Thursday 30 May 2024

On This Day in Math - May 30


The best review of arithmetic 
consists in the study of algebra.
~Florian Cajori

The 150th day of the year; 150 is the largest gap between consecutive twin prime pairs less than a thousand. It occurs between {659, 661} and {809, 811}. *Prime Curios

150 is a palindrome in base 4(2112), and in base 7(303) .

A Poly divisible number is an n-digit number so that for the first digit is divisible by one, the first two digits are divisible by two, the first three digits are divisible by three, etc up to n. There are 150 three-digit poly divisible numbers. Hat tip to Derek Orr .

In February of 1657 Fermat proposed a new problem to Frenicle: Find a number x which will make (ax2 + 1) a square, where a is a (nonsquare) integer.  Frenicle found solutions of the problem. In the second part of the Solutio (pp. 18–30) he cited his table of solutions for all values of a up to 150 and explained his method of solution. 

150 is the sum of eight consecutive primes starting with 7.

150 is a Harshad(joy-giver) number, divisible by the sum of its digits.

150 year celebration is called sesquicentennial of the event.
And... 150 is the number of degrees in the quincunx astrological aspect explored by Johannes Kepler.

Rubix Cube gotten too easy for you? Try the Professor's Cube, 150 movable facets.


1667 After much debate about the presence of a woman at a Royal Society meeting, the Duchess of Newcastle was allowed to observe a demonstration of a "experiments of colours", the "weighing of air in an exhausted receiver", and "the dissolving of flesh with a certain liquor of Mr. Boyle's suggesting." This was probably the first visit by a woman to the Royal Society. The Duchess, Margaret Cavendish, was a competent scientist in her own right. Her prolific writings in the nature of science earned her the nickname “Mad Madge”. I have a note from VFR that she was elected to FRS, but can not confirm, the note says "No other woman was elected FRS until 1945" .

1765 "Ms. Catherine Price, Daughter of the late Dr. Halley " was paid a sum of 100 Pounds for "causing to be delivered to the Commissioners of the Longitude, several of the said Dr. Halley's manuscript papers, which... may lead to discoveries useful to navigation." *Derek Howse, Britain's Board of Longitude, the Finances
Three of the Astronomers Royal are buried a mile from the Observatory in the old churchyard of St Margaret’s Lee. By a curious coincidence, the Greenwich Meridian as defined by WGS84 passes though the remains of the old church at its centre. The three Astronomers Royal are Edmond Halley, Nathaniel Bliss and John Pond. Halley and Pond are buried in the same tomb. The exact spot where Bliss is buried is unknown. His grave is unmarked.

The intriguing story of how they came to be buried at Lee rather than at St Alphege’s in Greenwich in which parish the Observatory is located, leaves many questions unanswered. So too does the available information on the restoration of Halley’s tomb in 1854.
A brief history of the church at Lee
In the time between Halley being buried in 1742 and Pond joining him in the same grave in 1836, the church of St Margaret was largely rebuilt. The original church of St Margaret was of medieval origin. By the start of the nineteenth century, it was in a poor state of repair. Apart from part of the tower, it was pulled down in 1813 to make way for a new building on the same site. This was designed by Joseph Gwilt and incorporated the original tower in modified form. Gwilt’s church was built on the old foundations and like its predecessor suffered from structural problems. The population of Lee grew rapidly after the church was built and it was soon apparent that a much larger church was needed. Most of Gwilt’s church was demolished on 31 May 1841 having been replaced by the present larger church which was built on the opposite side of the road and constructed between 1839–41 to the designs of John Brown. The new church was later altered by the architect James Brooks during the last quarter of the nineteenth century. The current church is grade II* listed whilst the ruined tower of the previous two churches is grade II listed.
The old churchyard as seen from Lee Terrace on 5 October 2017. The arrow (right) shows the location of Halley’s tomb. An information board with a plan of the graveyard can be seen bottom right.

1832 Galois mortally wounded by a gunshot wound to the abdomen in a duel of honor. He was left for dead after the duel but a peasant took him to a hospital. *VFR

The infamous duel with Pescheux d'Herbinville took place near the Glassier pond in the southern suburb of Gentilly. The duel was over Galois's involvement with Stéphanie-Félicie Poterine du Motel, who was d'Herbinville's fiancée, but it has been claimed that the affair was a political frame-up by government agents in order to eliminate Galois He died in the Cochin Hospital – this is now at 27 Rue du Faubourg St. Jacques, 14e, but I don't know how long it has been there. He was buried in a common grave at Montparnasse Cemetery, but no trace of the grave remains.
The Galois memorial in the cemetery of Bourg-la-Reine.
Évariste Galois was buried in a common grave and
 the exact location is still unknown. *Wik

1896   Widely considered to be the real first accident, this occurred on May 30, 1896, during a “horseless wagon race” in New York City. Henry Wells lost control of his vehicle and crashed into a bicyclist named Ebeling Thomas. The bicyclist broke his leg, and the driver was arrested. If only there was a New York Defensive Driving course back then, a lot of chaos could have been avoided. However, as there were several other bicyclists arrested that day for the 1896 equivalent of speeding, perhaps a certain amount of chaos was just par for the course at that time.*Improv

1903 Minor planet 511 Davida Discovered 1903 May 30 by R. S. Dugan at Heidelberg. Named by the discoverer in honor of David P. Todd (1855-1939), professor of astronomy and director of the Amherst College Observatory (1881-1920). David Todd was the husband of Mabel Todd, who wrote books about solar eclipses. David has also a drawing of a painting of a solar eclipse in one of his books. *NSEC
511 Davidais is a large C-type asteroid. It is one of the largest asteroids; approximately tied for 7th place, to within measurement uncertainties, and the 5th or 6th most massive.
almost a decagon in this cross section

 In 1971, the U.S. Mars space probe Mariner 9 blasted off from Cape Kennedy, Florida. It carried cameras, infrared spectrometer and radiometer, ultraviolet spectrometer, radio occultation and celestial mechanics instruments. On 13 Nov 1971, it entered orbit as the first artificial satellite of Mars. After waiting for a month-long planet-wide dust storm to clear, it began compiling a global mosaic of high-quality images for 100% of the Martian surface. The photos showed gigantic volcanoes, a grand canyon stretching 4,800 kilometers (3,000 miles) and relics of ancient riverbeds that were carved in the landscape of this seemingly dry and dusty planet. It also sent the first closeup pictures of the two Martian moons, Phobos and Deimos. *TIS

2000 almost 200 years after the (now called) tangrams exploded across Europe, the nation of Finland issued a stamp panel designed as a tangram square.  Only four of the seven shapes were postage stamps.  Each tangram shape featured an idea of education and science.  One triangle showed a Sierpinski triangle.


1423 Georg von Peurbach (or Peuerbach) (May 30, 1423 in Peuerbach near Linz – April 8, 1461 in Vienna)  He worked on trigonometry astronomy, and was the teacher of Regiomontanus. *VFR
He promoted the use of Arabic numerals (introduced 250 years earlier in place of Roman numerals), especially in a table of sines he calculated with unprecedented accuracy. He died before this project was finished, and his pupil, Regiomontanus continued it until his own death. Peurbach was a follower of Ptolomy's astronomy. He insisted on the solid reality of the crystal spheres of the planets, going somewhat further than in Ptolomy's writings. He calculated tables of eclipses in Tabulae Ecclipsium,observed Halley's comet in Jun 1456 and the lunar eclipse of 3 Sep 1457 from a site near Vienna. Peurbach wrote on astronomy, his observations and devised astronomical instruments. *TIS  The Renaissance Mathematicus has a nice piece about Peurbach and his life... the kind of detail that comes from a passion for his subject.  Check it out. 
Georg von Peuerbach:
Theoricarum novarum
planetarum testus, Paris 1515

1790 John Herapath (30 May 1790 – 24 February 1868) was an English physicist who gave a partial account of the kinetic theory of gases in 1820 though it was neglected by the scientific community at the time.  An English physicist and journalist, he was self-educated in mathematics and science. An early interest investigating a theory of lunar motion (1811) led to considering the nature of heat and derived an equation relating the pressure and volume of a gas to the number, mass and speed of its particles. He published a preliminary notice of his theory in Annals of Philosophy in 1816. In his later career, he took an interest in steam-powered transportation, and became the editor (1836) of Railway Magazine and Annals of Science. He published in it his own scientific papers, including one giving a calculation (1932) on the speed of sound in air, which is the first known calculation of the mean molecular speed of a molecule from the kinetic theory of gases, though it is often Joule's later work that is recognized for this accomplishment.*TIS

1800 Karl Wilhelm Feuerbach (30 May 1800 – 12 March 1834) born in Jena, Germany. His mathematical fame rests entirely on three papers. Most important was this contribution to Euclidean geometry: The circle which passes through the feet of the altitudes of a triangle touches all four of the circles which are tangent to the three sides; it is internally tangent to the inscribed circle and externally tangent to each of the circles which touches the sides of the triangle externally. *VFR

The circle is also commonly called the Nine-point circle. It passes through the feet of the altitudes, the midpoints of the three sides, and the point half way between the orthocenter and the vertices.

1814 Eugene Charles Catalan (30 May 1814 – 14 February 1894) was a Belgian mathematician who defined the numbers called after him, while considering the solution of the problem of dissecting a polygon into triangles by means of non-intersecting diagonals. *SAU The Catalan numbers have a multitude of uses in combinatorics.  There are many counting problems in combinatorics whose solution is given by the Catalan numbers. The book Enumerative Combinatorics: Volume 2 by combinatorialist Richard P. Stanley contains a set of exercises which describe 66 different interpretations of the Catalan numbers. 
One of the ways is Cn is the number of different ways n + 1 factors can be completely parenthesized (or the number of ways of associating n applications of a binary operator, as in the matrix chain multiplication problem). For n = 3, for example, we have the following five different parenthesizations of four factors:
((ab)c)d     (a(bc))d     (ab)(cd)     a((bc)d)     a(b(cd))

The first Catalan numbers for n = 0, 1, 2, 3, ... are

1, 1, 2, 5, 14, 42, 132, 429
A convex polygon with n + 2 sides can be cut into triangles by connecting vertices with non-crossing line segments (a form of polygon triangulation). The number of triangles formed is n and the number of different ways that this can be achieved is Cn. The following hexagons illustrate the case n = 4:


1874  Beatrice Mabel Cave-Browne-Cave, MBE AFRAeS (30 May 1874 – 9 July 1947) was an English mathematician who undertook pioneering work in the mathematics of aeronautics.  She studied the mathematical tripos at Girton College Cambridge. She taught mathematics at a High School for eleven years before becoming an assistant to Karl Pearson in the Galton Laboratory of University College, London. She later became an assistant to Leonard Bairstow in the Department of Aeronautics at the Imperial College, London. She published two papers with Pearson and two with Bairstow.
Thumbnail of Beatrice Mabel Cave-Browne-Cave*SAU
In 1916, Cave began working for the government on airplane design. She carried out original research for the government on the mathematics of aeronautics which remained classified under the Official Secrets Act for fifty years. She examined the effects of loads on different areas of planes during flight, and her research helped to improve aircraft stability and propeller efficiency.[2] Some of her works are held in UCL archives which include correspondence from her time at the Galton Laboratory for work on bomb trajectories, terminal velocities, timber tests, and detonators, for the Admiralty Air Department and Ministry of Munitions. 

Cave was elected an associate fellow of the Royal Aeronautical Society in 1919 and awarded an MBE in 1920. She later worked as an assistant to Sir Leonard Bairstow, the Zaharoff Professor of Aviation at Imperial College, and she worked on fluid motion. In 1922, Cave's studies on aircraft oscillations were published in an Advisory Committee for Aeronautics technical report. Cave's name was also included alongside Bairstow in his 1922 and 1923 published reports on fluid mechanics.*Wik

1889 Paul Ernest Klopsteg (May 30, 1889 – April 28, 1991) was an American physicist. The asteroid 3520 Klopsteg was named after him and the yearly Klopsteg Memorial Award was founded in his memory.
He performed ballistics research during World War I at the US Army's Aberdeen Proving Grounds in Maryland. He applied his knowledge of ballistics to the study of archery.
He was director of research at Northwestern University Technical Institution. From 1951 through 1958 he was an associate director of the National Science Foundation and was president of the American Association for the Advancement of Science from 1958 through 1959.*Wik

1908 Hannes Olof Gösta Alfvén (30 May 1908 in Norrköping, Sweden; 2 April 1995 in Djursholm, Sweden) Alfvén developed the theory of magnetohydrodynamics (MHD), the branch of physics that helps astrophysicists understand sunspot formation and the magnetic field-plasma interactions (now called Alfvén waves in his honor) taking place in the outer regions of the Sun and other stars. For this pioneering work and its applications to many areas of plasma physics, he shared the 1970 Nobel Prize in physics. *DEBORAH TODD AND JOSEPH A. ANGELO, JR., A TO Z OF SCIENTISTS IN SPACE AND ASTRONOMY

1909 Norris Edwin Bradbury (May 30, 1909 – August 20, 1997), was an American physicist who served as director of the Los Alamos National Laboratory for 25 years from 1945 to 1970. He succeeded Robert Oppenheimer, who personally chose Bradbury for the position of director after working closely with him on the Manhattan Project during World War II. Bradbury was in charge of the final assembly of "the Gadget", detonated in July 1945 for the Trinity test. *Wik

1916  Joseph William Kennedy (May 30, 1916 – May 5, 1957) was an American chemist who was a co-discoverer of plutonium, along with Glenn T. Seaborg, Edwin McMillan and Arthur Wahl. During World War II he was head of the CM (Chemistry and Metallurgy) Division at the Manhattan Project's Los Alamos Laboratory, where he oversaw research onto the chemistry and metallurgy of uranium and plutonium. After the war, he was recruited as a professor at Washington University in St. Louis, where he is credited with transforming a university primarily concerned with undergraduate teaching into one that also boasts strong graduate and research programs. He died of cancer of the stomach at the age of 40.

1927 Joan Sylvia Lyttle Birman (born May 30, 1927, in New York City) is an American mathematician, specializing in low-dimensional topology. She has made contributions to the study of knots, 3-manifolds, mapping class groups of surfaces, geometric group theory, contact structures and dynamical systems. Birman is research professor emerita at Barnard College, Columbia University, where she has been since 1973.n 1974, Birman was selected as a Sloan Research Fellow by the Alfred P. Sloan Foundation. In 1987, she was selected by the Association for Women in Mathematics to be a Noether Lecturer; this lecture honors women who have made fundamental and sustained contributions to the mathematical sciences. In 1994, she was selected as a Guggenheim Foundation Fellow by the John Simon Guggenheim Memorial Foundation. In 1996, the Mathematical Association of America awarded Birman the Chauvenet Prize, "the highest award for mathematical expository writing" for her 1993 essay New Points of View in Knot Theory.

In 2003, Birman was elected to the European Academy of Sciences. In 2005, she won the New York City Mayor's Award for Excellence in Science and Technology.

Birman received an honorary doctorate from the Technion Israel Institute of Technology.
In 2012, Birman was elected to the American Academy of Arts and Sciences In 2013, she became a fellow of the American Mathematical Society in the inaugural class.

In 2013 the Association for Women in Mathematics established the Joan & Joseph Birman Research Prize in Topology and Geometry, first awarded in 2015.

In 2015, Birman was named an honorary member of the London Mathematical Society.
The Association for Women in Mathematics included her in the 2020 class of AWM Fellows for "her groundbreaking research connecting diverse fields, and for her award-winning expository writing; for continuously supporting women in mathematics as an active mentor and a research role model; and for sponsoring multiple prize initiatives for women".
In 2021, Birman was elected to the National Academy of Sciences.
She is included in a deck of playing cards featuring notable women mathematicians published by the Association of Women in Mathematics


1778 (François Marie Arouet) Voltaire (
21 November 1694 – 30 May 1778) was a French author who popularized Isaac Newton's work in France by arranging a translation of Principia Mathematica to which he added his own commentary (1737). The work of the translation was done by the marquise de Châtelet who was one of his mistresses, but Voltaire's commentary bridged the gap between non-scientists and Newton's ideas at a time in France when the pre-Newtonian views of Descartes were still prevalent. Although a philosopher, Voltaire advocated rational analysis. He died on the eve of the French Revolution.*TIS

1912 Wilbur Wright  (April 16, 1867 – May 30, 1912), American aviation pioneer, who with his brother Orville, invented the first powered airplane, Flyer, capable of sustained, controlled flight (17 Dec 1903). Orville made the first flight, airborn for 12-sec. Wilbur took the second flight, covering 853-ft (260-m) in 59 seconds. By 1905, they had improved the design, built and and made several long flights in Flyer III, which was the first fully practical airplane (1905), able to fly up to 38-min and travel 24 miles (39-km). Their Model A was produced in 1908, capable of flight for over two hours of flight. They sold considerable numbers, but European designers became strong competitors. After Wilbur died of typhoid in 1912, Orville sold his interest in the Wright Company in 1915 *TIS

1926 Vladimir Andreevich Steklov (9 January 1864 – 30 May 1926)  made many important contributions to applied mathematics. In addition to the work for his master's thesis and his doctoral thesis referred to above, he reduced problems to boundary value problems of Dirichlet type where Laplace's equation must be solved on a surface. He wrote General Theory of Fundamental Functions in which he examined expansions of functions as series in an infinite system of orthogonal eigenfunctions. In fact the term "Fundamental Functions", which is due to Poincaré, means eigenfunctions in today's terminology.
Steklov was not the first to examine series expansions in terms of infinite sets of orthogonal eigenfunctions, of course Fourier had examined a special case of this situation many years before. Steklov, however, produced many papers on this topic which led him to a general theory to replace the special cases examined by others. He studied a generalisation of Parseval's equality for Fourier series to his general setting showing this to be a fundamental property. In all his list of publications contains 154 items. *SAU

1943 Anderson McKendrick (September 8, 1876 - May 30, 1943) trained as a medical doctor in Glasgow and came to Edinburgh as Superintendent of the College of Physicians Laboratory. He made some significant mathematical contributions to biology. *SAU
McKendrick's career as a mathematical epidemiologist began in India. In 1911, McKendrick rediscovered the logistic equation and fit it to bacterial growth data. In 1912 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were James Oliver, Diarmid Noel Paton, Ralph Stockman and Cargill Gilston Knott. He served as the Society's Vice President 1933-36. In 1933 he was elected a member of the Aesculapian Club.

In 1914 he published a paper in which he gave equations for the pure birth process and a particular birth–death process. In 1924 he was elected a Fellow of the Royal College of Physicians of Edinburgh. After his return to Scotland he published more. His 1926 paper, 'Applications of mathematics to medical problems' was particularly impressive, including the widely used McKendrick–Von Foerster partial differential equation.

Some of this paper's other results for stochastic models of epidemics and population growth were rediscovered by William Feller in 1939. Feller remarks in his An Introduction to Probability Theory and Its Applications (3rd edition p. 450), "It is unfortunate that this remarkable paper passed practically unnoticed." In 1927 McKendrick began a collaboration with William Ogilvy Kermack (1898–1970) which produced a notable series of papers on the Kermack–McKendrick theory, a general theory of infectious disease transmission.

W. M. Hirsch gives this picture of the man: "McKendrick was a truly Christian gentleman, a tall and handsome man, brilliant in mind, kind and modest in person, a skilful counsellor and administrator who gave of himself and knew how to enable others."*Wik

1964 Leo Szilard (11 Feb 1898; 30 May 1964 at age 66) Hungarian-American physicist who, with Enrico Fermi, designed the first nuclear reactor that sustained nuclear chain reaction (2 Dec 1942). In 1933, Szilard had left Nazi Germany for England. The same year he conceived the neutron chain reaction. Moving to N.Y. City in 1938, he conducted fission experiments at Columbia University. Aware of the danger of nuclear fission in the hands of the German government, he persuaded Albert Einstein to write to President Roosevelt, urging him to commission American development of atomic weapons. In 1943, Major General Leslie Groves, leader of the Manhattan Project designing the atomic bomb, forced Szilard to sell his atomic energy patent rights to the U.S. government. *TIS Frederik Pohl , talks about Szilard's epiphany about chain reactions in Chasing Science (pg 25),
".. we know the exact spot where Leo Szilard got the idea that led to the atomic bomb. There isn't even a plaque to mark it, but it happened in 1938, while he was waiting for a traffic light to change on London's Southampton Row. Szilard had been remembering H. G. Well's old science-fiction novel about atomic power, The World Set Free and had been reading about the nuclear-fission experiment of Otto Hahn and Lise Meitner, and the lightbulb went on over his head."

1992 Antoni Zygmund (December 25, 1900 – May 30, 1992) Polish-born mathematician who created a major analysis research centre at Chicago, and recognized in 1986 for this with the National Medal for Science. In 1940, he escaped with his wife and son from German controlled Poland to the USA. He did much work in harmonic analysis, a statistical method for determining the amplitude and period of certain harmonic or wave components in a set of data with the aid of Fourier series. Such technique can be applied in various fields of science and technology, including natural phenomena such as sea tides. He also did major work in Fourier analysis and its application to partial differential equations. Zygmund's book Trigonometric Series (1935) is a classic, definitive work on the subject.

1921 Rosalyn Sussman Yalow (July 19, 1921 – May 30, 2011) was an American biophysicist who shared (with Andrew V. Schally and Roger Guillemin) the 1977 Nobel Prize for Physiology or Medicine, making her the second woman to win the Nobel Prize in medicine, “for the development of radioimmuno assays (RIA) of peptide hormone.” RIA brought about a revolution in biological and medical research. With her coworkers, she applied RIA to study of the physiology of the peptide hormones insulin, ACTH, growth hormone, and also to throw light upon the pathogenesis of diseases caused by abnormal secretion of these hormones. This was pioneering work that opened diabetes research in new directions. She has been called the “Madame Curie of the Bronx..” *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

1 comment:

Patrick said...

Hey. Today is day 151! Figured I would periodically give you a heads up about having the wrong day of the year. Take care!