Friday, 28 August 2026

Not The End for the Happy Ending Couple

 

*Wik


On 28 August 2005, Esther Klein and her husband George passed away within an hour of each other. An unusual event made even more interesting by a beautiful mathematical problem, that linked them together, and spawned the mathematical areas called Ramsey Theory, and Combinatorial Geometry.

In 1933 a group of mostly male students met regularly in Budapest to discuss mathematics. At one such meeting, one of (perhaps the only??) women present, Esther Klein, asked a simple geometric question: Is it possible to place five points on a plane so that no four of them form a convex quadrilateral? None of the student's present could answer her challenge; a fact made more impressive in that one of the students was Paul Erdos, one of the most prolific problem solvers in mathematics history.  Another student present was George Szekeres, another prolific mathematician working in combinatorial mathematics and a prominent player in the problem Esther submitted.

Esther then went on to illustrate her proof. Today the problem and it's generalization is regarded as one of the foundational works in the field of combinatorial geometry.

Within four years, Esther and George were married, and Paul Erdos dubbed the problem the Happy Ending Problem as he felt it was the start of their relationship.



The common proof used today for the problem is to divide it into simple cases. It is assumed that the points are in general position, that is, no three are collinear. Pick three of the points to form a triangle. If any point(s) is outside the triangle, then a convex quadrilateral can be drawn using four points. For the case when the two other points are inside the triangle, the segment containing these two points and one side of the triangle can be united into a convex quadrilateral. Also see the nice illustration at Theorem of the Day.

Erdos and George Szekeres generalized the problem to the theorem: For any positive integer N, any sufficiently large finite set of points in the plane in general position has a subset of N points that form the vertices of a convex polygon.
But HOW BIG was a "sufficiently large finite set of points" for a given convex n-gon? For a triangle, three points was all that was necessary. For a quadrilateral, Esther had shown that five points would suffice. Erdos and George predicted that for a pentagon, it would require nine points, but the complete proof was not published until 1970. Shortly after the death of George and Esther Szekeres, the solution for a hexagon was published in the ANZIAM Journal. The paper, Computer solution to the 17-point Erdös-Szekeres problem by George Szekeres(deceased)and
Lindsay Peters, showed that for a convex hull of six sides, the required number would be 17 points. (A challenging problem for students would be to create 16 points in general position so that no six formed a convex hexagon.)
Beyond that.... we just don't know. It must be a finite number, and we know from another Erdos-Sekeres proof that for an n-gon, the number of points is greater than or equal to 1 + 2(n-2).  That would mean that to guarantee a convex polygon, there must be at least nine points in the plain with no three co-linear.  

Paul Erdos used to talk about "God's Book." A list of all the best solutions to every mathematical problem. Maybe they got a peak after they left this plane. And Happily, the generalized Happy Ending problem has not ended for us still here. Care to try for a convex heptagon.

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 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

The Kissing Number, the number of spheres that can be placed around a central sphere so that they all are touching it, for the eighth dimension is 240. Beyond the fourth dimension, only the eighth and twenty-fourth are known exactly. The 24th dimension is the highest dimension for which the exact "kissing number", is known. For the 24th dimension, the "kissing number is 196,560.

A highly symmetrical realization of the kissing number 12 in three dimensions is by aligning the centers of outer spheres with vertices of a regular icosahedron. This leaves slightly more than 0.1 of the radius between two nearby spheres. This was the subject of a famous disagreement between mathematicians Isaac Newton and David Gregory. Newton correctly thought that the limit was 12; Gregory thought that a 13th could fit.


240 is the smallest number expressible as the sum of consecutive primes in three ways, *Prime Curios (113+127, 53+59+61+67, 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43.)




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

Monument to Archimedes in Piazza Archimedes



1314  On this day in 1314, the University of St Andrews was founded. It is the third oldest university in the English-speaking world and was established by a papal bull from Pope Benedict XIII.

The University of St Andrews is a public university in St Andrews, Scotland. It is the oldest of the four ancient universities of Scotland and, following the universities of Oxford and Cambridge, the third-oldest university in the English-speaking world.



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

*Wik





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 Narwhal) horn and an argument ensued which led to the beating. More detail at Sloan Letters

Image:  Five foot long tusk from Nicholson Whaling Collection, Providence Public Library



Footnote: Skittles is a bowling game, usually with nine pens, or quills.  The winner was the one who got them all down with the smallest number of rolls.  The rules for what seems a simple game could be very complex.




1742 a letter from Euler to Goldbach in 1742, Euler proves no number of the form 4n4 +1 can be a prime. In the letter he showed that 1 + 4x4 =(2x2 + 2x + 1)(2x2 − 2x + 1) *Euler Correspondence 

 I think he must have been making an obvious exception of 5.  Almost all of them end in five except numbers where  n=5, 15, etc.  1+4(5^4) = 2501 =  [2 (5^2) + 2(5) + 1 ][2 (5^2) - 2(5) + 1}= 61 * 41




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. 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. He chose these names because Saturn, known in Greek mythology as Cronus, was the leader of the Titans. *Wik

It is about 500 kilometers (310 miles) in diameter, about a tenth of that of Saturn's largest moon, Titan.




1830  Peter Cooper, an American inventor and industrialist, died Apr. 4, 1883, at age 92. Cooper first came on the engineering scene in 1830, when he assembled from spare parts a locomotive that he called Tom Thumb, and on behalf of which he challenged a horse-drawn rail car to a race, which took place on Aug. 28, 1830 (first image). Tom Thumb lost the race (the caption to our first image notwithstanding), due to mechanical problems, , but he won the marathon, since the locomotive’s superiority was evident, and the Baltimore and Ohio Railroad decided to put their money on steam locomotives.  Their rapid expansion enabled them to buy iron rails from Cooper's iron works in Maryland, which was the whole idea behind Tom Thumb in the first place.  In the early 20th century, the Bureau of Public Roads (now the Federal Highway Administration) commissioned a painting of the race by their staff artist Carl Rakeman (as well as a hundred other events in highway and rail history). You may see them all here. *Linda Hall Org

The Iron Horse Wins, by Carl Wakeman, date unknown, 1930s?,
*Federal Highway Administration collection (fhwa.dot.gov)


1837 Pharmacists John Lea and William Perrins began manufacturing Worcester sauce on this day. Lea and Perrins sauce is still manufactured at the Midlands Road factory in Worcester, where production first began. In 1916 Perrins used some of the profits to found the Dyson Perrins organic chemistry laboratory at Oxford University. *rsc.org 

*Lucio Gelmini


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




1858 On this summer day in 1898, something very mundane took place in the town of New Bern, North Carolina.
At the drugstore on the corner of Middle and Pollock streets, patrons had their first taste of an old favorite under a new name. For several years they’d been calling it “Brad’s Drink,” after the drugstore’s owner, Bradham—Caleb Bradham, to be exact. Brad’s Drink was a refreshing, sweet mix of sugar, caramel, kola nut, lemon oil, nutmeg, and carbonated water.(I know you're already trying to guess, read on)
Apart from the drink being satiating during the sweltering summer, Bradham claimed that it also served as a digestive, aiding against dyspepsia. He started marketing it as Pepsi-Cola on August 28, 1898.

The name change had little to do with impressing local clientele: They already loved Brad’s Drink, not only for its taste but also because it provided an opportunity to gather with friends over a bubbly drink that was free of alcohol. The temperance movement was in full swing then, and the aversion to alcohol was especially strong in the rural South.
“Brad’s Drink” had a nice homey feel for New Bern, but Bradham knew it didn’t quite have the invigorating fizz of “Pepsi-Cola.”Indeed, the catchy rebranding helped transform a hometown favorite into one of the world’s most recognizable soft drinks, and PepsiCo, Inc. eventually became one of the largest food and beverage companies. *Britannica






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 1,5
00 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








2009  Apple Talk Says Good by  
With the release of Mac OS X 10.6, "Snow Leopard," Apple discontinued its support for the AppleTalk local area networking system. Introduced in 1985 as a quick way to connect Apple computers and peripherals to each other, AppleTalk was a low-cost, medium performance network, perfect for homes and many offices.

The basic AppleTalk hardware was built into every Mac computer so networks could be established without any prior setup or need for a centralized router or server. Apple Talk networks could also be connected to each other, forming internets, or use a variety of physical media like Ethernet, Token Ring or Apple’s own LocalTalk.

AppleTalk was ultimately displaced by TCP/IP-based systems, but for most of the 1980s and ‘90s was Apple's main networking technology.






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




1862 Roberto Marcolongo (August 28, 1862 in Rome – May 16, 1943 in Rome) was an Italian mathematician , known for his research in vector calculus and theoretical physics .

He graduated in 1886, and later he was an assistant of Valentino Cerruti in Rome. In 1895 he became professor of rational mechanics at the University of Messina . In 1908 he moved to the University of Naples , where he remained until retirement in 1935.

He worked on vector calculus together with Cesare Burali-Forti , which was then known as "Italian notation". In 1906 he wrote an early work which used the four-dimensional formalism to account for relativistic invariance under Lorentz transformations .

In 1921 he published to Messina one of the first treaties on the special relativity and general, where he used the absolute differential calculus without coordinates, developed with Burali-Forti, as opposed to the absolute differential calculus with coordinates of Tullio Levi-Civita and Gregorio Ricci-Curbastro .

He was a member of the Accademia dei Lincei and other Italian academies.




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.) 

The Oscillograph was not like the CRT Oscilloscopes that followed them.  I've searched in vane for images of them . If someone has one, would appreciate a copy/link.  From the images I see of new Techtronics High Definition scopes, I assume they no longer use CRTs either. 
Here is an image of CRT telescope from around the 70's...
*Wik

 

1867 Maxime Bochner  (August 28, 1867 – September 12, 1918) was an American mathematician who published about 100 papers on differential equations, series, and algebra. He also wrote elementary texts such as Trigonometry and Analytic Geometry. Bôcher's theorem, Bôcher's equation, and the Bôcher Memorial Prize are named after him. *Wik

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 Arnoldus Schouten (28 August 1883 – 20 January 1971) was a Dutch mathematician and Professor at the Delft University of Technology. He was an important contributor to the development of tensor calculus and Ricci calculus, and was one of the founders of the Mathematisch Centrum in Amsterdam.
Schouten's dissertation applied his "direct analysis", modeled on the vector analysis of Josiah Willard Gibbs and Oliver Heaviside, to higher order tensor-like entities he called affinors. The symmetrical subset of affinors were tensors in the physicists' sense of Woldemar Voigt.

Entities such as axiators, perversors, and deviators appear in this analysis. Just as vector analysis has dot products and cross products, so affinor analysis has different kinds of products for tensors of various levels. However, instead of two kinds of multiplication symbols, Schouten had at least twenty. This made the work a chore to read, although the conclusions were valid.

Schouten later said in conversation with Hermann Weyl that he would "like to throttle the man who wrote this book." (Karin Reich, in her history of tensor analysis, misattributes this quote to Weyl.) Weyl did, however, say that Schouten's early book has "orgies of formalism that threaten the peace of even the technical scientist." (Space, Time, Matter, p. 54). Roland Weitzenböck wrote of "the terrible book he has committed."

In 1906, L. E. J. Brouwer was the first mathematician to consider the parallel transport of a vector for the case of a space of constant curvature. In 1917, Levi-Civita pointed out its importance for the case of a hypersurface immersed in a Euclidean space, i.e., for the case of a Riemannian manifold immersed in a "larger" ambient space. In 1918, independently of Levi-Civita, Schouten obtained analogous results. In the same year, Hermann Weyl generalized Levi-Civita's results. Schouten's derivation is generalized to many dimensions rather than just two, and Schouten's proofs are completely intrinsic rather than extrinsic, unlike Tullio Levi-Civita's. Despite this, since Schouten's article appeared almost a year after Levi-Civita's, the latter got the credit. Schouten was unaware of Levi-Civita's work because of poor journal distribution and communication during World War I. Schouten engaged in a losing priority dispute with Levi-Civita. Schouten's colleague L. E. J. Brouwer took sides against Schouten. Once Schouten became aware of Ricci's and Levi-Civita's work, he embraced their simpler and more widely accepted notation. Schouten also developed what is now known as a Kähler manifold two years before Erich Kähler. Again he did not receive full recognition for this discovery. *Wik




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.
Friedrichs' greatest contribution to applied mathematics was his work on partial differential equations . He also did major research and wrote many books and papers on existence theory, numerical methods , differential operators in Hilbert space , non-linear buckling of plates, flows past wings, solitary waves, shock waves, combustion, magneto-fluid dynamical shock waves, relativistic flows, quantum field theory , perturbation of the continuous spectrum, scattering theory, and symmetric hyperbolic equations.  With Cartan ,  Friedrichs  gave a “geometrized” formulation of Newtonian gravitation theory—also known as “ Newton–Cartan theory ”— and later developed by Dautcourt, Dixon, Dombrowski and Horneffer, Ehlers , Havas, Künzle, Lottermoser, Trautman , and others.

A member of the National Academy of Sciences since 1959, Friedrichs received many honorary degrees and awards for his work. There is a student prize named after Friedrichs at NYU . The American Mathematical Society selected him as the Josiah Willards Gibbs lecturer for 1954.  In November 1977, Friedrichs received the National Medal of Science from President Jimmy Carter "for bringing the powers of modern mathematics to bear on problems in physics , fluid dynamics, and elasticity." *Wik



1910 Clarisse Doris Hellman Pepper (August 28, 1910 – March 28, 1973) was an American historian of science, "one of the first professional historians of science in the United States". She specialized in 16th- and 17th-century astronomy, wrote a book on the Great Comet of 1577, and was the translator of another book, a biography of Johannes Kepler. She became a professor at the Pratt Institute and later at the Queens College, City University of New York, and was recognized by membership in several selective academic societies. *Wik





1911 Shizuo Kakutani August 28 1911, August 17 2004) was a Japanese-born American mathematician, best known for his eponymous fixed-point theorem.
The Kakutani fixed-point theorem is a generalization of Brouwer's fixed-point theorem, holding for generalized correspondences instead of functions. Its most important uses are in proving the existence of Nash equilibria in game theory, and the Arrow–Debreu–McKenzie model of general equilibrium theory.
Kakutani's other mathematical contributions include the Kakutani skyscraper, a concept in ergodic theory (a branch of mathematics that studies dynamical systems with an invariant measure and related problems). They also include his solution of the Poisson equation using the methods of stochastic analysis.
The Collatz (or 3n+1) conjecture is also known as the Kakutani conjecture. *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




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




DEATHS



1875  Beppo Levi (14 May 1875 – 28 August 1961) was an Italian mathematician. He published high-level academic articles and books, not only on mathematics, but also on physics, history, philosophy, and pedagogy. Levi was a member of the Bologna Academy of Sciences and of the Accademia dei Lincei.

His early work studied singularities on algebraic curves and surfaces. In particular, he supplied a proof (questioned by some) that a procedure for resolution of singularities on algebraic surfaces terminates in finitely many steps. Later he proved some foundational results concerning Lebesgue integration, including what is commonly known as Beppo Levi's lemma.




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
The "Happy ending" couple near
the end and still happy. 



2006 Melvin Schwartz (November 2, 1932 – August 28, 2006) was an American physicist. He s hared the 1988 Nobel Prize in Physics with Leon M. Lederman and Jack Steinberger for their development of the neutrino beam method and their demonstration of the doublet structure of the leptons through the discovery of the muon neutrino.




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 




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


On This Day in Math - October 24

    

Gauss-Weber Monument in Gotttingen


Now it is quite clear to me that there are no solid spheres in the heavens, and those that have been devised by authors to save the appearances, exist only in their imagination, for the purpose of permitting the mind to conceive the motion which the heavenly bodies trace in their courses.
~Tycho Brahe

Happy kilobit day, 1024 = 2 10

The 297th day of the year; 2972 = 88209 and 88+209 = 297. (Numbers that have this property are a type of Kaprekar number; there are only three such numbers of three digits, now you know one of them.)

And this one from * Jim Wilder @wilderlab 2973=26,198,073 and 26+198+073=297 
Anyone for 297^4???



EVENTS

1676 Newton summarized the stage of development of his method in the “Epistola posterior,” which he sent to Oldenburg to transmit to Leibniz. *VFR (see Oct 26, 1676) This may be the first time Newton used irrational exponents in communication to others. It is one of the earlier uses by anyone. In the letter to Oldenburg, Newton remarks that Leibniz had developed a number of methods, one of which was new to him.  Newton had sent (June 13, 1676) Oldenburg his  “Epistola prior” . Among other things it contained the first statement of the binomial theorem for negative and fractional exponents.  This may be the first use of fractional and negative exponents in the modern sense (cajori, 308 pgs 370-371)
The idea and limited use had been mentioned by Viete, but in a rhetorical manner. Wallis, twenty years earlier, had mentioned both negative and fractional "indices" and gives an example using 1/sqrt(2) has index (-1/2). Oresme was The first to use fractional and irrational powers to explore his knowledge of music, but he did not write them as raised numbers. 
Michael Stifel Introduced the term exponent. His work with exponents only included numbers that had a base of 2, but he  also used negative exponents. Therefore he discovered the geometric sequence: ...-1/8, -1/4, -1/2, 1, 2, 4, 8 ...
It all began when young Newton read John Wallis’ Arithmetica Infinitorum, a seminal work of 17th-century math. Wallis included a novel and inductive method of determining the value of pi, and Newton wanted to devise something similar. He started with the problem of finding the area of a “circular segment” of adjustable width x. This is the region under the unit circle, defined by y=1x2, that lies above the portion of the horizontal axis from 0 to x. Here x could be any number from 0 to 1, and 1 is the radius of the circle. The area of a unit circle is pi, as Newton well knew, so when x=1, the area under the curve is a quarter of the unit circle, π4. But for other values of x, nothing was known.
Newton's Epistoa prior seemed to be designed to scare Leibniz away from the approach suggesting indirectly that he might not be ready sor the challenging problem.  The Epistola posterior was a more gentle with many details filled in.


*Getty



1729 Euler mentioned the gamma function in a letter to Goldbach. In 1826 Legendre gave the function its symbol and name. * F. Cajori, After earlier giving him the definition as an integral, he presents the function as Γ(1) = 1, Γ(x + 1) = xΓ(x) , History of Mathematical Notations, vol. 2, p. 271 (the Oct 13 date is for the Julian Calendar still used in Russia when Euler wrote from there. It was the 24th in most of the rest of the world using the Gregorian Calendar.)

1826 Abel wrote Holmboe his impressions of continental mathematics and mathematicians.
Upon reaching Paris from Berlin, he worked on what would be called the Paris Treatise that he submitted to the Academy in October 1826. In this memoir, Abel obtained among other things, an important addition theorem for algebraic integrals. It is also in this treatise that we see the first occurrence of the concept of the genus of an algebraic function. Cauchy and Legendre were appointed referees of this memoir. In Paris, Abel was disappointed to find little interest in his work, which he had saved for the Academy. He wrote to Holmboe, “I showed the treatise to Mr. Cauchy, but he scarcely deigned to glance at it."
*Krishnaswami Alladi, NEILS HENRIK ABEL, Norwegian mathematical genius (paper on UFL website)



1844 Michael Faraday in a letter (his first?) to Ada Lovelace declines an invitation to be her tutor. She had written him on 16 October and wrote, " "Perhaps no one has read your paper with such full appreciation as myself of it's practical bearings; or has valued it so justly".  The conversations were mostly about science but she told him at some point of her interest in mesmerism. In Faraday's response to her questions about his religion, he describes himself as, "of a small and despised sect of Christians, known, if they are known at all, as Sandemanian." Michael Brooks, in his book Free Radicals, describes the sect as responsible for Faraday's lack of much interest in the applications of his scientific discoveries; "It was his calling, as he saw it, to study nature, which was 'written by the finger of God', and make clear the eternal power and divine nature of the creator."



In 1851, William Lassell discovered Ariel and Umbriel, satellites of Uranus. All of Uranus's moons are named after characters from the works of William Shakespeare or Alexander Pope's The Rape of the Lock. The names of all four satellites of Uranus then known were suggested by John Herschel in 1852 at the request of Lassell. Ariel has an approx. diameter of 1160-km, an orbital period of 2.52 days, and orbital radius of 191,240-km from Uranus. The name Umbriel comes from Alexander Pope's The Rape of the Lock. Umbriel has a diameter of 1170-km, an orbital period of about 4 days and orbit radius of 266,000-km. Lassell, a British astronomer, had previously also discovered Neptune's largest satellite, Triton and (with Bond) discovered Saturn's moon Hyperion. He was a successful brewer before turning to astronomy.*TIS *Wik



1871 One of the largest mass lynchings in U.S. history occurred in the original Chinese Quarter of Los Angeles on October 24, 1871, and left at least 18 Chinese immigrants dead at the hands of a largely white and Latino mob. Although it was one of the most severe incidents of racist violence in U.S. history and one of the largest massacres of Asian people on U.S. soil, the incident was deliberately covered up and largely unacknowledged until the 21st century.
In the mid-1800s California was a place of rapid growth, as the territory gained statehood in 1850. The California gold rush that began in 1848 brought hundreds of thousands of new residents to the California territory, many of whom settled in southern California after their gold-tinged dreams failed to pan out. About the same time, the development of the railroads increased the demand for manual laborers, spurring an influx of immigration from China and an accompanying rise in xenophobia. A serious crop failure in southern China in 1852 prompted thousands of people to immigrate that year, and racial tensions continued to grow. In 1854 institutional racism was reaffirmed when the California Supreme Court, in People v. Hall, overturned a murder conviction that had been based on the testimony of Chinese witnesses. As a result, the state prohibited the use of Chinese individuals’ testimony in cases against white defendants, placing Chinese immigrants alongside Native Americans and African Americans, groups that were already barred from testifying against white people. Furthermore, most Chinese immigrants at that time were deemed as “aliens ineligible for citizenship” and thus could not vote or claim other civil rights. *Britannica 

A cartoon drawn by Thomas Nast in 1869 takes a sympathetic view of the difficult conditions faced by Chinese immigrants. 

Britannica



1902 In Science, George Bruce Halsted wrote that his student R. L. Moore, who had proved that one of Hilbert’s betweenness axioms was redundant, “was displaced in favor of a local schoolmarm,” Miss Mary E. Decherd. *VFR  Dechard was a well-connected but, perhaps, less qualified candidate with roots in the area.
Halstead was contentious in many ways, and Moore's rejection may have been a response to the fact that Halstead had suggested him. Halstead would be fired himself on December 11 of the same year. *D. Reginald Traylor , Creative Teaching: The Heritage of R. L. Moore, pg 35-37
George Bruce Halsted (1853–1922) was a gifted yet deeply controversial figure in the history of American mathematics. He is remembered both for his pioneering work introducing non-Euclidean geometry to English-speaking audiences and for his volatile personality, which created many enemies and overshadowed much of his academic legacy.
Halsted’s letters and classroom manner were famously sharp. One former student recalled:

“He flayed us with sarcasm, yet gloried in the wounds as proofs of progress.”

Another student remembered that Halsted “never corrected—only condemned,” calling slow learners “intellectual fossils.”




1904 Emmy Noether matriculated at the University of Erlangen. *VFR The University was only yards from her house. Images of both are at this site from The Renaissance Mathematicus.
Emmy was born in this house on the Hauptstraße in Erlangen





1927 From the 24th to 29th October 1927 in Brussels, the fifth Solvay Conference took place, Perhaps the most famous science conference in history. 17 of the 29 attendees were or became Nobel Prize winners. It is also famously remembered for it was at this conference that Einstein, who liked to invent catchy phrases, uttered his, "God does not play dice" . Bohr replied, "Einstein, stop telling God what to do". Of the attendees, only two were American Born.  The influence of USA in Physics was just beginning.
A. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, Th. de Donder, E. Schrödinger, J.E. Verschaffelt, W. Pauli, W. Heisenberg, R.H. Fowler, L. Brillouin; P. Debye, M. Knudsen, W.L. Bragg, H.A. Kramers, P.A.M. Dirac, A.H. Compton, L. de Broglie, M. Born, N. Bohr;
I. Langmuir, M. Planck, M. Skłodowska-Curie, H.A. Lorentz, A. Einstein, P. Langevin, Ch.-E. Guye, C.T.R. Wilson, O.W. Richardson

1956  Time Magazine does a feature "Close-Up" on Danish Scientist/Mathematician/poet Piet Hein, "A Poet with a Slide Rule."  Hein was the  creator of the term Super Ellipse, which already had the perfectly good name of Lame curve, after Gabriel Lame.  

Hein used a particular Lame curve for his design of a round-about in Stockholm, in 1959.  He is also the creator of the Soma Cube, and the mathematical game Hex, and many others.  
His poetry is often in the form of what he calls Gruks,  My personal favorite is :
Problems worthy of attack
Prove their worth by fighting back.






1989 “Welcome to the White House on this glorious fall day. I’m sorry if I’m just a little bit late. I was sitting in there trying to solve a few quadratic equations. [Laughter] Somewhat more difficult than balancing the budget, I might say. And then I thought it might be appropriate to have a moment of silence in memory of those substitute teachers back home. [Laughter].” Remarks by President George Bush (the elder) at the Presentation Ceremony for the Presidential Awards for Excellence in Science and Math Teaching. (A few years later when I won the award, he and Barbara walked by the group and gave us a wave.  )





1994 Lynchburg College Professor Thomas Nicely, Reports a flaw in the Pentium chip by Intel that he discovered while he was trying to calculate Brun's constant,(The sum of the reciprocals of all the twin primes, 1/3+1/5+1/5+1/7+1/11+1/13.... which converges to about 1.902).
The Pentium chip occasionally gave wrong answers to a floating-point (decimal) division calculations due to errors in five entries in a lookup table on the chip. Intel spent millions of dollars replacing the faulty chips.
Nicely first noticed some inconsistencies in the calculations on June 13, 1994 shortly after adding a Pentium system to his group of computers, but was unable to eliminate other factors until October 19, 1994. On October 24, 1994 he reported the issue to Intel. According to Nicely, his contact person at Intel later admitted that Intel had been aware of the problem since May 1994, when the flaw was discovered during testing of the FPU for its new P6 core, first used in the Pentium Pro. *Wik





BIRTHS

1632 Antonie van Leeuwenhoek (24 Oct 1632; 26 Aug 1723.) Dutch microscopist who was the first to observe bacteria and protozoa. His researches on lower animals refuted the doctrine of spontaneous generation, and his observations helped lay the foundations for the sciences of bacteriology and protozoology.*TIS "The 31th of May, I perceived in the same water more of those Animals, as also some that were somewhat bigger. And I imagine, that [ten hundred thousand] of these little Creatures do not equal an ordinary grain of Sand in bigness: And comparing them with a Cheese-mite (which may be seen to move with the naked eye) I make the proportion of one of these small Water-creatures to a Cheese-mite, to be like that of a Bee to a Horse: For, the circumference of one of these little Animals in water, is not so big as the thickness of a hair in a Cheese-mite. "




1804 Wilhelm Eduard Weber (24 Oct 1804; 23 Jun 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

Around 1833, Gauss and Weber were both professors at the University of Göttingen. They were collaborating on research in electromagnetism, following the discoveries of Ørsted and Ampère.
They constructed an electromagnetic telegraph that connected the physics institute to the astronomical observatory, a distance of about 1 kilometer (roughly 3,000 feet). This Gauss–Weber telegraph predated Samuel Morse’s system (1837) by several years. It’s often cited as the first practical electromagnetic telegraph line ever built.



Gauss-Weber Telegraph




1821 Philipp Ludwig von Seidel (23 October 1821, Zweibrücken, Germany – 13 August 1896, Munich)  formulated the notion of uniform convergence.*VFR 
 Lakatos credits von Seidel with discovering, in 1847, the crucial analytic concept of uniform convergence, while analyzing an incorrect proof of Cauchy's. In 1857, von Seidel decomposed the first order monochromatic aberrations into five constituent aberrations. They are now commonly referred to as the five Seidel Aberrations.   The Gauss–Seidel method is a useful numerical iterative method for solving linear systems. *Wik



1853 Heinrich Maschke (24 October 1853 in Breslau, Germany (now Wrocław, Poland) – 1 March 1908 Chicago, Illinois, USA) was a German mathematician who proved Maschke's theorem.
Maschke earned his Ph.D. degree from the University of Göttingen in 1880. He came to the United States in 1891, and took up an Assistant Professor position at the University of Chicago in 1892.*Wik




1873 Sir Edmund Taylor Whittaker (24 Oct 1873; 24 Mar 1956) English mathematician who made pioneering contributions to the area of the special functions, which is of particular interest in mathematical physics. Whittaker is best known work is in analysis, in particular numerical analysis, but he also worked on celestial mechanics and the history of applied mathematics and physics. He wrote papers on algebraic functions and automorphic functions. His results in partial differential equations (described as most sensational by Watson) included a general solution of the Laplace equation in three dimensions in a particular form and the solution of the wave equation. On the applied side of mathematics he was interested in relativity theory and he also worked on electromagnetic theory. *TIS



1898 Lillian Rose Vorhaus Kruskal Oppenheimer (October 24, 1898 in New York City – July 24, 1992) was an American origami pioneer. She popularized origami in the West starting in the 1950s, and is credited with popularizing the Japanese term origami in English-speaking circles, which gradually supplanted the literal translation paper folding that had been used earlier. In the 1960s she co-wrote several popular books on origami with Shari Lewis.  Lillian taught origami to Persi Diaconis when he was working as a magician;
She was the mother of three sons William Kruskal(developed the Kruskal-Wallis one-way analysis of variance), Martin David Kruskal(co-inventor of solitons and of surreal numbers), and Joseph Kruskal ( Kruskal's algorithm for computing the minimal spanning tree (MST) of a weighted graph) who all went on to be prominent mathematicians. Her grandson Clyde P. Kruskal (son of Martin) is an American computer scientist,working on parallel computing architectures, models, and algorithms. *Wik



1906 Aleksandr Osipovich Gelfond (24 Oct 1906; 7 Nov 1968) Russian mathematician who originated basic techniques in the study of transcendental numbers (numbers that cannot be expressed as the root or solution of an algebraic equation with rational coefficients). He profoundly advanced transcendental-number theory, and the theory of interpolation and approximation of complex-variable functions. He established the transcendental character of any number of the form ab, where a is an algebraic number different from 0 or 1 and b is any irrational algebraic number, which is now known as Gelfond's theorem. This statement solved the seventh of 23 famous problems that had been posed by the German mathematician David Hilbert in 1900. *TIS
The mathematical coincidence,  e^π−π=19.99909997...
The constant e^π is called Gelfond's Constant after Gelfond, who proved that the number was transcendental.




1908 John Tuzo Wilson, CC, OBE, FRS, FRSC, FRSE (October 24, 1908 – April 15, 1993) the world-renowned Canadian geophysicist, served as Director General of the Ontario Science Centre from 1974 to 1985. He was instrumental in developing the theory of Plate Tectonics in the 1960s. This theory describes the formation, motion and destruction of the Earth's crust, the origin of volcanic eruptions and earthquakes, and the growth of mountains. Dr. Wilson's significant contributions to this theory revolutionized Earth Sciences. He proposed the existence of transform faults to explain the numerous narrow fracture zones and earthquakes along oceanic ridges. He also showed that rising magma plumes beneath the Earth's crust could create stationary hot spots, leading to the formation of mid-plate volcanic chains like the Hawaiian Islands.
The first graduate of geophysics from the University of Toronto in 1930, Dr. Wilson went on to study at Cambridge and Princeton, earning his doctorate in 1936. After spending two years with the Geological Survey of Canada and almost a decade with the Canadian Military Engineers, he accepted the position of Professor of Geophysics at the University of Toronto in 1946. Internationally recognized for his major contributions as a research scientist, educator and visionary, Dr. Wilson received many prestigious
awards, including the Vetlesen Prize, the Earth Sciences equivalent of the Nobel Prize.*THE HISTORICAL MARKER DATABASE



1922 Werner Buchholz​  (24 October 1922 – 11 July 2019) He was a member of the teams that designed the IBM 701​ and Stretch models. Buchholz used term byte to describe eight bits—although in the 1950s, when the term first was used, equipment used six-bit chunks of information, and a byte equaled six bits. Buchholz described a byte as a group of bits to encode a character, or the numbers of bits transmitted in parallel to and from input-output. *CHM



1932 Pierre-Gilles de Gennes (24 Oct 1932; 18 May 2007) French physicist who was awarded the 1991 Nobel Prize for Physics for "discovering that methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter, in particular to liquid crystals and polymers." He described mathematically how, for example, magnetic dipoles, long molecules or molecule chains can under certain conditions form ordered states, and what happens when they pass from an ordered to a disordered state. Such changes of order occur when, for example, a heated magnet changes from a state in which all the small atomic magnets are lined up in parallel to a disordered state in which the magnets are randomly oriented. Recently, he has been concerned with the physical chemistry of adhesion. *TIS



1946 Ola Bratteli (24 October 1946 – 8 February 2015) was a Norwegian mathematician.

He was a son of Trygve Bratteli and Randi Bratteli (née Larssen). He received a PhD degree in 1974. He was appointed as professor at the University of Trondheim in 1980 and at the University of Oslo in 1991. He was a member of the Norwegian Academy of Science and Letters. *Wik






DEATHS

1601 Tycho Brahe (14 December 1546 – 24 October 1601) Kepler inherited his vast accurate collection of astronomical data. He used this to derive his laws of planetary motion. *VFR In 1901, on the three hundredth anniversary of his death, the bodies of Tycho Brahe and his wife Kirstine were exhumed in Prague. They had been embalmed and were in remarkably good condition, but the astronomer’s artificial nose was missing, apparently filched by someone after his death. It had been made for him in gold and silver when his original nose was sliced off in a duel he fought in his youth at Rostock University after a quarrel over some obscure mathematical point. He always carried a small box of glue in his pocket for use when the new nose became wobbly. Tycho Brahe was famous for the most accurate and precise observations achieved by any astronomer before the invention of the telescope. Born to an aristocratic family in Denmark in 1546, he was one of twin boys – the other twin was still-born – and while still a baby Tycho was stolen from his parents by a rich, childless uncle, who paid for his education and sent him to Leipzig University to study law. His imagination had been fired, however, by a total eclipse of the sun in 1560 and he was determined to be an astronomer. He found that the existing tables recording the positions of planets and stars were wildly inaccurate and dedicated himself to correcting them. *History Today Was Tycho Murdered? Read an excellent blog on "The crazy life and crazier death of Tycho Brahe, history’s strangest astronomer".




1635 Wilhelm Shickard (22 April 1592 – 24 October 1635) He invented and built a working model of the first modern mechanical calculator. *VFR
Schickard's machine could perform basic arithmetic operations on integer inputs. His letters to Kepler explain the application of his "calculating clock" to the computation of astronomical tables.
In 1935 while researching a book on Kepler, a scholar found a letter from Schickard and a sketch of his calculator, but did not immediately recognize the designs or their great importance. Another twenty years passed before the book's editor, Franz Hammer, found additional drawings and instructions for Schickard's second machine and released them to the scientific community in 1955.A professor at Schickard's old university, Tübingen, reconstructed the calculator based upon Schickard's original plans; it is still on display there today. 
He was a friend of Kepler and did copperplate engravings for Kepler's Harmonice Mundi. He built the first calculating machine in 1623, but it was destroyed in a fire in the workshop in 1624.

1655 Pierre Gassendi (22 Jan 1592, 24 Oct 1655) French scientist, mathematician, and philosopher who revived Epicureanism as a substitute for Aristotelianism, attempting in the process to reconcile Atomism's mechanistic explanation of nature with Christian belief in immortality, free will, an infinite God, and creation. Johannes Kepler had predicted a transit of Mercury would occur in 1631. Gassendi used a Galilean telescope to observed the transit, by projecting the sun's image on a screen of paper. He wrote on astronomy, his own astronomical observations and on falling bodies. *TIS




1870 Charles Joseph Minard (27 Mar 1781; 24 Oct 1870 at age 89) French civil engineer who made significant contributions to the graphical representations of data. His best-known work, Carte figurative des pertes successives en hommes de l'Armee Français dans la campagne de Russe 1812-1813, dramatically displays the number of Napoleon's soldiers by the width of an ever-reducing band drawn across a map from France to Moscow. At its origin, a wide band shows 442,000 soldiers left France, narrowing across several hundred miles to 100,000 men reaching Moscow. With a parallel temperature graph displaying deadly frigid Russian winter temperatures along the way, the band shrinks during the retreat to a pathetic thin trickle of 10,000 survivors returning to their homeland. *TIS Minard advocated the graphing idea that the ratio of information to ink should be as high as possible.


1930 Paul Emile Appell (27 Sept 1855 in Strasbourg, France - 24 Oct 1930) Appell's first paper in 1876 was based on projective geometry continuing work of Chasles. He then wrote on algebraic functions, differential equations and complex analysis. In 1878 he noted the physical significance of the imaginary period of elliptic functions in the solution of the pendulum which had been though to be purely a mathematical curiosity. He showed that the double periodicity follows from physical considerations. *SAU



1940 Pierre-Ernest Weiss (25 Mar 1865, 24 Oct 1940) French physicist who investigated magnetism and determined the Weiss magneton unit of magnetic moment. Weiss's chief work was on ferromagnetism. Hypothesizing a molecular magnetic field acting on individual atomic magnetic moments, he was able to construct mathematical descriptions of ferromagnetic behaviour, including an explanation of such magnetocaloric phenomena as the Curie point. His theory succeeded also in predicting a discontinuity in the specific heat of a ferromagnetic substance at the Curie point and suggested that spontaneous magnetization could occur in such materials; the latter phenomenon was later found to occur in very small regions known as Weiss domains. His major published work was Le magnetisme ( 1926).*TIS




1927 John McCarthy (September 4, 1927 – October 24, 2011) was an American computer scientist and cognitive scientist. He was one of the founders of the discipline of artificial intelligence. He co-authored the document that coined the term "artificial intelligence" (AI), developed the programming language family Lisp, significantly influenced the design of the language ALGOL, popularized time-sharing, and invented garbage collection.

McCarthy spent most of his career at Stanford University. He received many accolades and honors, such as the 1971 Turing Award for his contributions to the topic of AI, the United States National Medal of Science, and the Kyoto Prize.




 1952 Ida Martha Metcalf (August 26, 1857 – October 24, 1952) was the second American woman to receive a PhD in mathematics.  She was born in Texas to Charles A. and Martha C. (Williams) Metcalf. During her youth, her family moved about the south. After her father’s death, she moved to New England with her mother and siblings. By 1870, she was living in Massachusetts, where she taught school for many years.
In 1883, Ida began studying at Boston University where she received a Bachelor’s in Philosophy (Ph.B.) in 1886. From 1888 to 1889, she was a graduate student at Cornell University, earning a master's degree in mathematics. After teaching at Bryn Mawr School in Baltimore, she returned to Cornell and receive her Ph.D. in 1893.
For many years after receiving her Ph.D., Ida taught high school and worked in several financial firms and as a Civil Service Examiner. In 1912, she became a statistician in the Department of Finance for New York City, where she remained until her retirement in 1921.
After retirement, Ida continued to work intermittently as a Civil Service Examiner until 1939. Beginning with the onset of a serious illness in 1948, she lived in nursing homes until her death at the age of ninety-six.*Wik



1966 Sofya Aleksandrovna Yanovskaya (also Janovskaja; 31 January 1896 – 24 October 1966) was a Soviet mathematician, philosopher and historian, specializing in the history of mathematics, mathematical logic, and philosophy of mathematics. She is best known for her efforts in restoring the research of mathematical logic in the Soviet Union and publishing and editing the mathematical works of Karl Marx. *Wik



2014 Johanna Weber (8 August 1910 – 24 October 2014) was a German-born British mathematician and aerodynamicist. She is best known for her contributions to the development of the Handley Page Victor bomber and the Concorde.

In 1939, Weber joined the Aerodynamics Research Institute (Aerodynamische Versuchsanstalt Göttingen) in Göttingen. She was part of a small theoretical team, and her initial training in aerodynamics consisted of wind tunnel corrections. Here she met and began her lifelong collaboration with Dietrich Küchemann.

Scientists at Institute had by then worked out a consistent theory of flow around an aircraft. This was, however, an approximation, using singularities to represent the vortices that generated lift, and Weber was given the task of improving it. She realised that some of her work overlapped with Küchemann's research on jet engine intakes. They teamed up, with Weber doing the theoretical development and wind tunnel testing, and Küchemann setting the direction of their research based on his consultation with manufacturers. Over the period of the Second World War, they created a substantial body of work.

Weber also began her research into supersonic transport. In 1955, she showed that a thin delta wing with a high angle of attack could generate sufficient lift to provide the take-off and landing capability, while simultaneously enabling efficient supersonic performance. Küchemann then advocated this wing configuration with the UK Government, resulting in the support for a Mach 2 airliner by the Supersonic Transport Advisory Committee (STAC) in 1956.

In 1961, a prototype aircraft, the Handley Page HP.115, was built to test the low speed performance of the slender delta wing.*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