created water by burning "inflammable air". Lavoisier's dissatisfaction with the Cavendish's "dephlogistinization" theory led him to the concept of a chemical reaction, which he reported to the Royal Academy of Sciences on 24 June 1783, effectively founding modern chemistry. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1789 *wik

1835 Mobius receives a letter from Bellavitis with a method for adding and subtracting non-collinear vectors. (A history of vector analysis: the evolution of the idea of a vectorial system By Michael J. Crowe) A geometrical work by Bellavitis was published in 1832 which also contains vector type quantities. His basic objects are line segments AB and he considers AB and BA as two distinct objects. He defines two line segments as 'equipollent' if they are equal and parallel, so, in modern notation, two line segments are equipollent if they represent the same vector. Bellavitis then defines the 'equipollent sum of line segments' and obtains an 'equipollent calculus' which is essentially a vector space. *SAU

1868 Christopher Latham Sholes receives a patent for an invention he calls the "Type-Writer." *OnThisDay & Facts ‏@NotableHistory (Sholes was an American inventor who invented the first practical typewriter and the QWERTY keyboard still in use today. He was also a newspaper publisher and Wisconsin politician.)

1993 Over the course of three lectures delivered at Isaac Newton Institute for Mathematical Sciences on June 21, 22, and 23 of 1993, Wiles announced his proof of the Taniyama–Shimura conjecture, and hence of Fermat's Last Theorem. There was a relatively large amount of press coverage afterwards. After announcing his results, (Nick) Katz was a referee on his manuscript and he asked Wiles a series of questions that led Wiles to recognize that the proof contained a gap. There was an error in a critical portion of the proof which gave a bound for the order of a particular group: the Euler system used to extend Flach's method was incomplete. Wiles and his former student Richard Taylor spent almost a year resolving it. Wiles indicates that on the morning of September 19, 1994 he realized that the specific reason why the Flach approach would not work directly suggested a new approach with the Iwasawa theory which resolved all of the previous issues with the latter and resulted in a CNF that was valid for all of the required cases. On 6 October Wiles sent the new proof to three colleagues including Faltings. The new proof was published and, despite its size, widely accepted as likely correct in its major components. *Wik

1988 Global warming became more widely popular after 23 June, 1988 when NASA climate scientist James Hansen used the term in a testimony to Congress. He said: "global warming has reached a level such that we can ascribe with a high degree of confidence a cause and effect relationship between the greenhouse effect and the observed warming." His testimony was widely reported and afterward global warming was commonly used by the press and in public discourse. *Wik

2013 The Moon will make its closest approach to the Earth (at perigee) for the year on Sunday, 23 June, at 11:11 (UTC), and at this time the Moon will be 356,989 km from the Earth (that means 221,823 miles for us non-geeks). *Bob Mrotek

1612 André Tacquet (23 June 1612 Antwerp – 22 December 1660 Antwerp, also referred to by his Latinized name Andrea Tacquet) was a Flemish mathematician and Jesuit Priest. His work prepared ground for the eventual discovery of the calculus.
He was born in Antwerp, and entered the Jesuit Order in 1629. From 1631 to 1635, he studied mathematics, physics and logic at Leuven. Two of his teachers were Saint-Vincent and Francois d'Aguilon.
Tacquet became a brilliant mathematician of international fame and his works were often reprinted and translated (into Italian and English). He helped articulate some of the preliminary concepts necessary for Isaac Newton and Gottfried Leibniz to recognize the inverse nature of the quadrature and the tangent. He was one of the precursors of the infinitesimal calculus, developed by John Wallis. His most famous work, which influenced the thinking of Blaise Pascal and his contemporaries, is Cylindricorum et annularium (1651). In this book Tacquet presented how a moving point could generate a curve and the theories of area and volume. *Wik

1756 Thomas Jones (23 June 1756 – 18 July 1807) was Head Tutor at Trinity College, Cambridge for twenty years and an outstanding teacher of mathematics. He is notable as a mentor of Adam Sedgwick.
He was born at Berriew, Montgomeryshire, in Wales. On completing his studies at Shrewsbury School, Jones was admitted to St John's College, Cambridge on 28 May 1774, as a 'pensioner' (i.e. a fee-paying student, as opposed to a scholar or sizar). He was believed to be an illegitimate son of Mr Owen Owen, of Tyncoed, and his housekeeper, who afterwards married a Mr Jones, of Traffin, County Kerry, Thomas then being brought up as his son.
On 27 June 1776, Jones migrated from St John's College to Trinity College. He became a scholar in 1777 and obtained his BA in 1779, winning the First Smith's Prize and becoming Senior Wrangler. In 1782, he obtained his MA and became a Fellow of Trinity College in 1781. He became a Junior Dean, 1787–1789 and a Tutor, 1787-1807. He was ordained a deacon at the Peterborough parish on 18 June 1780. Then he was ordained priest, at the Ely parish on 6 June 1784, canon of Fen Ditton, Cambridgeshire, in 1784, and then canon of Swaffham Prior, also 1784. On 11 December 1791, he preached before the University, at Great St Mary's, a sermon against duelling (from Exodus XX. 13), which was prompted by a duel that had lately taken place near Newmarket between Henry Applewhaite and Richard Ryecroft, undergraduates of Pembroke, in which the latter was fatally wounded. Jones died on 18 July 1807, in lodgings in Edgware Road, London. He is buried in the cemetery of Dulwich College. A bust and a memorial tablet are in the ante-chapel of Trinity College. *Wik

1775 Étienne-Louis Malus (23 Jun 1775, 24 Feb 1812 at age 36)French physicist who discovered that light, when reflected, becomes partially plane polarized; i.e., its rays vibrate in the same plane. He served in Napoleon's corps of engineers, fought in Egypt, and contracted the plague during Napoleon's aborted campaign in Palestine. Posted to Europe after 1801, he began research in optics. In 1808, he discovered that light rays may be polarized by reflection, while looking through a crystal of Iceland spar at the windows of a building reflecting the rays of the Sun. He noticed that on rotating the crystal the light was extinguished in certain positions. Applying corpuscular theory, he argued that light particles have sides or poles and coined the word "polarization." *TIS

1824 Johann Martin Zacharias Dase (June 23, 1824, Hamburg – September 11, 1861, Hamburg) was a German mental calculator.
He used to spend a lot of time playing dominoes, and suggested that this played a significant role in developing his calculating skills. Dase suffered from epilepsy from early childhood throughout his life.

At age 15 he began to travel extensively, giving exhibitions in Germany, Austria and England. Among his most impressive feats, he multiplied 79532853 × 93758479 in 54 seconds. He multiplied two 20-digit numbers in 6 minutes; two 40-digit numbers in 40 minutes; and two 100-digit numbers in 8 hours 45 minutes. The famous mathematician Carl Friedrich Gauss commented that someone skilled in calculation could have done the 100-digit calculation in about half that time with pencil and paper.

These exhibitions however did not earn him enough money, so he tried to find other employments. In 1844 he obtained a position in the Railway Department of Vienna, but this didn't last long since in 1845 he was reported in Mannheim and in 1846 in Berlin.

In 1844, Dase calculated π to 200 decimal places over the course of approximately two months, a record for the time, from the Machin-like formula:

\( \frac{\pi}{4} = \arctan \frac{1}{2} + \arctan \frac{1}{5} + \arctan \frac{1}{8} \)

He also calculated a 7-digit logarithm table and extended a table of integer factorizations from 7,000,000 to 10,000,000.

Dase had very little knowledge of mathematical theory. The mathematician Julius Petersen tried to teach him some of Euclid's theorems, but gave up the task once he realized that their comprehension was beyond Dase's capabilities. Gauss however was very impressed with his calculating skill, and he recommended that the Hamburg Academy of Sciences should allow Dase to do mathematical work on a full-time basis, but Dase died shortly thereafter.

The book "Gödel, Escher, Bach" by Douglas Hofstadter mentions his calculating abilities. "... he also had an uncanny sense of quantity. That is, he could just 'tell', without counting, how many sheep were in a field, or words in a sentence, and so forth, up to about 30." *Wik

1902 Dr. Howard T. Engstrom (23 Jun 1902, 9 Mar 1962 at age 59 American computer designer who promoted the first commercially available digital computer, the Univac. As a Yale professor he had written a paper on the mathematical basis for cryptanalysis techniques. During WW II he was called to the Navy and placed in command of the OP-20-G automated machines "Research Section" for message decryption. After the war, he was a co-founder of Engineering Research Associates, a private company to work on electronic digital circuit technology for the Navy on a contract basis, with former Navy researchers. ERA delivered its first Atlas computer to the National Security Agency in Dec 1950. As vice president for research, Engstrom took the initiative to make a commercial version, renamed Univac.*TIS

1912 Alan Mathison Turing (23 June 1912 – 7 June 1954) born. This British mathematician was one of the founders of recursion theory, invented the Turing machine (an abstract model of a computer), did important work in cryptography, and invented the computer. *Alan Turing. The Enigma by Andrew Hodges, 1983.

1941 Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic. Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator. He gained his bachelor degree as a Mathematics Scholar at Wadham College, Oxford, and an MSc (Econ) in Mathematical Logic and the Philosophy of Science at the London School of Economics in 1966. He gained both the doctorate (PhD) in 1969, and higher doctorate (D.Sc.) in 1978, in the History of Science at the University of London. He was Emeritus Professor of the History of Mathematics and Logic at Middlesex University, and a Visiting Research Associate at the London School of Economics.
He was awarded the Kenneth O. May Medal for services to the History of Mathematics by the International Commission for the History of Mathematics (ICHM) on 31 July 2009, at Budapest, on the occasion of the 23rd International Congress for the History of Science. In 2010, he was elected an Honorary Member of the Bertrand Russell Society.
He spent much of his career at Middlesex University. He was a fellow at the Institute for Advanced Study in Princeton, New Jersey, and is a member of the Académie Internationale d'Histoire des Sciences. *Wik

1944 Richard Peter Stanley (June 23, 1944; New York City, New York - ) is the Norman Levinson Professor of Applied Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts. He received his Ph.D. at Harvard University in 1971 under the supervision of Gian-Carlo Rota. He is an expert in the field of combinatorics and its applications to other mathematical disciplines.
Stanley is known for his two-volume book Enumerative Combinatorics (1986–1999). He is also the author of Combinatorics and Commutative Algebra (1983) and well over 100 research articles in mathematics. He has served as thesis advisor to more than 45 doctoral students, many of whom have had distinguished careers in combinatorial research.
Stanley's distinctions include membership in the National Academy of Sciences (elected in 1995), the 2001 Leroy P. Steele Prize for mathematical exposition, the 2003 Schock Prize, a plenary lecture at the 2006 meeting of the ICM (in Madrid, Spain), and election in 2012 as a fellow of the American Mathematical Society
Stanley created the symbol \( (\binom{n}{k}) = \binom {n+k-1}{k} \) for binomial selection with replacement. *John D Cook, Wik


1891 Wilhelm Eduard Weber (24 October 1804 – 23 June 1891)   German physicist who investigated terrestrial magnetism. For six years, from 1831, Weber worked in close collaboration with Gauss. Weber developed sensitive magnetometers, an electromagnetic telegraph (1833) and other magnetic instruments during this time. His later work (1855) on the ratio between the electrodynamic and electrostatic units of charge proved extremely important and was crucial to Maxwell in his electromagnetic theory of light. (Weber found the ratio was 3.1074 x 108 m/sec but failed to take any notice of the fact that this was close to the speed of light.) Weber's later years were devoted to work in electrodynamics and the electrical structure of matter. The magnetic unit, weber, is named after him.*TIS

1891 Norman Robert Pogson (23 Mar 1829; 23 Jun 1891 at age 62) English astronomer who devised the magnitude scale of the brightness of stars (1850) now in use. He divided the classical scale in which a first magnitude star is one hundred times brighter than a sixth magnitude star using five integer steps. Each step represents a fifth-root of 100 (about 2.512) increase in brightness. The Sun's magnitude on this scale is -26.91, whereby negative numbers denote objects brighter than first magnitude. Sirius is magnitude -1.58, Aldebaran is 1 and the faintest star detected is 30. His interest in astronomy began in his youth; by age 18 he had calculated orbits for two comets. He discovered 8 asteroids, 21 new variable stars and compiled a massive star catalogue. In 1860 he moved to India for the remainder of his life's work.*TIS

1892 Pierre Ossian Bonnet (22 December 1819, Montpellier – 23 June 1892, Paris)died. He worked on minimal surfaces, geodesics, and integral geometry. *VFR  Bonnet made major contributions introducing the notion of geodesic curvature. A formula for the line integral of the geodesic curvature along a closed curve is known as the Gauss-Bonnet theorem. Gauss published a special case.

*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Thursday, 22 June 2017

On This Day in Math - June 22

The mathematical education of the young physicist [Albert Einstein ] was not very solid, which I am in a good position to evaluate since he obtained it from me in Zurich some time ago.
~Hermann Minkowski

The 173rd day of the year; the only prime whose sum of cubed digits equals its reversal: 13 + 73 + 33 = 371. *Prime Curioos

The smallest prime inconsummate number, i.e., no number is 173 times the sum of its digits. (The term inconsummate number was created by John Conway from the Latin for unfinished. [when?])

173 is the largest known prime whose square (29929) and cube (5177717) consist of different digits.


1633 Galileo, under threat of torture from the inquisition, was forced to "abjure, curse, and detest" his Copernican heliocentric views.
The recantation of GALILEO took place in the Great Hall of the former monastery of Santa Maria sopra Minerva, then the headquarters of the Dominican order. This is where he supposedly said "E pur si muove" (Nevertheless, it does move). For a long time, these words were believed to be a much later invention, but they probably date back to c1643 [Fahie, pp. 72 75]. Galileo was never officially imprisoned except for the few hours between his trial and the sentencing. In 1992, the Vatican officially declared that Galileo had been the victim of an error.
Galileo before the Holy Office, a 19th-century painting by Joseph-Nicolas Robert-Fleury

In 1675, the Royal Greenwich Observatory was created by Royal Warrant in England by Charles II. Building designed by Sir Christopher Wren (who was also a Professor of Astronomy) was commenced 10 Aug 1675 and finished the following year by John Flamsteed was appointed as the first Astronomer Royal. Its primary uses were in practical astronomy - navigation, timekeeping, determination of star positions. In 1767 the observatory began publishing The Nautical Almanac, which established the longitude of Greenwich as a baseline for time calculations. The almanac's popularity among navigators led in part to the adoption (1884) of the Greenwich meridian as the Earth's prime meridian (0° longitude) and the international time zones.*TIS

1714 second reading of the Longitude Bill in British Parliament *@Lordoflongitude

1799 France adopted the metric system of weights and measures. *VFR

1902 In response to a letter from Bertrand Russell dated 16 June 1902, Gottlob Frege responded with characteristic scientific honesty that “your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build arithmetic.” [van Heijenoort, From Frege to G¨odel, 125–128] *VFR
Russell had found a class of contradictions to Frege's 1879 Begriffsschrift. This contradiction can be stated as "the class of all classes that do not contain themselves as elements".

1978 evidence of the first moon of Pluto was discovered by astronomer James W. Christy of the Naval Observatory in Flagstaff, Ariz. when he obtained a photograph of Pluto that showed the orb to be distinctly elongated.. Furthermore, the elongations appeared to change position with respect to the stars over time. After eliminating the possibility that the elongations were produced by plate defects and background stars, the only plausible explanation was that they were caused by a previously unknown moon orbiting Pluto at a distance of about 19,600 kilometers (12,100 miles) with a period of 6.4 days. The moon was named Charon, after the boatman in Greek mythology who took the souls of the dead across the River Styx to Pluto's underworld. *TIS (actually Christy created the name in honor of his wife, whose nickname was Char. He did not know the mythical name when he proposed it. It is said he still persists in pronouncing the moon with a "sh" sound rather than the hard k sound used in mythology.)

2004 Humans are officially slow learners... In 2004, a study led by Richard Doll was published in the British Medical Journal, the first research that quantified the damage over the lifetime of a generation, based on a 50-year study of a group of almost 35,000 British doctors who smoked. The study found that almost half of persistent cigarette smokers were killed by their habit, and a quarter died before age 70. Further, those who quit by age 30 had the same life expectancy as a nonsmoker. Even quitting at age 50 saved six more years of life over those who continued smoking. At age 80, 65% of non-smokers were still alive, but only 32% of smokers. Fifty years before, Doll published in the same journal the first report of a study that linked cigarette smoking to lung cancer*TIS

2011 One of the 15th century copies of a manuscript of Fibonacci's Liber Abacci that was owned by Boncompagni and was until recently in Brown University Maths library is for sale, by auction, on June 22, 2011, in New York and is estimated to fetch in excess of \( $120,000\). (It seems it brought even more,"Fibonacci, manuscript copy of the Liber Flos, \($338,000\) at Bonhams New York on June 22. "


1837 Paul Gustav Heinrich Bachmann born (22 June 1837 – 31 March 1920). He wrote (1892–1923) a five volume survey of the state of number theory including an evaluation of the various methods of proof. He also devoted time to composing, playing the piano, and serving as a music critic for various newspapers. *VFR

1860 Mario Pieri (22 June 1860 in Lucca, Italy - 1 March 1913 in S Andrea di Compito (near Lucca), Italy) Pieri's main area was projective geometry and he is an important member of the Italian School of Geometers. However, after he moved to Turin, Pieri became influenced by Peano at the University and Burali-Forti who was a colleague at the Military Academy. This influence led Pieri to study the foundations of geometry.
In 1895 he set up an axiomatic system for projective geometry with three undefined terms, namely points, lines and segments. He improved on results of Pasch and Peano and then, in 1905, Pieri gave the first axiomatic definition of complex projective geometry which does not build on real projective geometry.
In 1898 Pieri published the memoir The principles of the geometry of position through the Academy of Sciences of Turin. Russell was impressed by this memoir and wrote, in his Principia, "This is, in my opinion, the best work on the present subject." *SAU

1864 Herman Minkowski born (June 22, 1864 – January 12, 1909) . The motto on his Akademie-Schrift was “Rien n’est beau que le vrai, le vrai seul est aimable” (Nothing is beautiful but the truth, only the truth is lovable). *VFR He developed the geometrical theory of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity. By 1907, Minkowski realised that the work of Lorentz and Einstein could be best understood in a non-euclidean space. He considered space and time, which were formerly thought to be independent, to be coupled together in a four-dimensional "space-time continuum". Minkowski worked out a four-dimensional treatment of electrodynamics. His idea of a four-dimensional space (since known as "Minkowski space"), combining the three dimensions of physical space with that of time, laid the mathematical foundation of Albert Einstein's general theory of relativity.*TIS My favorite Minkowski story from Constance Reid's Hilbert, Once in a topology lecture he brought up the Four-color theorem. "This theorem has not been proved, but that is because only mathematicians of the third rank have occupied themselves with it" he announced with unusual arrogance. "I belive I can prove it." He began on the spot to work out the problem and continued over several classes to develop the work. After several weeks he entered one rainy day and a crash of thunder accompanied his entrance. Turning to his students he announced, "Heaven is angered by my arrogance, My proof is defective."

1866 Kazimierz Żorawski (June 22, 1866 – January 23, 1953) was a Polish mathematician. His work earned him an honored place in mathematics alongside such Polish mathematicians as Wojciech Brudzewski, Jan Brożek (Broscius), Nicolas Copernicus, Samuel Dickstein, Stefan Banach, Stefan Bergman, Marian Rejewski, Wacław Sierpiński, Stanisław Zaremba and Witold Hurewicz.[citation needed]
Żorawski's main interests were invariants of differential forms, integral invariants of Lie groups, differential geometry and fluid mechanics. His work in these disciplines was to prove important in other fields of mathematics and science, such as differential equations, geometry and physics (especially astrophysics and cosmology).*Wik

1880 Alfred Rosenblatt born. He worked in analysis and probability theory. *VFR

1906 Ott-Heinrich Keller was a German mathematician who worked on algebraic geometry and topology*SAU

1910 Konrad Zuse, (22 June 1910
Berlin, German Empire - 18 December 1995 (aged 85) Hünfeld, Germany) inventor of the first fully functional programmable digital computer. *VFR a German civil engineer and computer pioneer. His greatest achievement was the world's first functional program-controlled Turing-complete computer, the Z3, which became operational in May 1941.

Zuse was also noted for the S2 computing machine, considered the first process-controlled computer. He founded one of the earliest computer businesses in 1941, producing the Z4, which became the world's first commercial computer. In 1946, he designed the first high-level programming language, Plankalkül. In 1969, Zuse suggested the concept of a computation-based universe in his book Rechnender Raum (Calculating Space).
Much of his early work was financed by his family and commerce, but after 1939 he was given resources by the Nazi German government. Due to World War II, Zuse's work went largely unnoticed in the United Kingdom and the United States. Possibly his first documented influence on a US company was IBM's option on his patents in 1946. *Wik

1920 James H. Pomerene (June 22, 1920 – December 7, 2008) American computer pioneer. In Apr 1946 he joined John von Neumann and Herman Goldstine in their newly organized Electronic Computer Project at the Institute for Advanced Study in Princeton, New Jersey. This project was to build a parallel stored-program computer. He designed the adder portion of the arithmetic unit and then was entirely responsible for the development and construction of the electrostatic (Williams tube) memory and became the chief engineer of the project 1951-56. Then he joined IBM to assist development of the HARVEST computer, a special system built for the National Security Agency. It had two levels of program control and also had a tape and tape library system that was fully automatic and of great capacity.*TIS

1940 Daniel Gray "Dan" Quillen (June 22, 1940 – April 30, 2011) was an American mathematician. From 1984 to 2006, he was the Waynflete Professor of Pure Mathematics at Magdalen College, Oxford. He is renowned for being the "prime architect" of higher algebraic K-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 1978.
Quillen was a Putnam Fellow in 1959.
Quillen retired at the end of 2006. He died from complications of Alzheimer's disease on April 30, 2011, aged 70, in Florida. *Wik

1950 Benedict Hyman Gross (June 22, 1950; ) is an American mathematician, the George Vasmer Leverett Professor of Mathematics at Harvard University and former Dean of Harvard College.
He is known for his work in number theory, particularly the Gross–Zagier theorem on L-functions of elliptic curves, which was work with Don Zagier. *Wik


1388 Giovanni Dondi died (1330–1388). In 1381 he built one of the earliest geared equatoria driven by clockwork. There is a model of it in the Smithsonian. It has a heptagonal frame with a planet on each face. Dials show the time of sunrise, sunset, movable feasts, and the nodes of the moon’s orbit. *VFR He is remembered today as a pioneer in the art of clock design and construction. The Astrarium, which he designed and built over a period of 16 years, was a highly complex astronomical clock and planetarium, constructed only 60 or so years after the very first mechanical clocks had been built in Europe, and demonstrated an ambitious attempt to describe and model the solar system with mathematical precision and technological sophistication. *Wik

1429  Jamshid al-Kashi (1380 - 22 June 1429 (several different dates are given for his death)
was an Islamic mathematician who published some important teaching works and anticipated Stevin's work on decimals.*SAU
Al-Kashi was one of the best mathematicians in the Islamic world. He was born in 1380, in Kashan, in central Iran. This region was controlled by Tamurlane, better known as Timur. Al-Kashi lived in poverty during his childhood and the beginning years of his adulthood.

The situation changed for the better when Timur died in 1405, and his son, Shah Rokh, ascended into power. Shah Rokh and his wife, Goharshad, a Persian princess, were very interested in the sciences, and they encouraged their court to study the various fields in great depth. Consequently, the period of their power became one of many scholarly accomplishments. This was the perfect environment for al-Kashi to begin his career as one of the world’s greatest mathematicians.

Eight years after he came into power in 1409, their son, Ulugh Beg, founded an institute in Samarkand which soon became a prominent university. Students from all over the Middle East, and beyond, flocked to this academy in the capital city of Ulugh Beg’s empire. Consequently, Ulugh Beg harvested many great mathematicians and scientists of the Muslim world. In 1414, al-Kashi took this opportunity to contribute vast amounts of knowledge to his people. His best work was done in the court of Ulugh Beg, and it is said that he was the king’s favourite student.

Al-Kashi was still working on his book, called “Risala al-watar wa’l-jaib” meaning “The Treatise on the Chord and Sine”, when he died in 1429. Some scholars believe that Ulugh Beg may have ordered his murder, while others say he died a natural death. The details are unclear. *Wik

1925 Felix Klein died. Curiously, this was the birthday of his dear friend Minkowski. *VFR German mathematician whose synthesis of geometry as the study of the properties of a space that are invariant under a given group of transformations, known as the Erlanger Programm, profoundly influenced mathematical development. He created the Klein bottle, a one-sided closed surface. A Klein bottle cannot be constructed in Euclidean space. It is best pictured as a cylinder looped back through itself to join with its other end. However this is not a continuous surface in 3-space as the surface cannot go through itself without a discontinuity. It is possible to construct a Klein bottle in non-Euclidean space.*TIS

1936 Moritz Schlick, philosopher of science and leader of the Vienna Circle, was murdered by a deranged former student, on the steps of an academic building. *VFR

1977 Harold Calvin Marston Morse developed variational theory in the large with applications to equilibrium problems in mathematical physics, a theory which is now called Morse theory and forms a vital role in global analysis*SAU

1990 Ilya Mikhaylovich Frank Russian physicist who, with Tamm, theoretically explained the mechanism of Cherenkov radiation. In 1934, Cherenkov discovered that a peculiar blue light is emitted by charged particles traveling at very high speeds through water. Frank and Tamm provided the theoretical explanation of this effect, which occurs when the particles travel through an optically transparent medium at speeds greater than the speed of light in that medium. This discovery resulted in the development of new methods for detecting and measuring the velocity of high-speed particles and became of great importance for research in nuclear physics. For this, Frank received the Nobel Prize for Physics in 1958 (jointly with Pavel A. Cherenkov and Igor Y. Tamm).*TIS

1994 Julius Adams Stratton (May 18, 1901 – June 22, 1994) was a U.S. electrical engineer and university administrator. He attended the University of Washington for one year, then transferred to the Massachusetts Institute of Technology (MIT), from which he graduated with a bachelor's degree in 1923 and a master's degree in electrical engineering (EE) in 1926. He then followed graduate studies in Europe and the Technische Hochschule of Zurich (ETH Zurich), Switzerland, awarded him the degree of Doctor of Science in 1927. *Wik He worked with the blind-landing research program during WWII to help develop Glide-slope-approach radar.

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Wednesday, 21 June 2017

On This Day in Math - June 21

I had this rare privilege of being able 
to pursue in my adult life, 
what had been my childhood dream.
~Andrew Wiles

The 172nd day of the year; seventeen 2's followed by two 17's is prime.*Prime Curios
222222222222222221717 is prime

\( 172 = \pi(1+7+2) * p_{(1*7*2)} \). It is the only known number (up to 10^8) with this property.
pi(n) is the number of primes less than or equal to n, and pn is the nth prime.


1667 Louis XIV, The Sun King of France, attends the ceremony of inauguration of the Observatoire de Paris, the oldest working observatory in the world. *Amir D. Aczel, Pendulum, pg 66

1669 Christopher Wren gives first proof that the hyperboloid of one sheet (Wren uses the term Hyperbolic Cylindroid.) is doubly ruled in the Philosophical Transactions of the Royal Society. The only three doubly ruled surfaces are the plane, the hyperboloid of one sheet, and the hyperbolic paraboloid. Wren includes an image of the hyperboloid of one sheet that may be the earliest ever in print. In a footnote in Boyer's History of History of Analytic Geometry he notes that there is a figure in Kepler's Stereometria which looks like it might be this shape. (It is interesting that in his work on the geometry of a barrel, Kepler gives an approximation formula for the volume of a barrel that is exact for the hyperboloid of one sheet.)
The invention of the telescope and efforts to reduce distortion in the lenses led to suggestions of hyperbolic lenses, and Wren's paper pointed out "an application thereof for grinding hyperbolical glasses." Newton had applied the knowledge that the hyperboloid of one sheet was doubly ruled in his notes in 1666 when he demonstrated how to turn the shape on a lathe holding the cutting tool obliquely to the axis of rotation.
The image of Newton's method below is from a paper by Professor Rickey on the net.
*Wik, *VFR,

1798 Cavendish reads a paper to the Royal Society of London describing experiments to measure the density of the earth, and hence its weight, with results that it is 5.48 times the density of water. (the figures seem to include at least one calculating error) *Philosophical Transactions, 1798, Part II, pgs 469-526

1808 on 30 June, Humphry Davy announced he had separated the element boron. However, working independently, French chemist, Joseph Louis Gay-Lussac had announced* the same accomplishment nine days ealier, on 21 Jun 1808*TIS

In 1886, the foundation stone of the Tower Bridge in London, England was laid (over a time capsule) by the Prince of Wales. The need to cross the River Thames at this point had become increasingly urgent for many years, and finally the necessary Act was passed in 1885. The bridge, designed by Mr. Wolfe Barry, CB, was completed at a cost of about £1,000,000. To permit the passage of tall ships between the towers, two bascule spans, each of 100-ft length, are raised. The side spans to the towers are of the more familiar suspension type. Pedestrians can traverse a high-level footway nearly at the top of the towers, even when the bridge is raised. It was officially opened 30 Jun 1894, by the Prince of Wales, later Edward VII, on behalf of Queen *TIS

In 1893, the first Ferris wheel premiered at Chicago's Columbian Exposition, America's third world's fair. It was invented by George Washington Ferris, a Pittsburgh bridge builder, for the purpose of creating an attraction like the Eiffel Tower in Paris. Each of the 36 cars carried 60 passengers, making a full passenger load of 150 tons. Ferris didn't use rigid spokes: instead, he used a web of taut cables, like a bicycle wheel. Supported by two 140 foot steel towers, its 45 foot axle was the largest single piece of forged steel at the time in the world. The highest point of the wheel was 264 feet. The wheel and cars weighed 2100 tons, with another 2200 tons of associated levers and machinery. Ferris died just four years later, at the age of only 38. *TIS

1929 Kazimierz Kuratowski (1896–1980) at a meeting of the Warsaw Section of the Polish Mathemat­ical Society, announced that a graph is planar iff it does not contain a subgraph homeomorphic to either K–5, the complete graph on 5 points, or K–3–3, the complete bipartite graph on two sets of three points. See HM 12, 258, for a discussion of the early history of this theorem which is now the most cited result in graph theory. *VFR (See June 18) 
 "A finite graph is planar if and only if it does not contain a subgraph that is a subdivision of K5 (the complete graph on five vertices) or K3,3 (complete bipartite graph on six vertices, three of which connect to each of the other three)." *Wik 
 (in more simple, but less exact terms,  "it can be drawn in such a way that no edges cross each other."  The well-known recreational problem of connecting three houses to three utilities is not possible to draw because it is K3,3 (below).  The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any of the gas/water/electric lines/pipes pass over any other. (1913 Dudeney: first publication of Gas, Water and Electricity Problem. according to David Singmaster, Gardner says 1917)

1948 the first stored-program computer, the Small-Scale Experimental Machine, SSEM, ran its first program. Written by Professor Tom Kilburn, it took 52 minutes to run. The tiny experimental computer had no keyboard or printer, but it successfully tested a memory system developed at Manchester University in England. The system, based on a cathode-ray tube, could store programs. Previous electronic computers had to be rewired to execute each new problem. The Manchester computer proved theories set forth by John von Neumann in a report that proposed modifications to ENIAC, the electronic computer built at the University of Pennsylvania in the mid-1940s. The report also proposed the use of binary instead of digital numbers. *TIS

1976 Kenneth Appel and Wolfgang Haken announced that with the aid of a computer that they had proved the four color problem. Because of the use of the computer the solution was not quickly accepted by all, but today most mathematicians accept the proof as correct. However, no simple proof is known as yet. *VFR  {A really nice article on the four color theorem and its history}
In 1963 Donald B. Gillies had found three new primes. When the primes were confirmed the UIUC Math dept (which has a postal branch) used this cancellation stamp on all mail from roughly 1964 - 1976. When Appel and Haken proved the four color theorem ("Four Colors Suffice") a new stamp was created. Trivia question : how far away from Gillies did Appel live in Urbana Illinois ??
Answer : He lived 3 houses away. *Wik
*Wik courtesy of Chris Caldwell

1993   Andrew Wiles  begins the three days of lectures leading to a solution of Taniyama-Shimura conjecture, and completing the proof of Fermat’s last theorem.. See (June 23)

2011  On non-leap years (until 2039), this day marks the summer solstice in the northern hemisphere and the winter solstice in the southern hemisphere, and this is the day of the year with the longest hours of daylight in the northern hemisphere and the shortest in the southern hemisphere.*Wik


1710 James Short (June 10 {June 21 NS), 1710, Edinburgh, Scot. -  June 14, 1768, London, Eng) British optician and astronomer who produced the first truly
parabolic and elliptic (hence nearly distortionless) mirrors for reflecting telescopes. During his working life of over 35 years, Short made about 1,360 instruments - not only for customers in Britain but also for export: one is still preserved in Leningrad, another at Uppsala and several in America. Short was principal British collator and computer of the Transit of Venus observations made throughout the world on 6th June 1761. His instruments travelled on Endeavour with Captain Cook to observe the next Transit of Venus on 3rd June 1769, but Short died before this event took place.

 1781 Siméon-Denis Poisson ( 21 June 1781 – 25 April 1840) French mathematician known for his work on definite integrals, advances in Fourier series, electromagnetic theory, and probability. The Poisson distribution (1837) describes the probability that a random event will occur in a time or space interval under the conditions that the probability of the event occurring is very small, but the number of trials is very large so that the event actually occurs a few times. His works included applications to electricity and magnetism, and astronomy. He is also known for the Poisson's integral, Poisson's equation in potential theory, Poisson brackets in differential equations, Poisson's ratio in elasticity, and Poisson's constant in electricity.*TIS   Libri wrote of him: “His only passion has been science: he lived and is dead for it.” *VFR

1852 Eduard Weyr (1852-1903) He and his brother, Emil Weyr (1848–1894) were the leading members of the Austrian geometrical school. They worked in descriptive geometry, projective geometry, and then became interested in algebraic and synthetic methods. Eduard found a canonical form for matrices that deserves to be better known (American Mathematical Monthly, December 1999). *VFR

1863 Maximilian Franz Joseph Cornelius Wolf was a German astronomer who founded and directed the Königstuhl Observatory. He used wide-field photography to study the Milky Way and used statistical treatment of star counts to prove the existence of clouds of dark matter. He was among the first astronomers to show that the spiral nebulae have absorption spectra typical of stars and thus differ from gaseous nebulae. His most important contribution was the introduction of photography to discover hundreds of asteroids, the first of which he named Brucia in honor of the donor of his 16-inch double telescope, Catherine Wolfe Bruce.*TIS

1918 Tibor Szele worked in group theory. *VFR  Hungarian mathematician, working in combinatorics and abstract algebra. After graduating at the Debrecen University, he became a researcher at the Szeged University in 1946, then he went back to Debrecen University in 1948 where he became full professor in 1952. He worked especially in the theory of Abelian groups and ring theory. He generalized Hajós's theorem. He founded the Hungarian school of algebra. *Wik

1954 David Ríos Insua (born June 21, 1964 in Madrid) is a Spanish mathematician, and son and disciple of Sixto Ríos, father of Spanish Statistics. He is currently also the youngest Fellow of the Spanish Royal Academy of Sciences (de la Real Academia de Ciencias Exactas, Físicas y Naturales, RAC),[1] which he joined in 2008.[2][3] He received a PhD in Computational Sciences at the University of Leeds. He is Full Professor of the Statistics and Operations Research Department at Rey Juan Carlos University (URJC),[4] and he has been Vice-dean of New Technologies and International Relationships at URJC (2002–2009). He has worked in fields such as Bayesian inference in neuronal networks, MCMC methods in decision analysis, Bayesian robustness or adversarial risk analysis. He has also worked in applied areas such as Electronic Democracy,[5] reservoirs management, counterterrorism model and many others. He is married and has two daughters. Wik


1874 Anders Jonas Ångström was a Swedish physicist whose pioneering use of spectroscopy is recognised in the name of the angstrom, a unit of length equal to 10-10 metre. In 1853, he studied the spectrum of hydrogen for which Balmer derived a formula. He announced in 1862 that analysis of the solar spectrum showed that hydrogen is present in the Sun's atmosphere. In 1867 he was the first to examine the spectrum of aurora borealis (northern lights). He published his extensive research on the solar spectrum in Recherches sur le spectre solaire (1868), with detailed measurements of more than 1000 spectral lines. He also published works on thermal theory and carried out geomagnetical measurements in different places around Sweden.*TIS

1913  Gaston Tarry was a French combinatorialist whose best-known work is a method for solving mazes.*SAU  He also was able to confirm Leonhard Euler's conjecture that no 6×6 Graeco-Latin square was possible. 
In mathematics, the Prouhet–Tarry–Escott problem asks for two disjoint sets A and B of n integers each, such that:
\sum_{a\in A} a^i = \sum_{b\in B} b^i
for each integer power  i from 1 to a given k.
For example, a solution with n = 6 and k = 5 is the two sets { 0, 5, 6, 16, 17, 22 } and { 1, 2, 10, 12, 20, 21 }, because:
01 + 51 + 61 + 161 + 171 + 221 = 11 + 21 + 101 + 121 + 201 + 211
02 + 52 + 62 + 162 + 172 + 222 = 12 + 22 + 102 + 122 + 202 + 212
03 + 53 + 63 + 163 + 173 + 223 = 13 + 23 + 103 + 123 + 203 + 213
04 + 54 + 64 + 164 + 174 + 224 = 14 + 24 + 104 + 124 + 204 + 214
05 + 55 + 65 + 165 + 175 + 225 = 15 + 25 + 105 + 125 + 205 + 215.
This problem was named after Eugène Prouhet, who studied it in the early 1850s, and Gaston Tarry and Escott, who studied it in the early 1910s.

1940 Wolfgang Döblin, known in France as Vincent Doblin, (17 March 1915 – 21 June 1940) was a German-French mathematician. Wolfgang was the son of the Jewish-German novelist, Alfred Döblin. His family escaped from Nazi Germany to France where he became a citizen. Studying probability theory at the Institute Henri Poincaré under Fréchet, he quickly made a name for himself as a gifted theorist. He became a doctor at age 23. Drafted in November 1938, after refusing to be exempted of military service, he had to stay in the active Army when World War II broke out in 1939, and was quartered at Givet, in the Ardennes, as a telephone operator. There, he wrote down his latest work on the Chapman-Kolmogorov equation, and sent this as a "pli cacheté" (sealed envelope) to the French Academy of Sciences. His company, sent to the sector of the Saare on the ligne Maginot in April 1940, was caught in the German attack in the Ardennes in May, withdrew to the Vosges, and capitulated on June 22, 1940. On June 21, Doeblin had committed suicide in Housseras (a small village near to Epinal), at the moment where German troops came in sight of the place. In his last moments, he burned his mathematical notes.
The sealed envelope was opened in 2000, revealing that Döblin was ahead of his time in the development of the theory of Markov processes. In recognition of his results, Itō's lemma is now referred to as the Itō–Doeblin Theorem.
His life was recently the subject of a movie by Agnes Handwerk and Harrie Willems, A Mathematician Rediscovered. *Wik

1948 D'Arcy Thompson graduated from Cambridge University in Zoology. He was a appointed Professor of Biology at Dundee and later Professor of Natural History at St Andrews. He combined skills in a way that made him unique. He was a Greek scholar, a naturalist and a mathematician. He was the first biomathematician. He became an honorary member of the EMS in 1933. *SAU

1957  Johannes Stark German physicist who won the 1919 Nobel Prize for Physics for his discovery in 1913 that an electric field would cause splitting of the lines in the spectrum of light emitted by a luminous substance; the phenomenon is called the Stark effect. *TIS

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Tuesday, 20 June 2017

On This Day in Math - June 20

the enormous success of mathematics in the natural
sciences is something bordering on the mysterious and ...
there is no natural explanation for it.
—Eugene Wigner

The 171st day of the year; 171 has the same number of digits in Roman numerals as its cube.

\( 10^171 - 171 is prime \)

Google calculator gives 171! = infinity.

171 is the last year-day that is both a triangular number and a palindrome. *Ben Vitale


1686 Halley Writes to Newton that Hooke has protested his "discovery" of the inverse square law should be noted in Principia. Newton will respond On July 14, 1686, with a peace offering; "And now having sincerely told you the case between Mr Hooke and me, I hope I shall be free for the future from the prejudice of his letters. I have considered how best to compose the present dispute, and I think it may be done by the inclosed scholium to the fourth proposition." This scholium was "The inverse law of gravity holds in all the celestial motions, as was discovered also independently by my countrymen Wren, Hooke and Halley."

1688 Newton, in a letter to Edmund Halley, again expresses his exasperation with carping critics. [Thanks to Howard Eves]*VFR

1788; Washington Writes to Nicholas Pike to Thank him for a copy of his "A New and Complete System of Arithmetic" , published in 1786 by Nicholas Pike, a Newburyport schoolmaster. In his letter, sent June 20, 1788, from Mount Vernon, Washington writes: "The handsome manner in which that Work is printed and the elegant manner in which it is bound, are pleasing proofs of the progress which the Arts are making in this Country. Washington's letter to Pike also commended him on his accomplishments and the importance of his work.
Pike had written to  Washington on March 25,1786 requesting permission to dedciate the book to Washington. On June 20 of 1786, Washington had replied that, "I must therefore beg leave to decline the honour which you would do me, as I have before done in two or three cases of a similar kind."

1808 Poisson submitted his first paper on the stability of the planetary system, one day before his twenty-seventh birthday. *VFR

1831 János Bolyai's pioneering work, The Absolutely True Science of Space, was published in 1832. This important work was published as an appendix to the first volume of his father,Farkas Bolyai's Tentamen , but its off-print had already been ready the previous year, in April 1831. The latter was the version which, together with a letter, was sent to Gauss by Farkas Bolyai on the 20th of June 1831. Gauss got the letter but János's work was lost on the way. On the 16th of January 1832 Farkas sent the Appendix to his friend again with another letter in which he wrote: ``My son appreciates Your critique more than that of whole Europe and it is the only thing he is waiting for''.
After twenty-three years of silence, Gauss replied to his ``old, unforgettable friend'' on the 6th of March 1832. One of his well-known sentences was: ``if I praised your son's work I would praise myself''. The letter deeply afflicted and upset János Bolyai, although it reflects appreciation, too: ``... I am very glad that it is my old friend's son who so splendidly preceded me'' *Komal Journal

1877 Georg Cantor, in a letter to Dedekind, announced a proof that the points inside a square are in one-to-one correspondence with those on a line segment. Three years earlier, Cantor had intimated that this was clearly impossible. *VFR

1908 Count Zeppelin made his first flight in his fourth new airship at Friedrichshafen, Germany. The Luftschiff LZ4 had its first flight 20 Jun 1908. Its first extended flight (12 hours) was taken to Switzerland 1 Jul 1908. At the beginning of August, it embarked on an extended flight which had taken it among other places to Basel, Straussberg, and many of the major cities of southern Germany. While moored at Echterdingen on 5 Aug 1908, it was torn from the mast by high winds and destroyed. As interest in the Zeppelins ran high in German, the incident was felt as a national disaster. Spontaneous donations resulted in approximately 5.5 million Marks and made it possible for Zeppelin to continue his work. *TIS


1775 Jacques Frédéric Français (20 June 1775 in Saverne, Bas-Rhin, France - 9 March 1833 in Metz, France) In September 1813 Français published a work in which he gave a geometric representation of complex numbers with interesting applications. This was based on Argand's paper which had been sent, without disclosing the name of the author, by Legendre to François Français. Although Wessel had published an account of the geometric representation of complex numbers in 1799, and then Argand had done so again in 1806, the idea was still little known among mathematicians. This changed after Français' paper since a vigorous discussion between Français, Argand and Servois took place in Gergonne's Journal. In this argument Français and Argand believed in the validity of the geometric representation, while Servois argued that complex numbers must be handled using pure algebra. *SAU

1838 Theodor Reye (20 June 1838 in Ritzebüttel, Germany and died 2 July 1919 in Würzburg, Germany) worked in Geometry and Projective Geometry.*SAU

1873 Alfred Loewy born.(20 June 1873 in Rawitsch, Germany (now Rawicz, Poznań, Poland) - 25 Jan 1935 in Freiburg im Breisgau, Germany) He worked in group theory and differential equations. *VFR

1940 Leonard Susskind ( June(20ish 1940)(The professor's real birthday seems difficult to determine; perhaps only known to him and his parents, perhaps only to his parents) is the Felix Bloch Professor of Theoretical Physics at Stanford University, and Director of the Stanford Institute for Theoretical Physics. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology. He is a member of the National Academy of Sciences, and the American Academy of Arts and Sciences, an associate member of the faculty of Canada's Perimeter Institute for Theoretical Physics,[6] and a distinguished professor of the Korea Institute for Advanced Study.
Susskind is widely regarded as one of the fathers of string theory, having, with Yoichiro Nambu and Holger Bech Nielsen, independently introduced the idea that particles could in fact be states of excitation of a relativistic string. He was the first to introduce the idea of the string theory landscape in 2003. *Wik


1800 Abraham Kästner (27 September 1719 – 20 June 1800) was a German mathematician who compiled encyclopaedias and wrote text-books. He taught Gauss. *SAU

1807 Ferdinand Berthoud (19 March 1727 – 20 June 1807) Outstanding Swiss horologist and author of extensive treatises on timekeeping who became involved in the attempt to solve the problem of determining longitude at sea. His major achievement was his further development of an accurate and practical marine clock, or chronometer. (Such an instrument had previously been constructed in expensive and delicate prototypes by Pierre Leroy of France and John Harrison of England.) He made his first chronometer in 1754, which was sent for trial in 1761. Berthoud's improvements to the chronometer have been largely retained in present-day designs. *TIS

1861 Sir Frederick Gowland (Hoppy)Hopkins OM PRS (20 June 1861 – 16 May 1947) was an English biochemist who was awarded the Nobel Prize in Physiology or Medicine in 1929, with Christiaan Eijkman, for the discovery of vitamins. He also discovered the amino acid tryptophan, in 1901. He was President of the Royal Society from 1930 to 1935. His Cambridge students included neurochemistry pioneer Judah Hirsch Quastel and pioneer embryologist Joseph Needham.
During his life, in addition to the Nobel Prize, Hopkins was awarded the Royal Medal of the Royal Society in 1918 and the Copley Medal of the Royal Society in 1926. Other significant honours were his election in 1905 to fellowship in the Royal Society, Great Britain's most prestigious scientific organisation; his knighthood by King George V in 1925; and the award in 1935 of the Order of Merit, Great Britain's most exclusive civilian honour. From 1930 -1935 he served as president of the Royal Society and in 1933 served as President of the British Association for the Advancement of Science. *Wik

1865 Sir John William Lubbock, (London, England, 26 March 1803 - Downe, Kent, England, 20 June 1865 )English astronomer and mathematician. He made a special study of tides and of the lunar theory and developed a method for calculating the orbits of comets and planets. In mathematics he applied the theory of probability to life insurance problems. He was a strong proponent of Continental mathematics and astronomy.
Lubbock, third Baron Lubbock, was born into a London banking family. After attending Eton, he moved to Trinity College, Cambridge, where he became a student of William Whewell.(it was at the request of Lubbock that Whewell created the term "biometry".) He excelled in mathematics and traveled to France and Italy to deepen his knowledge of the works of Pierre-Simon de Laplace and Joseph Lagrange. Entering his father’s banking firm as a junior partner, he devoted his free time to science.
Lubbock strongly supported Lord Brougham’s Society for the Diffusion of Useful Knowledge [SDUK], which produced scientific and technical works designed for the working class. His articles on tides for the Society’s publications resulted in a book, *An Elementary Treatise on the Tides, in 1839. *Biographical Encyclopedia of Astronomers

1966 Georges (Henri) Lemaître was a Belgian astronomer and cosmologist, born in Charleroi, Belgium. He was also a civil engineer, army officer, and ordained priest. He did research on cosmic rays and the three-body problem. Lemaître formulated (1927) the modern big-bang theory. He reasoned that if the universe was expanding now, then the further you go in the past, the universe’s contents must have been closer together. He envisioned that at some point in the distant past, all the matter in the universe was in an exceedingly dense state, crushed into a single object he called the "primeval super-atom" which exploded, with all its constituent parts rushing away. This theory was later developed by Gamow and others.*TIS

2003 I. Bernard Cohen (1 March 1914 – 20 June 2003) was the Victor S. Thomas Professor of the history of science at Harvard University and the author of many books on the history of science and, in particular, Isaac Newton.
Cohen was the first American to receive a Ph.D. in history of science, was a Harvard undergraduate ('37) and then a Ph.D. student and protégé of George Sarton who was the founder of Isis and the History of Science Society. Cohen taught at Harvard from 1942 until his death, and his tenure was marked by the development of Harvard's program in the history of science. *Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell