## Monday, 29 August 2016

### On This Day in Math - August 29

 Jeannie at VLA

In most sciences one generation tears down what another has built,
and what one has established, another undoes.
In mathematics alone each generation adds a new storey to the old structure.
~Hermann Hankel

The 242nd day of the year; 242 has six divisors...but 243, 244, and 245 also each has six divisors. 242 is the smallest integer to begin a run of four consecutive integers all of which have the same number of divisors. (What is the smallest integer that begins a run of three consecutive integers with an equal number of divisors?)

242 is not only a palindrome in base ten, it is also a palindrome in base 3 and base 7.  (What palindrome in base ten is also a palindrome in the most other bases 2-9?)

EVENTS

1609 Galileo writes to his brother in Florence to tell him about his telescope presentation to the Doge on the 24th of August.

1654 Fermat to Pascal Saturday, August 29, 1654
Monsieur,
Our interchange of blows still continues, and I am well pleased that our thoughts are in such complete adjustment as it seems since they have taken the same direction and followed the same road. Your recent Trait´e du triangle arithmetique and its applications are an authentic proof and if my computations do me no wrong, your eleventh consequence went by post from Paris to Toulouse while my theorem, on figurate numbers, which is virtually the same, was going from Toulouse to Paris. I have not been on watch for failure while I have been at work on the problem and I am persuaded that the true way to escape failure is by concurring with you. But if I should say more, it would he of the nature of a Compliment and we have banished that enemy of sweet and easy conversation. It is now my turn to give you some of my numerical discoveries, but the end of the parliament augments my duties and I hope that out of your goodness you will allow me due and almost necessary respite.
In the same letter he states that, "Meditate however, if you find it convenient, on this theorem: The squared powers of 2 augmented by unity [I.e. 22n+1] are always prime numbers. [That is,] The square of 2 augmented by unity makes 5 which is a prime number;The square of the square makes 16 which, when unity is added makes 17, a prime number; The square of 16 makes 256 which, when unity is added, makes 257, a prime number; The square of 256 makes 65536 which, when unity is added, makes 65537, a prime number; and so to infinity. This is a property whose truth I will answer to you. The proof of it is very difficult (impossible, since the statement, as Euler would show later, is not true)and I assure you that I have not yet been able to find it fully." * York University Maths Dept

1692 For his services to the field of astronomy, Johann Philipp von Wurzelbauer was ennobled in 1692 by Leopold I, Holy Roman Emperor and added the von to his name. *Wik

1831 Michael Faraday discovered electrical induction. *VFR In 1831, Michael Faraday wound a thick iron ring on one side with insulated wire that was connected to a battery. He then wound the opposite side with wire connected to a galvanometer. He found that upon closing the battery circuit, there was a deflection of the galvanometer in the second circuit. Then he was astonished to see the galvanometer needle jump in the opposite direction when the battery circuit was opened. He had discovered that a current was induced in the secondary when a current in the primary was connected and an induced current in the opposite direction when the primary current was disconnected.*TIS

1899 Dedekind sends a letter to Georg Cantor that includes a proof of the Schroder-Bernstein Theorem (Let A and B be sets. If there is a 1-1 correspondence from A to B and a 1-1 corespondence from B to A, then the sets have the same cardinality.) *Cantorian Set Theory and Limitation of Size By Michael Hallett

In 1940, Sir Henry Tizard led a mission of leading British and Canadian scientists to the USA to brief official American representatives on devices under active development for war use and to enlist the support of American scientists. Thus began a close cooperation of Anglo-American scientists in such fields as aeronautics and rocketry. His influence probably made the difference between defeat or victory at the Battle of Britain in 1940. *TIS

1949 the USSR tested their first atomic device, "First Lightning." It was an an implosive type plutonium bomb, detonated at the Semipalatinsk test range, giving up to a 20 kiloton yield. In the U.S. it was calledJoe No. 1 ("Joe" was nickname for Y. Stalin.) This event came five years earlier than anyone in the West had predicted, largely due to one man, the spy Klaus Fuchs. As a Los Alamos physicist, Fuchs had passed detailed blue prints of the original American Trinity bomb design to the Russians. With the emergence of the USSR as a nuclear rival, America's monopoly of atomic weaponry was ended giving the U.S. strong motivation for intensifying its program of nuclear testing. Thus the Cold War was launched.*TIS

1970 Oscar Morgenstern writes in his diary that Gödel would NOT publish his ontological proof for the existence of God. The first version of the ontological proof in Gödel's papers is dated "around 1941". Gödel is not known to have told anyone about his work on the proof until 1970, when he thought he was dying. In February, he allowed Dana Scott to copy out a version of the proof, which circulated privately. In August 1970, Gödel told Oskar Morgenstern that he was "satisfied" with the proof, but Morgenstern recorded in his diary entry for 29 August 1970, that Gödel would not publish because he was afraid that others might think "that he actually believes in God, whereas he is only engaged in a logical investigation (that is, in showing that such a proof with classical assumptions (completeness, etc.) correspondingly axiomatized, is possible) *Wik

1990 The British Computer Misuse Act goes into effect One of the earliest laws anywhere designed to address computer fraud, the Act resulted from a long debate in the 1980s over failed prosecutions of hackers -- in one well-publicized case, two men hacked into a British Telecom computer leaving messages in the Duke of Edinburgh's private mailbox. *CHM

BIRTHS

1756 Jan Śniadecki (August 29, 1756– November 9, 1830) was a Polish mathematician, philosopher and astronomer at the turn of the 18th and 19th centuries.
Born in Żnin, Śniadecki studied at Kraków University and in Paris. He was rector of the Imperial University of Vilnius, a member of the Commission of National Education, and director of astronomical observatories at Kraków and Vilnius. He died at Jašiūnai Manor near Vilnius.
Śniadecki published many works, including his observations on recently discovered planetoids. His O rachunku losów (On the Calculation of Chance, 1817) was a pioneering work in probability. *Wik He is considered as the best Polish mathematician born in the 18th century.

1876 Charles F. Kettering (29 Aug 1876; 25 Nov 1958) was an American engineer whose 140 patents included the electric starter, car lighting and ignition systems. In his early career, with the National Cash Register Co., Dayton (1904-09), he created the first electric cash register with an electric motor that opened the drawer. When he co-founded the Dayton Engineering Laboratories Company (DELCO, with Edward A. Deeds) he invented the key-operated self-starting motor for the Cadillac (1912) and it spread to nearly all new cars by the 1920's. As vice president and director of research for General Motors Corp. (1920-47) he developed engines, quick-drying lacquer finishes, anti-knock fuels, and variable-speed transmissions.*TIS

1881 Ferdinand Springer born, The founder of an important publishing house,. Today Springer-Verlag is one of the most important publishers of advanced work on mathematics. *VFR

1904 Leonard Roth (29 August 1904 Edmonton, London, England – 28 November 1968 Pittsburgh, Pennsylvania) British Mathematician who worked primarily in Algebraic Geometry. *SAU

DEATHS

1873 Hermann Hankel (14 February 1839 - 29 August 1873) He studied and worked with, among others, Möbius, Riemann, Weierstrass and Kronecker. His 1867 exposition on complex numbers and quaternions is particularly memorable. For example, Fischbein notes that he solved the problem of products of negative numbers by proving the following theorem: "The only multiplication in R which may be considered as an extension of the usual multiplication in R+ by respecting the law of distributivity to the left and the right is that which conforms to the rule of signs." *Wik

1930 James Bolam (1839 in Newcastle, England - 29 Aug 1930 in St Helen's, Drumchapel, Dumbartonshire, Scotland) was educated at Newcastle. He became head of the Government Navigation School (later the Leith Nautical College). He was a founder member of the EMS and became an honorary member in 1923. *SAU

1937 Otto Ludwig Hölder (December 22, 1859 – August 29, 1937) worked on the convergence of Fourier series and in 1884 he discovered the inequality now named after him. He became interested in group theory through Kronecker and Klein and proved the uniqueness of the factor groups in a composition series. *SAU

1967 Charles Brace Darrow (10 Aug 1889, 29 Aug 1967) was an American inventor who designed the board game Monopoly. He had invented the game on 7 Mar 1933, though it was preceded by other real-estate board games. On 31 Dec 1935, a patent was issued for the game of Monopoly assigned to Parker Brothers, Inc., by Charles Darrow of Pennsylvania (No. 2,026,082). The patent titled it a "Board Game Apparatus" and described it as "intended primarily to provide a game of barter, thus involving trading and bargaining" in which "much of the interest in the game lies in trading and in striking shrewd bargains." Illustrations included with the patent showed not only the playing board and pieces, cards, and the scrip money. *TIS

1975 Éamon de Valera (14 October 1882, 29 August 1975) was one of the dominant political figures in twentieth century Ireland, serving as head of government of the Irish Free State and head of government and head of state of Ireland. He also introduced the Constitution of Ireland.
De Valera was a leader of Ireland's struggle for independence from Britain in the Irish War of Independence and of the anti-Treaty forces in the ensuing Irish Civil War (1922–23). In 1926, he founded Fianna Fáil and was head of government from 1932–48, 1951–54 and 1957–59 and President of Ireland from 1959–73.
In his youth he had trained as a mathematician and taught mathematics prior to the Easter Rising. Throughout his life he maintained an interest in mathematics and returned to it with a passion in his later life. *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

## Sunday, 28 August 2016

### On This Day in Math - August 28

As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.
~Joseph Louis Lagrange

The 241st day of the year; 241 is the larger of a pair of twin primes. The larger of a pair of twin primes is always one more than a multiple of six; the smaller is always one less than a multiple of six.

2+4+1 is prime. 241 is the 53rd prime. (53 is also prime) *Derek Orr

241 is also The smallest prime p such that p plus the reversal of p equals a palindromic prime.  241 + 142 = 383; which is a prime palindrome.

And it is the largest known prime p such that the reversal of (p! + p) is prime.  (241! + 241 ends with a string of fifty-five zeros, and then 241 :
980360372638941007038951797078339359751464353463061342202811
188548638347461066010066193275864531994024640834549254693776
854464608509281547718518965382728677985343589672835884994580
815417004715718468026937051493675623385569404900262441027874
255428340399091926993707625233667755768320823071062785275404
107485450075779940944580451919726756974354635829128751944137
27644867102380111026020691554782580923999494640500736
0000000000000000000000000000000000000000000000000000000241....
and if you write the reversal of that, it's prime.

EVENTS

412 BC The ancient city of Syracuse suffered heavily under siege by the Athenians during the Peloponnesian War. A turn of events occurred during the Second Battle of Syracuse: on Aug. 28, 41.C. a lunar eclipse occurred, causing the superstitious Athenians to delay departure. The Syracuseans took advantage of Athenian indecision and decisively defeated the unprotected Athenian expedition as it sat exposed in the harbor. *listosaur.com

1666 John Evelyn Records in his diary: "to the Royal Society, where one Mercator, an excellent mathematician, produced his rare clock and new motion to perform the equations, and Mr. Rooke, his new pendulum." The Mercator is Nicholas Mercator who taught mathematics in London (1658–1682). He designed a marine chronometer for Charles II, and designed and constructed the fountains at the Palace of Versailles. Mathematically, he is most well known for his treatise Logarithmo-technica on logarithms, published in 1668 in which he described the Mercator series, also independently discovered by Gregory Saint-Vincent $\ln(1 + x) = x - \frac{1}{2}x^2 + \frac{1}{3}x^3 - \frac{1}{4}x^4 + \cdots.$
I suspect the "Mr Rooke" should have been Hooke who is mentioned at the meeting in Pepys' Diary. *Wik, *John Evelyn Diary

1730 Murder by Unicorn Horn on a Holborn skittle-ground : On the 28th of August 1730, Joseph Hastings died after receiving “several mortal Bruises with an Unicorn’s Horn”, wielded by John Williams of St. Andrew’s Holborn eleven days earlier. The assault occurred on a Holborn skittle-ground, witnessed by several local men.
Williams was angered by Hastings response to his offer to purchase the (probably Narwhale) horn and an argument ensued which led to the beating. More detail at Sloan Letters

In 1789, Enceladus, the sixth-largest moon of Saturn, was discovered by Fredrick William Herschel on August 28, 1789, during the first use of his new 1.2 m (47 in) telescope, then the largest in the world. Little was known about Enceladus until the two Voyager spacecraft passed near it in the early 1980s.
Enceladus is named after the giant Enceladus of Greek mythology.[14] The name Enceladus—like the names of each of the first seven satellites of Saturn to be discovered—was suggested by William Herschel's son John Herschel in his 1847 publication Results of Astronomical Observations made at the Cape of Good Hope.[30] He chose these names because Saturn, known in Greek mythology as Cronus, was the leader of the Titans. *Wik

 Scientific American ‏@sciam
1845 the first issue of the Scientific American was published by Rufus Porter (1792-1884), a versatile if eccentric Yankee, who was by turns a portrait-painter, schoolmaster, inventor and editor. While the paper was still a small weekly journal with a circulation less than 300, he offered it for sale. It was bought for $800 in July 1846 by 20-year-old Alfred Ely Beach (1826-1896) as editor, and Orson Desaix Munn (1824-1907). Together, they built it over the years into a great and unique periodical. Their circulation reached 10,000 by 1848, 20,000 by 1852, and 30,000 by 1853.*TIS 1893 The first day of the Evanston Colloquial lectures by Felix Klein which would continue until 9 September. *Karen Hunger Parshall, David E. Rowe; The Emergence of the American Mathematical Research Community, 1876-1900 1961 The Board of Governors of the MAA voted to name Dr. Mina S. Rees, (ﬁrst) Dean of Graduate Studies at the City University of New York, the ﬁrst recipient of their Award for Distinguished Service to Mathematics. From 1946 to 1953 she held several important positions at the Office of Naval Research and was instrumental in getting ONR to adopt the policy that mathematics was part of this country’s total scientiﬁc effort and should be properly supported by government-sponsored research programs. [AMM 69(1962), pp. 185-187]. *VFR 1974 Sweden issued a stamp picturing a spool and thread, with the thread stretched to form a string ﬁgure of a hyperbola. [Scott #1094]. *VFR HT to Emma L Bell, Storax Sedan, and Glen Carlson for image 1993, a picture was taken showing the first moon of an asteroid. The asteroid 243 Ida and its newly-discovered moon, Dactyl was imaged by NASA's Galileo spacecraft, about 14 minutes before its closest approach (within 2,400-km or 1,500 miles) to the asteroid. Ida is about 52 km (32 mi) in length and is irregularly shaped. It shows numerous craters, including many degraded craters, indicating Ida's surface is older than previously thought. Dactyl is only about 1.4-km in diameter, and it is spectrally different from Ida data. The picture was released on 26 Mar 1994. Galileo had encountered the first asteroid - 951 Gaspra - on 29 Oct 1991. Galileo continued on its mission to study Jupiter, beginning its orbit of the planet on 7 Dec 1995.*TIS 2009 The Australian Govt replies to a letter written "To A Top Scientist" by an Australian schoolboy shortly after the launch of Sputnik fifty-two years earlier with his suggested designs for a rocket ship. See all the details at this page from *Letters of Note BIRTHS 1796 Irénée-Jules Bienaymé (28 August 1796, 19 October 1878), was a French statistician. He built on the legacy of Laplace generalizing his least squares method. He contributed to the fields and probability, and statistics and to their application to finance, demography and social sciences. In particular, he formulated the Bienaymé-Chebyshev inequality concerning the law of large numbers and the Bienaymé formula for the variance of a sum of uncorrelated random variables.*Wik 1801 Antoine-Augustin Cournot (28 Aug 1801; 31 Mar 1877) French economist and mathematician, who was the first economist who applied mathematics to the treatment of economic questions. In 1838, he published Recherches sur les principes mathématiques de la théorie des richesses (Researches into the Mathematical Principles of the Theory of Wealth) which was a treatment of mathematical economics. In particular, he considered the supply-and-demand functions. Further, he studied the conditions for equilibrium with monopoly, duopoly and perfect competition. He included the effect of taxes, treated as changes in production costs, and discussed problems of international trade. His definition of a market is still the basis for that presently used in economics. In other work, he applied probability to legal statistics *TIS 1863 Andre-Eugene Blondel (28 Aug 1863; 15 Nov 1938) was a French physicist who invented (1893) the electromagnetic oscillograph, a device that allowed electrical researchers to observe the intensity of alternating currents. In 1894, he proposed the lumen and other new photometric units for use in photometry, based on the metre and the Violle candle. Endorsed in 1896 by the International Electrical Congress, his system is still in use with only minor modifications. Blondel was a pioneer in the high voltage long distance transport of electric power, and also contributed to developments in wireless telegraphy, acoustics, and mechanics. He proposed theories for induction motors and coupling of a.c. generators.*TIS (Invention of the Oscillograph is also credited to William Du Bois Duddell.) 1867 Maxime Bˆochner born. After receiving his doctorate under Felix Klein in 1891 he returned to Harvard for a lifetime of teaching and research in differential equations. *VFR 1883 Jan A Schouten worked on tensor analysis and its applications.*SAU 1901 Kurt Otto Friedrichs (September 28, 1901 – December 31, 1982) was a noted German American mathematician. He was the co-founder of the Courant Institute at New York University and recipient of the National Medal of Science.*Wik 1911 Shizuo Kakutani (角谷 静夫 Kakutani Shizuo?, August 28 1911, August 17 2004) was a Japanese-born American mathematician, best known for his eponymous fixed-point theorem. *Wik 1912 George Eric Deacon Alcock (August 28, 1912 – December 15, 2000) George Alcock was an English astronomer. He was one of the most successful visual discoverers of novae and comets. He was also a very good (probably under-respected) teacher of the 4th year at Southfields Junior School in Stanground, Peterborough. In 1953 he decided to start searching for comets and in 1955 began searching for novae. His technique was to memorize the patterns of thousands of stars, so that he would visually recognize any intruder. In 1959 he discovered comet C/1959 Q1 (Alcock), the first comet discovered in Britain since 1894, and only five days later discovered another, C/1959 Q2 (Alcock). He discovered two more comets in 1963 and 1965. He later discovered his first nova, Nova Delphini 1967 (HR Delphini), which turned out to have an unusual light curve. He discovered two more novas, LV Vul (in 1968) and V368 Sct (in 1970). He found his fifth and final comet in 1983: C/1983 H1 (IRAS-Araki-Alcock). In 1991 he found the nova V838 Her. Alcock won the Jackson-Gwilt Medal of the Royal Astronomical Society in 1963 and Amateur Achievement Award of the Astronomical Society of the Pacific in 1981. After his death, a plaque was placed in Peterborough Cathedral in his memory. *TIA 1919 Sir Godfrey Newbold Hounsfield (28 August 1919 – 12 August 2004) English electrical engineer who shared the 1979 Nobel Prize for Physiology or Medicine (with Allan Cormack) for creation of computerised axial tomography (CAT) scanners. He originated the idea during a country walk in 1967 when he realized that the contents of a box could be reconstructed by taking readings at all angles through it. He applied the concept for scanning the brain using hundreds of X-ray beams imaging cross-sections that were reconstructed as high-resolution graphics by a computer program handling complex algebraic calculations. By 1973 his CAT scanner could produce cross-section images of a brain in 4-1/2-min, invaluable for the diagnosis of brain diseases. He later built a larger machines able to make a full body scan. *TIS 1921 Ralph Asher Alpher (February 3, 1921 – August 12, 2007) was an American cosmologist. Alpher's dissertation in 1948 dealt with a subject that came to be known as Big Bang nucleosynthesis. In a strange mathematical pun, his pre-publication of his thesis may have caused his independent role to have been minimized. Although his name appears on the paper, Hans Bethe had no direct part in the development of the theory, although he later worked on related topics; Gamow added his name to make the author list Alpher, Bethe, Gamov, a pun on alpha, beta, gamma (α, β, γ), the first three letters of the Greek alphabet. Thus, Alpher's independent dissertation was first published on April 1, 1948 in the Physical Review with three authors. The humor engendered by the prodigious Gamow may at times have obscured the critical role Alpher played in developing the theory. This seminal paper was based on his dissertation (defended shortly thereafter). With the award of the 2005 National Medal of Science, Alpher's original contributions (nucleosynthesis and the cosmic microwave background radiation predicition) to the modern big bang theory are beginning to receive due recognition. Neil deGrasse Tyson was instrumental in a NSF committee recommendation. In 2005 Alpher was awarded the National Medal of Science. The citation for the award reads "For his unprecedented work in the areas of nucleosynthesis, for the prediction that universe expansion leaves behind background radiation, and for providing the model for the Big Bang theory." The medal was presented to his son Dr. Victor S. Alpher on July 27, 2007 by President George W. Bush, as his father could not travel to receive the award. Ralph Alpher died following an extended illness on August 12, 2007. He had been in failing health since falling and breaking his hip in February 2007. *Wik 1919 Sir Godfrey Newbold Hounsfield (28 Aug 1919; 12 Aug 2004) English electrical engineer who shared the 1979 Nobel Prize for Physiology or Medicine (with Allan Cormack) for creation of computerised axial tomography (CAT) scanners. He originated the idea during a country walk in 1967 when he realized that the contents of a box could be reconstructed by taking readings at all angles through it. He applied the concept for scanning the brain using hundreds of X-ray beams imaging cross-sections that were reconstructed as high-resolution graphics by a computer program handling complex algebraic calculations. By 1973 his CAT scanner could produce cross-section images of a brain in 4-1/2-min, invaluable for the diagnosis of brain diseases. He later built larger machines able to make a full body scan. *TIS 1939 John Frank Charles Kingman (28 August 1939, )worked in Statistics and made significant advances in queuing theory. He was N. M. Rothschild and Sons Professor of Mathematical Sciences and Director of the Isaac Newton Institute at the University of Cambridge from 2001 until 2006, when he was succeeded by Sir David Wallace. He is famous for developing the mathematics of the coalescent, a theoretical model of inheritance, which is fundamental to modern population genetics. *Wik 1951 Edward Witten (born August 26, 1951) is an American theoretical physicist with a focus on mathematical physics who is a professor of Mathematical Physics at the Institute for Advanced Study at Princeton, New Jersey. Witten is a researcher in superstring theory, a theory of quantum gravity, supersymmetric quantum field theories and other areas of mathematical physics.[1] He has made contributions in mathematics and helped bridge gaps between fundamental physics and other areas of mathematics. In 1990 he became the first physicist to be awarded a Fields Medal by the International Union of Mathematics. In 2004, Time magazine stated that Witten was widely thought to be the world's greatest living theoretical physicist. *Wik DEATHS 2005 George Szekeres (29 May 1911 – 28 August 2005) was a Hungarian-born mathematician who worked for most of his life in Australia on geometry and combinatorics. *SAU Szekeres worked closely with many prominent mathematicians throughout his life, including Paul Erdős, Esther Szekeres (née Esther Klein), Paul Turán, Béla Bollobás, Ronald Graham, Alf van der Poorten, Miklós Laczkovich, and John Coates. The so-called Happy Ending problem is an example of how mathematics pervaded George's life. During 1933, George and several other students met frequently in Budapest to discuss mathematics. At one of these meetings, Esther Klein proposed the following problem: Given five points in the plane in general position, prove that four of them form a convex quadrilateral. After allowing George, Paul Erdős, and the other students to scratch their heads for some time, Esther explained her proof. Subsequently, George and Paul wrote a paper (1935) that generalizes this result; it is regarded as one of the foundational works in the field of combinatorial geometry. Erdős dubbed the original problem the "Happy Ending" problem because it resulted in George and Esther's marriage in 1937. George and Esther died within an hour of each other, on the same day, 28 August 2005, in Adelaide, Australia.*Wik 2005 Esther (Klein) Szekeres (20 February 1910 – 28 August 2005) was a Hungarian–Australian mathematician with an Erdős number of 1. She was born to Ignaz Klein in a Jewish family in Budapest, Kingdom of Hungary in 1910. As a young woman in Budapest, Klein was a member of a group of Hungarians including Paul Erdős, George Szekeres and Paul Turán that convened over interesting mathematical problems. In 1933, Klein proposed to the group a combinatorial problem that Erdős named as the Happy Ending problem as it led to her marriage to George Szekeres in 1937, with whom she had two children. Following the outbreak of World War II, Esther and George Szekeres emigrated to Australia after spending several years in Hongkew, a community of refugees located in Shanghai, China. In Australia, they originally settled in Adelaide before moving to Sydney in the 1960s. In Sydney, Esther lectured at Macquarie University and was actively involved in mathematics enrichment for high-school students. In 1984, she jointly founded a weekly mathematics enrichment meeting that has since expanded into a program of about 30 groups that continue to meet weekly and inspire high school students throughout Australia and New Zealand. In 2004, she and George moved back to Adelaide, where, on 28 August 2005, she and her husband passed away within an hour of each other *Wik 2007 Paul Beattie MacCready (29 Sep 1925, 28 Aug 2007) was an American engineer who invented not only the first human-powered flying machines, but also the first solar-powered aircraft to make sustained flights. On 23 Aug 1977, the pedal-powered aircraft, the Gossamer Condor successfully flew a 1.15 mile figure-8 course to demonstrate sustained, maneuverable manpowered flight, for which he won the £50,000 ($95,000) Kremer Prize. MacCready designed the Condor with Dr. Peter Lissamen. Its frame was made of thin aluminum tubes, covered with mylar plastic supported with stainless steel wire. In 1979, the Gossamer Albatross won the second Kremer Prize for making a flight across the English Channel. *TIS

2011 Anthony Edgar Sale (or Tony Sale) (30 January 1931 - 28 August 2011) led the construction of a Colossus computer replica at Bletchley Park, completed in 2007 *Wik
In 1994, a team led by Tony Sale began a reconstruction of a Colossus at Bletchley Park. Here, in 2006, Sale (right) supervises the breaking of an enciphered message with the completed machine. *Wik Photo

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

## Saturday, 27 August 2016

### On This Day in Math - August 27

Questions that pertain to the foundations of mathematics,
although treated by many in recent times,
still lack a satisfactory solution.
The difficulty has its main source in the ambiguity of language.

Giuseppe Peano,
Opening of the paper Arithmetices principia in which he introduced axioms for the integers.

The 240th day of the year; 240 has more divisors (20 of them) than any previous number. What would be the next number that has more?

240 is the product of the first 6 Fibonacci numbers  240 = 1*1*2*3*5*8    *Derek Orr
These are often called Fibonacci factorials or fibonorials. 240 would be $6!_F$, also called the Fibonacci factorial

EVENTS

In 413 BC, a lunar eclipse caused panic among the sailors of the Athens fleet and thus affected the outcome of a battle in the Peloponnesian War. The Athenians were ready to move their forces from Syracuse when the Moon was eclipsed. The soldiers and sailors were frightened by this celestial omen and were reluctant to leave. Their commander, Nicias, consulted the soothsayers and postponed the departure for 27 days. This delay gave an advantage to their enemies, the Syracusans, who then defeated the entire Athenian fleet and army, and killed Nicias.*TIS

1666 John Evelyn makes an on-site visit to Old St. Pauls with Christopher Wren.  "We went about to survey the general decays of that ancient and venerable church, and to set down the particulars in writing, what was fit to be done.."  Five days later the reports would be rendered meaningless by the Great London Fire.  *Lisa Jardine, Ingenious Pursuits, pgs 69-70

1760 Leonhard Euler, in his Letters to a German Princess on various topics of physics and philosophy, explains how a surveyor uses a level. As an example he asks which end of the straight line between their homes is higher. He discusses the ﬂow of the rivers that connect their homes, but gives the wrong answer to his question. For discussion of this famous error, see Eves, Adieu, 34 *VFR

1771 Joseph Priestley finds a mint plant rejuvenates "spent" air. He had set out ten days earlier to test the rejuvenating effect of mint growing in a sealed container. He placed a candle in the covered glass and let it burn out in the presence of the mint. On the 27th he would return to the experiment and relight the candle and find, "it burned perfectly well in it." *Steven Johnson, The Invention of Air

1776 Even in the onset of the American Revolution, (Nathan Hale was executed for treason only five days before) future President John Adams, wrote of a visit to the Princeton Orrery: "Here we saw a most beautiful machine--an Orrery or planetarium constructed by Mr. Rittenhouse of Philadelphia. It exhibits almost every motion in the astronomical world."
David Rittenhouse was a renowned American astronomer, clockmaker, mathematician, surveyor, scientific instrument craftsman, and public official. Rittenhouse was a president of the American Philosophical Society; Treausrer of Pennsylvania; & the first director of the United States Mint. *Barbara Wells Sarudy

1783 Jacques A. C. Charles (for whom Charles' Law is named) and the Robert brothers launched the world's first hydrogen filled balloon on August 27, 1783, from the Champ de Mars, (now the site of the Eiffel Tower) where Ben Franklin was among the crowd of onlookers. The balloon was comparatively small, a 35 cubic metre sphere of rubberised silk, and only capable of lifting circa 9 kg (20 lb). It was filled with hydrogen that had been made by pouring nearly a quarter of a tonne of sulphuric acid onto a half a tonne of scrap iron. The hydrogen gas was fed into the balloon via lead pipes; but as it was not passed through cold water, great difficulty was experienced in filling the balloon completely (the gas was hot when produced, but as it cooled in the balloon, it contracted).
Daily progress bulletins were issued on the inflation; and the crowd was so great that on the 26th the balloon was moved secretly by night to the Champ de Mars, a distance of 4 kilometres. (This may not have been very secret as another source says there were processions of torchlights along the route.)
The balloon flew northwards for 45 minutes, pursued by chasers on horseback, and landed 21 kilometers away in the village of Gonesse where the reportedly terrified local peasants destroyed it with pitchforks or knives. *Wik

1784 One year after the Charles Flight (above) James Tytler became the first person in Britain to fly by ascending in a hot air balloon (He had made a minimal flight on 25 August in Edinburgh when his balloon rose a few feet from the ground. On the 27th he managed to reach a height of some 350 feet, traveling for half a mile between Green House on the northern edge of what is now Holyrood Park to the nearby village of Restalrig. *Wik

1798 Egyptian Institute founded by Napoleon in imitation of the Institut de France *VFR

1911 A century ago, on August 27, 1911, headlines of the New York Times announced that Martians had completed stunning feats of engineering and construction: two 1000-mile-long canals built on Mars in a two-year period.  These canals had not only been seen and sketched by astronomers, but also had been captured photographically, appearing in the photos as “the most marked features on that part of the planet”. *The Renaissance Mathematicus

1947 China (there was only one until 1949) issued four stamps honoring Confucius. [Scott #741-4]. *VFR

1993 Compaq Computer Corp. announced its Presario family of personal computers, intended to be user friendly and cheap. For \$1,399, the Presario included a monitor, modem, and software to access the recently popularized online world through Prodigy and America Online. *CHM

BIRTHS
1850 Augusto Righi (27 August 1850 – 8 June 1920) was an Italian physicist and a pioneer in the study of electromagnetism. He was born and died in Bologna.
Righi was the first person to generate microwaves,[citation needed] and opened a whole new area of the electromagnetic spectrum to research and subsequent applications. His work L'ottica delle oscillazioni elettriche (1897), which summarised his results, is considered a classic of experimental electromagnetism. Marconi was his student. *Wik

1858 Birthdate of Giuseppe Peano (27 Aug 1858; 20 Apr 1932) early contributor to symbolic logic. Through the use of symbols, equations are more easily understood by anyone regardless of their language. For example, Peano introduced symbols to represent "belongs to the set of" and "there exists." In Arithmetics principia (1889), a pamphlet he wrote in Latin, Peano published his first version of a system of mathematical logic, giving his Peano axioms defining the natural numbers in terms of sets. In 1903, Peano unsuccessfully proposed an international, artificial language he called "Latino sine flexione." It was based on Latin without grammar. Its vocabulary comprised words from English, French, German and Latin. *TIS Thony Christie maintains that this may overstate his contribution. "I've been here before. Peano made a substantial contribution to the history of symbolic logic, especially the fact that it was his work that inspired Russell. However I think Boole, Jevons, Demorgan, Venn, McColl, Frege, Peirce, Ladd-Franklin and quite a few others who were doing symbolic logic before Peano might object to him being called its founder. To say nothing of the Stoics! "

1915 Norman Foster Ramsey (27 Aug 1915, )American physicist who shared (with Wolfgang Paul and Hans Georg Dehmelt) the 1989 Nobel Prize for Physics in 1989 for "for the invention of the separated oscillatory fields method and its use in the hydrogen maser and other atomic clocks." His work produced a more precise way to observe the transitions within an atom switching from one specific energy level to another. In the cesium atomic clock, his method enables observing the transitions between two very closely spaced levels (hyperfine levels). The accuracy of such a clock is about one part in ten thousand billion. In 1967, one second was defined as the time during which the cesium atom makes exactly 9,192,631,770 oscillations.*TIS

1923 Jacob Willem "Wim" Cohen (27 August 1923, 12 November 2000) was a Dutch mathematician, well known for over a hundred scientific publications and several books in queueing theory. *Wik

1926 Kristen Nygaard (August 27, 1926, August 10, 2002) was a Norwegian computer scientist, programming language pioneer and politician. He was born in Oslo and died of a heart attack in 2002. Internationally he is acknowledged as the co-inventor of object-oriented programming and the programming language Simula with Ole-Johan Dahl in the 1960s.

DEATHS

1898 John Hopkinson (27 Jul 1849, 27 Aug 1898)British physicist and electrical engineer who worked on the application of electricity and magnetism in devices like the dynamo and electromagnets. Hopkinson's law (the magnetic equivalent of Ohm's law) bears his name. In 1882, he patented his invention of the three-wire system (three phase) for electricity generation and distribution. He presented the principle the synchronous motors (1883), and designed electric generators with better efficiency. He also studied condensers and the phenomena of residual load. In his earlier career, he became (1872) engineering manager of Chance Brothers and Co., a glass manufacturer in Birmingham, where he studied lighthouse illumination, improving efficiency with flashing groups of lights.*TIS

1912 Mikhail Vashchenko-Zakharchenko worked on the theory of linear differential equations, the theory of probability and non-euclidean geometry.*SAU

1958 Ernest Orlando Lawrence (8 Aug 1901, 27 Aug 1958 ) American physicist who was awarded the 1939 Nobel Prize for Physics for his invention of the cyclotron, the first device for the production of high energy particles. His first device, built in 1930 used a 10-cm magnet. He accelerated particles within a cyclinder at high vacuum between the poles of an electromagnetic to confine the beam to a spiral path, while a high A.C. voltage increased the particle energy. Larger models built later created 8 x 104 eV beams. By colliding particles with atomic nuclei, he produced new elements and artificial radioactivity. By 1940, he had created plutonium and neptunium. He extended the use of atomic radiation into the fields of biology and medicine. Element 103 was named Lawrencium as a tribute to him. *TIS

1988 Max Black​ (24 February 1909, 27 August 1988) was a British-American philosopher and a leading influence in analytic philosophy in the first half of the twentieth century. He made contributions to the philosophy of language, the philosophy of mathematics and science, and the philosophy of art, also publishing studies of the work of philosophers such as Frege. His translation (with Peter Geach) of Frege's published philosophical writing is a classic text. *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

## Friday, 26 August 2016

### On This Day in Math - August 26

Thanks for the great memories, Students of Lakenheath

Perhaps... some day the precision of the data will be brought so far that the mathematician will be able to calculate at his desk the outcome of any chemical combination, in the same way, so to speak, as he calculates the motions of celestial bodies.
~Antoine-Laurent Lavoisier

The 239th day of the year; When expressing 239 as a sum of square numbers, 4 squares are required, which is the maximum that any integer can require; it is the largest number that needs the maximum number (9) of positive cubes (Only one other number requires nine cubes, can you find it?)

and a hundred years (+/-) ago (many people included 1 as a prime then; see more) 239 would have been a prime that is the sum of the first 14 primes; 239 = 1+2+3+5+7+11+...+37+41 *Derek Orr

239 appears in one of the earliest known geometrically converging formulas for computing Pi:
Pi/4 = 4 arctan(1/5) - arctan(1/239) *.archimedes-lab.org

EVENTS

1735 Euler’s Konisburg bridge solution, "The Solution of a problem related to the Geometry of Position", was presented to the St. Petersburg Academy on August 26, 1735. He showed that there were no continuous walks across the seven bridges across the Pregel River in Konisburg. It is often cited as the earliest paper in both topology and graph theory.*VFR

1768 Capt. James Cook began the ﬁrst circumnavigation of the globe. *VFR Cook and his ninety-eight foot bark, Endeavour, carried the Venus transit observation crew mounted by the Royal Society, led by a future Royal Soc. President, Joseph Banks. They would erect an observation station at Point Venus in Tahiti to observe the June 3, 1769 observation under clear blue skys. *Timothy Ferris, Coming of Age in the Milky Way

1770 Lagrange, in a letter to d’Alembert, ﬁrst uses the notation f‘ (x) for the derivative. He ﬁrst used it in print in a paper published in 1772. Although Lagrange used the notation in his diagramless Mecanique Analytique (1788), it did not catch on until after he used it in his Theorie de functions analytiques (1797). *Oeuvres de Lagrange, 13, p. 181.

1774 John Adams notes in his diary that he had toured Princeton’s library with Professor Euston (William Churchill Houston, first professor of mathematics and natural philosophy) and then into the “apparatus room” where he saw the “most beautiful machine”. It was an orrery made by David Rittenhouse, a renowned American astronomer, inventor, clockmaker, mathematician, surveyor, scientific instrument craftsman and public official. Professor Houston served in combat in the revolution when Princeton was closed by the occupation of the British. After the college was reopened, he returned to teaching but was soon selected to represent New Jersey as a representative to the Continental Congress, and then to the Constitutional Convention. He died shortly after the close of the Constitutional Convention. *The Teaching and History of Mathematics in The United States, F. Cajori (pgs 71-72)

1831 Darwin had been committed to a life as a clergyman when he received a letter from George Peacock inviting him to sail with Captain Fitzroy. The rest, as they say, is history.
My dear Sir
I received Henslow’s (Darwin's botany professor) letter last night too late to forward it to you by the post, a circumstance which I do not regret, as it has given me an opportunity of seeing Captain Beaufort at the admiralty (the Hydrographer) & of stating to him the offer which I have to make to you: he entirely approves of it & you may consider the situation as at your absolute disposal: I trust that you will accept it as it is an opportunity which should not be lost & I look forward with great interest to the benefit which our collections of natural history may receive from your labours
The circumstances are these
Captain Fitzroy (a nephew of the Duke of Graftons) sails at the end of September in a ship to survey in the first instance the S. Coast of Terra del Fuego, afterwards to visit the South Sea Islands & to return by the Indian Archipelago to England: The expedition is entirely for scientific purposes & the ship will generally wait your leisure for researches in natural history &c: Captain Fitzroy is a public spirited & zealous officer, of delightful manners & greatly beloved by all his brother officers: he went with Captain Beechey and  spent 1500£ in bringing over and educating at his own charge 3 natives of Patagonia:f2 he engages at his own expense an artist at 200 a year to go with him: you may be sure therefore of having a very pleasant companion, who will enter heartily into all your views
The ship sails about the end of September you must lose no time in making known your acceptance to Captain Beaufort, Admiralty hydr I have had a good deal of correspondence about this matter, whof3 feels in common with myself the greatest anxiety that you should go. I hope that no other arrangements are likely to interfere with it
Captain will give you the rendezvous & all requisite information: I should recommend you to come up to London, in order to see him & to complete your arrangements I shall leave London on Monday: perhaps you will have the goodness to write to me at Denton, Darlington, to say that you will go.
The Admiralty are not disposed to give a salary, though they will furnish you with an official appointmentf4 & every accomodation: if a salary should be required however I am inclined to think that it would be granted
Believe me | My dear Sir | Very truly yours | Geo Peacock

If you are with Sedgwick I hope you will give my kind regards to him

In 1895, electricity was first transmitted commercially from the first large-scale utilization of Niagara Falls power, the current being used by the Pittsburgh Reduction Company in the electrolytic production of aluminium metal from its ore. Buffalo subsequently received power for commercial use on 15 Nov 1896. The equipment was the result of a contract made on 24 Oct 1893 whereby Westinghouse Electric and Manufacturing Company of Pittsburgh, Pa., would install three 5,000-hp generators producing two-phase currents at 2,200 volts, 25 hertz. The first such tuboalternator unit was completed within 18 months. Prior capacity had been limited to generators no larger than 1,000 hp.*TIS

1966 Professor Stephen Smale, who received the Fields medal ten days earlier, condemned American military intervention in Vietnam and Soviet intervention in Hungary at a news conference in Moscow. For Smale’s fascinating personal account see “On the Steps of Moscow University,” The Mathematical Intelligencer, 6, no. 2, pp. 21–27. *VFR

1984 Miss Manners​ addresses computer correspondence
Miss Manners confronts a new realm of etiquette in her August 26 column as she responded to a reader's concern about typing personal correspondence on a personal computer. The concerned individual said that using the computer was more convenient but that they were worried about the poor quality of her dot-matrix printer and about copying parts of one letter into another.
Miss Manners replied that computers, like typewriters, generally are inappropriate for personal correspondence. In the event a word processor is used, she warned, the recipient may confuse the letter for a sweepstakes entry. And, she noted, if any one of your friends ever sees that your letter to another contains identical ingredients, you have will no further correspondence problems.*CHM

BIRTHS

1728 Johann Heinrich Lambert (August 26, 1728 – September 25, 1777) was born in Mulhouse, Alsace. His most famous results are the proofs of the irrationality of π and e  *VFR In 1766, Lambert wrote Theorie der Parallellinien, a study of the parallel postulate. By assuming that the parallel postulate was false, he deduced many non-euclidean results. He noticed that in this new geometry the sum of the angles of a triangle increases as its area decreases. Lambert conjectured that e and p are transcendental, though this was not proved for another century. He is responsible for many innovations in the study of heat and light, devised a method of measuring light intensity, as well as working on the theory of probability.*TIS (Lambert's credit for a vigorous proof of the irrationality of π is generally agreed to, but  Euler Scholar Ed Sandifer has written that Euler's proof was fully rigorous prior to Lambert.  *How Euler Did It, Feb 2006).

1740 Joseph-Michel Montgolfier (26 Aug 1740; 26 Jun 1810)French balloon pioneer, with his younger brother, Étienne. An initial experiment with a balloon of taffeta filled with hot smoke was given a public demonstration on 5 Jun 1783. This was followed by a flight carrying three animals as passengers on 19 Sep 1783, shown in Paris and witnessed by King Louis XVI. On 21 Nov 1783, their balloon carried the first two men on an untethered flight. In the span of one year after releasing their test balloon, the Montgolfier brothers had enabled the first manned balloon flight in the world.*TIS

 Jacques Louis David
1743 Antoine-Laurent Lavoisier (26 August 1743 – 8 May 1794) French scientist, the "father of modern chemistry," was a brilliant experimenter also active in public affairs. An aristocrat, he invested in a private company hired by the government to collect taxes. With his wealth he built a large laboratory. In 1778, he found that air consists of a mixture of two gases which he called oxygen and nitrogen. By studying the role of oxygen in combustion, he replaced the phlogiston theory. Lavoisier also discovered the law of conservation of mass and devised the modern method of naming compounds, which replaced the older nonsystematic method. During the French Revolution, for his involvement with tax-collecting, he was guillotined.*TIS
"This great double portrait at right was painted when the artist, at the peak of his powers, had become the standard-bearer of French Neoclassicism. Lavoisier is known for his pioneering studies of oxygen, gunpowder, and the chemical composition of water. In 1789 he published a treatise on chemistry illustrated by his wife, who is believed to have been David's pupil." *Metropolitan Museum of Art

1875 Giuseppe Vitali (26 August 1875 – 29 February 1932) was an Italian mathematician who worked in several branches of mathematical analysis. He was the first to give an example of a non-measurable subset of real numbers, see Vitali set. His covering theorem is a fundamental result in measure theory. He also proved several theorems concerning convergence of sequences of measurable and holomorphic functions. Vitali convergence theorem generalizes Lebesgue's dominated convergence theorem. Another theorem bearing his name gives a sufficient condition for the uniform convergence of a sequence of holomorphic functions on an open domain D⊂ℂ to a holomorphic function on D. This result has been generalized to normal families of meromorphic functions, holomorphic functions of several complex variables, and so on. *Wik

1882 James Franck (26 Aug 1882; 21 May 1964) German-born American physicist who shared the Nobel Prize for Physics in 1925 with Gustav Hertz for research on the excitation and ionization of atoms by electron bombardment that verified the quantized nature of energy transfer.*TIS
In 1933, after the Nazis came to power, Franck, being a Jew, decided to leave his post in Germany and continued his research in the United States, first at Johns Hopkins University in Baltimore and then, after a year in Denmark, in Chicago. It was there that he became involved in the Manhattan Project during World War II; he was Director of the Chemistry Division of the Metallurgical Laboratory[5] at the University of Chicago. He was also the chairman of the Committee on Political and Social Problems regarding the atomic bomb; the committee consisted of himself and other scientists at the Met Lab, including Donald J. Hughes, J. J. Nickson, Eugene Rabinowitch, Glenn T. Seaborg, J. C. Stearns and Leó Szilárd. The committee is best known for the compilation of the Franck Report, finished on 11 June 1945, which recommended not to use the atomic bombs on the Japanese cities, based on the problems resulting from such a military application.*Wik

1886 Jerome C. Hunsaker (26 Aug 1886; 10 Sep 1984)American aeronautical engineer who made major innovations in the design of aircraft and lighter-than-air ships, seaplanes, and carrier-based aircraft. His career had spanned the entire existence of the aerospace industry, from the very beginnings of aeronautics to exploration of the solar system. He received his master's degree in naval architecture from M.I.T. in 1912. At about the same time seeing a flight by Bleriot around Boston harbour attracted him to the fledgling field of aeronautics. By 1916, he became MIT's first Ph.D. in aeronautical engineering. He designed the NC (Navy Curtiss) flying boat with the capability of crossing the Atlantic. It was the largest aircraft in the world at the time, with four engines and a crew of six.*TIS

1899 Wolfgang Krull (26 August 1899 - 12 April 1971) proved the Krull-Schmidt theorem for decomposing abelian groups and defined the Krull dimension of a ring.*SAU

1918 Katherine Coleman Goble Johnson (August 26, 1918 in White Sulphur Springs, W. Va {pop 800)-) is an American physicist, space scientist, and mathematician who contributed to America's aeronautics and space programs with the early application of digital electronic computers at NASA. Known for accuracy in computerized celestial navigation, she calculated the trajectory for Project Mercury and the 1969 Apollo 11 flight to the Moon. From 1953 through 1958, Johnson worked as a "computer" for NACA (later to become NASA), doing analysis for topics such as gust alleviation for aircraft. She calculated the trajectory for the space flight of Alan Shepard, the first American in space, in 1959. She also calculated the launch window for his 1961 Mercury mission. She plotted backup navigational charts for astronauts in case of electronic failures. In 1962, when NASA used computers for the first time to calculate John Glenn's orbit around Earth, officials called on her to verify the computer's numbers (other versions say it was Glenn himself who requested she check the data).
On November 24, 2015, President Barack Obama her with the Presidential Medal of Freedom and cited as a pioneering example of African American women in STEM *Wik

1951 Edward Witten (26 Aug 1951, )American mathematical physicist who was awarded the Fields Medal in 1990 for his work in superstring theory. This is work in elementary particle theory, especially quantum field theory and string theory, and their mathematical implications. He elucidated the dynamics of strongly coupled supersymmetric field. The deep physical and mathematical consequences of the electric-magnetic duality thus exploited have broadened the scope of Mathematical Physics. He also received the Dirac Medal from the International Centre for Theoretical Physics (1985) and the Dannie Heineman Prize from the American Physical Society (1998), among others.*TIS

DEATHS

1349 Thomas Bradwardine, (c. 1290-26 August 1349) archbishop of Canterbury, died of the plague. This medieval mathematical physicist studied the notion of change. *VFR Bradwardine was a noted mathematician as well as theologian and was known as 'the profound doctor'. He studied bodies in uniform motion and ratios of speed in the treatise De proportionibus velocitatum in motibus (1328). This work takes a rather strange line between supporting and criticising Aristotle's physics. Perhaps it is not really so strange because Aristotle views were so fundamental to learning at that time that perhaps all that one could expect of Bradwardine was the reinterpretation of Aristotle's views on bodies in motion and forces acting on them. It is likely that his intention was not to criticise Aristotle but rather to justify mathematically a reinterpretation of Aristotle's statements. He was also the first mathematician to study "star polygons". They were later investigated more thoroughly by Kepler *SAU A star polygon {p/q}, with p,q positive integers, is a figure formed by connecting with straight lines every qth point out of p regularly spaced points lying on a circumference. The number q is called the density of the star polygon. Without loss of generality, take q less than p/2. *Wolfram MathWorld

1572 Peter Ramus (1515 – 26 August 1572) was cruelly murdered, by hired assassins, during the St. Bartholomew’s Day Massacre. He was an early opponent of the teachings of Aristotle. *VFR Peter Ramus was a French mathematician who wrote a whole series of textbooks on logic and rhetoric, grammar, mathematics, astronomy, and optics. His assassination was due to religious conflict.

1865 Johann Encke (23 Sep 1791, 26 Aug 1865) German astronomer who established the period of Encke's Comet at 3.3 years (shortest period of any known). *TIS He also discovered the gap in the A-ring of Saturn and determent an accurate value of the solar parallax. The Royal Society
mentioned the death to be 26 or 28 August 1865. *NSEC

1929 Thomas John l'Anson Bromwich (8 Feb 1875 in Wolverhampton, England - 26 Aug 1929 in Northampton, England) He worked on infinite series, particularly during his time in Galway. In 1908 he published his only large treatise An introduction to the theory of infinite series which was based on lectures on analysis he had given at Galway. He also made useful contributions to quadratic and bilinear forms and many consider his algebraic work to be his finest. In a series of papers he put Heaviside's calculus on a rigorous basis treating the operators as contour integrals*SAU G. H. Hardy described him as the “best pure mathematician among the applied mathematicians at Cambridge, and the best applied mathematician among the pure mathematicians.” *VFR

1961 Howard Percy Robertson (27 Jan 1903 in Hoquiam, Washington, USA - 26 Aug 1961) made outstanding contributions to differential geometry, quantum theory, the theory of general relativity, and cosmology. He was interested in the foundations of physical theories, differential geometry, the theory of continuous groups, and group representations. He was particularly interested in the application of the latter three subjects to physical problems.
His contributions to differential geometry came in papers such as: The absolute differential calculus of a non-Pythagorean non-Riemannian space (1924); Transformation of Einstein space (1925); Dynamical space-times which contain a conformal Euclidean 3-space (1927); Note on projective coordinates (1928); (with H Weyl) On a problem in the theory of groups arising in the foundations of differential geometry (1929); Hypertensors (1930); and Groups of motion in space admitting absolute parallelism (1932). *SAU

1977 Robert Schatten (January 28, 1911 – August 26, 1977) His principal mathematical achievement was that of initiating the study of tensor products of Banach spaces. The concepts of crossnorm, associate norm, greatest crossnorm, least crossnorm, and uniform crossnorm, all either originated with him or at least first received careful study in his papers. He was mainly interested in the applications of this subject to linear transformations on Hilbert space. In this subject, the Schatten Classes perpetuate his name. Schatten had his own way of making abstract concepts memorable to his elementary classes. Who could forget what a sequence was after hearing Schatten describe a long corridor, stretching as far as the eye could see, with hooks regularly spaced on the wall and numbered 1, 2, 3, ...? "Then," Schatten would say, "I come along with a big bag of numbers over my shoulder, and hang one number on each hook." This of course was accompanied by suitable gestures for emphasis. *SAU

1992 Daniel E. Gorenstein (January 1, 1923 – August 26, 1992) was an American mathematician. He earned his undergraduate and graduate degrees at Harvard University, where he earned his Ph.D. in 1950 under Oscar Zariski, introducing in his dissertation a duality principle for plane curves that motivated Grothendieck's introduction of Gorenstein rings. He was a major influence on the classification of finite simple groups.
After teaching mathematics to military personnel at Harvard before earning his doctorate, Gorenstein held posts at Clark University and Northeastern University before he began teaching at Rutgers University in 1969, where he remained for the rest of his life. He was the founding director of DIMACS in 1989, and remained as its director until his death.
Gorenstein was awarded many honors for his work on finite simple groups. He was recognised, in addition to his own research contributions such as work on signalizer functors, as a leader in directing the classification proof, the largest collaborative piece of pure mathematics ever attempted. In 1972 he was a Guggenheim Fellow and a Fulbright Scholar; in 1978 he gained membership in the National Academy of Sciences and the American Academy of Arts and Sciences, and in 1989 won the Steele Prize for mathematical exposition. *Wik

1998 Frederick Reines (16 Mar 1918, 26 Aug 1998) American physicist who was awarded the 1995 Nobel Prize for Physics for his detection in 1956 of neutrinos, working with his colleague Clyde L. Cowan, Jr. The neutrino is a subatomic particle, a tiny lepton with little or no mass and a neutral charge which had been postulated by Wolfgang Pauli in the early 1930s but had previously remained undiscovered. (Reines shared the Nobel Prize with physicist Martin Lewis Perl, who discovered the tau lepton.)*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