Thursday 2 May 2024

On This Day in Math - May 2


We call a thing big or little
with reference to what it is wont to be, 
as we speak of a small elephant
or a big rat.

D'Arcy Thompson, "On Growth and Form"

The 122nd day of the year; there are 122 different ways to partition the number 24 into distinct parts.  Euler showed that this is the same as the number of ways to partition a number into odd parts.

122 ends in the digit two when written in base 3, 4, 5, 6, 8, 10, 12, 15, and 20.  How unusual is that?

122 squared minus each of its prime factors squared is also prime
and 122 is the smallest sum of two non-consecutive factorials of distinct primes (2! + 5!) *Prime Curios

Not sure how unusual this is, but there are no twin primes between 121^2 and 122^2?  There is no larger number which has this property.

122 Added to its reverse (221) it gives a palindrome cube (343 = 73).

*ExpertSays  Also 122² is the only known sum for power 4 and 5 122² =11⁴+3⁵


On May 2  in 1736, an expedition set out from Dunkirk to travel to Lapland to measure the length of a degree along the meridian. It was headed by Maupertuis and included the scientists Clairaut and Camus.


1775 Benjamin Franklin completed the first scientific study of the Gulf Stream. His observations began in 1769 when as deputy postmaster of the British Colonies he found ships took two weeks longer to bring mail from England than was required in the opposite direction. Thus, Franklin became the first to chart the Gulf Stream.He described the Gulf Stream as a river of warm water and mapped it as flowing north from the West Indies, along the East Coast of North America and east across the Atlantic Ocean to Europe. *TIS

In 1800, English chemist William Nicholson was the first to produce a chemical reaction by electricity. He had been working with Anthony Carlisle, a London surgeon, experimenting with Allesandro Volta's voltaic pile. The new effect was discovered when wires from the poles of the battery being used came into contact with water and bubbles of gas were released as current flowed through the water. Closer examination of the electrolysis showed oxygen was released at the (positive) anode, and hydrogen appeared at the cathode. Electricity had separated the molecules of water. Further, the effect of the amount of hydrogen and oxygen set free by the current was proportional to the amount of current used.*TIS
In 1785 a Dutch scientist named Martin van Marum had created an electrostatic generator that he used to reduce tin, zinc and antimony from their salts using a process later known as electrolysis. Though he unknowingly produced electrolysis, it was not until 1800 when William Nicholson and Anthony Carlisle discovered how electrolysis works.
The word "electrolysis" was introduced by Michael Faraday in 1834, using the Greek words ἤλεκτρον [ɛ̌ːlektron] "amber", which since the 17th century was associated with electrical phenomena, and λύσις [lýsis] meaning "dissolution". Nevertheless, electrolysis, as a tool to study chemical reactions and obtain pure elements, precedes the coinage of the term and formal description by Faraday.*Wik


1880 The first commercial order of an Edison Lighting system was installed on the newly launched Steamship Columbia. The dynamo and lights were installed by Edison Engineers and first lighting was on May 2, 1880. The event was featured in the May issue of Scientific American. John Roach and Sons had built the ship in their Chester, Pennsylvania ship works and launched it on Feb 24, 1880. *The History of the American Bureau of Shipping.

In his letter to Science dated May 2, 1889, which was quite brief, FitzGerald proposed that the best way to explain the null result of the Michelson-Morley experiment was to assume that the length of an object was not a constant, but that objects moving through the ether with a velocity v were contracted by a factor of v^2/c^2, where c is the speed of light. *Linda Hall Org

*Linda Hall Org

1983 Microsoft Introduces 2-button Mouse:
Microsoft Corp. announced the two-button Microsoft Mouse, which it introduced to go along with its new Microsoft Word processor. Microsoft built about 100,000 of these fairly primitive units for use with IBM and IBM-compatible personal computers but sold only 5,000 before finding success in a 1985 version that featured, among other improvements, near-silent operation on all surfaces.*CHM
In ensuing years, as mice made their way to personal computers, there was something of a battle waged between proponents of 2-button and 3-button mice, with Logitech favoring the 3-button variety.
 The mouse featured two green buttons and is available by itself or will later be bundled with the new Microsoft Word software, which Microsoft would release in September. Because of the green buttons, the mouse was nicknamed the “Green-Eyed Mouse”, which may have been a fitting name given it’s similarity to the Shakesperian phrase “green-eyed monster” to describe jealously. It was no secret Bill Gates was very envious of what Apple was creating with the Lisa and later Macintosh computers and their mouse-driven interfaces. Microsoft will manufacture nearly one hundred thousand units of their first mouse, but will only sell five thousand before introducing a second, more popular version in 1985.

Microsoft would go on to create a very successful line of mice and other computing peripherals over the years, but almost ironically Microsoft announced in April of 2023, nearly 40 years later, that they would end the production of Microsoft-branded peripherals and focus on their Surface-branded peripherals. This came months after Microsoft announced a 30% year-over-year drop in revenue from devices, cut 10,000 jobs, and announced “changes to their hardware portfolio”. *This Day in Tech History


1588 Etienne Pascal (Clermont, May 2, 1588 - Paris, September 24, 1651), for whom the limacon of Pascal was named. He was the father of Blaise Pascal. The limacon was named by another Frenchman Gilles-Personne Roberval in 1650 when he used it as an example of his methods of drawing tangents
i.e. differentiation.
The name "limacon" comes from the Latin limax meaning 'a snail'. Étienne Pascal corresponded with Mersenne whose house was a meeting place for famous geometers including Roberval.
Dürer should really be given the credit for discovering the curve since he gave a method for drawing the limacon, although he did not call it a limacon, in Underweysung der Messungpublished in 1525. *SAU [Etienne Pascal was one of the "nine lovers of literature established a regular meeting. In 1635, Richelieu organized them into an Académie Libre or ACADÉMIE FRANÇAISE." This was the forerunner of the ACADÉMIE DES SCIENCES. pb]

1601 Athanasius Kircher (2 May 1601; 28 Nov 1680 at age 79) German Jesuit priest and scholar, sometimes called the last Renaissance man. Kircher's prodigious research activity spanned a variety of disciplines including geography, astronomy, physics, mathematics, language, medicine, and music. He made an early, though unsuccessful attempt to decipher hieroglyphics of the Coptic language. During the pursuit of experimental knowledge, he once had himself lowered into the crater of Vesuvius to observe its features soon after an eruption. He made one of the first natural history collections. Kircher studied animal luminescence, writing two chapters of his book Ars Magna Lucis et Umbrae to bioluminescence, and debunked the idea that that an extract made from fireflies could be used to light houses.*TIS

from his 1665 book (Mundus Subterraneus)
*Linda Hall Org 

1773 Henrik Steffens (2 May 1773–13 February 1845), was a Norwegian-born Danish philosopher, scientist, and poet. He was one of the so-called "Philosophers of Nature", a friend and adherent of Schelling and of Schleiermacher. More than either of these two thinkers he was acquainted with the discoveries of modern science, and was thus able to correct or modify the highly imaginative speculations of Schelling. He held that, throughout the scheme of nature and intellectual life, the main principle is Individualisation. As organisms rise higher in the scale of development, the sharper and more distinct become their outlines, the more definite their individualities. This principle he endeavoured to deduce from his knowledge of geology, in contrast to Lorenz Oken, who developed the same theory on biological grounds. His influence was considerable, and both Schelling and Schleiermacher modified their theories in deference to his scientific deductions.*Wik

1860 Sir D'Arcy Wentworth Thompson (2 May 1860; 21 Jun 1948 at age 88)
Scottish zoologist and classical scholar, who is noted for his influential work On Growth and Form (1917, new ed. 1942). It is a profound consideration of the shapes of living things, starting from the simple premise that “everything is the way it is because it got that way.” Hence one must study not only finished forms, but also the forces that moulded them: “the form of an object is a ‘diagram of forces’, in this sense, at least, that from it we can judge of or deduce the forces that are acting or have acted upon it.”' One of his great themes is the tremendous light cast on living things by using mathematics to describe their shapes and fairly simple physics and chemistry to explain them..*TIS
He graduated from Cambridge University in Zoology and was appointed Professor of Biology at Dundee and later Professor of Natural History at St Andrews. He combined skills in a way that made him unique. He was a Greek scholar, a naturalist and a mathematician. He was the first biomathematician. He became an honorary member of the EMS in 1933.*SAU [The University of Dundee and the University of St Andrews joined to host a celebration of Thompson's sesquicentennial birth year (2010) with a series of events. They have a photo gallery still available at the time of this writing. ]
He was the first biomathematician. His book On Growth and Form had a great influence on both biologists and mathematicians.

Graphical deformation producing an assortment of crab carapaces, left, and two copepods, right, from Thompson, On Growth and Form, 1945 (Linda Hall Library)
Royal Society of Edinburgh portrait


1868 Robert W. Wood (2 May 1868; 11 Aug 1955 at age 87) was an American physicist who photographed the reflection of sound waves in air, and investigated the physiological effects of high-frequency sound waves. The zone plate he devised could replace the objective lens of a telescope. He invented an improved diffraction grating, did research in spectroscopy, and extended the technique of Raman spectroscopy (a method to study matter using the light scattered by it.) He made photographs showing both infrared and ultraviolet radiation and was the first to photograph ultraviolet fluorescence. Wood was the first to observe the phenomenon of field emission in which charged particles are emitted from conductors in an electric field. *TIS
According to a post at Greg Ross' Futility Closet:
"How to clean a 40-foot spectrograph, from R.W. Wood’s Researches in Physical Optics, 1913:
The long tube was made by nailing eight-inch boards together, and was painted black on the inside. Some trouble was given by spiders, which built their webs at intervals along the tube, a difficulty which I surmounted by sending our pussy-cat through it, subsequently destroying the spiders with poisonous fumes.
This was the least of Wood’s exploits. Walter Bruno Gratzer, in Eurekas and Euphorias, writes that the physicist “would alarm the citizens of Baltimore by spitting into puddles on wet days, while surreptitiously dropping in a lump of metallic sodium, which would explode in a jet of yellow flame.”

Wood also proposed and built a reflection telescope with the parabolic mirror formed by the surface of a rotating pool of mercury and debunked the "N-rays" mistakenly "discovered" by Blondlot.  HT to Alexandre Zagoskin



1901 Edouard Zeckendorf
 (2 May 1901 - 16 May 1983) was a Belgian doctor, army officer and mathematician. In mathematics, he is best known for his work on Fibonacci numbers and in particular for proving Zeckendorf's theorem. Zeckendorf's theorem states that every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers.
Zeckendorf was born in Liège in 1901. He was the son of a Dutch dentist. In 1925, Zeckendorf graduated as a medical doctor from the University of Liège and joined the Belgian Army medical corps. When Germany invaded Belgium in 1940, Zeckendorf was taken prisoner and remained a prisoner of war until 1945. During this period, he provided medical care to other allied POWs. *Wik

1921 Walter Rudin (May 2, 1921 – May 20, 2010) was an Austrian-American mathematician and professor of Mathematics at the University of Wisconsin–Madison. 

In addition to his contributions to complex and harmonic analysis, Rudin was known for his mathematical analysis textbooks: Principles of Mathematical Analysis, Real and Complex Analysis, and Functional Analysis. Rudin wrote Principles of Mathematical Analysis only two years after obtaining his Ph.D. from Duke University, while he was a C. L. E. Moore Instructor at MIT. Principles, acclaimed for its elegance and clarity, has since become a standard textbook for introductory real analysis courses in the United States.

Rudin's analysis textbooks have also been influential in mathematical education worldwide, having been translated into 13 languages, including Russian, Chinese, and Spanish

They are so common and long lived on Campuses that they have their own nicknames; "Baby Rudin" is used for his  Principles of Mathematical Analysis, an undergraduate text.   "Big Rudin" is  for his Real and Complex Analysis, a graduate level text.

In 1970 Rudin was an Invited Speaker at the International Congress of Mathematicians in Nice. He was awarded the Leroy P. Steele Prize for Mathematical Exposition in 1993 for authorship of the now classic analysis texts, Principles of Mathematical Analysis and Real and Complex Analysis. He received an honorary degree from the University of Vienna in 2006.

In 1953, he married fellow mathematician Mary Ellen Estill, known for her work in set-theoretic topology.  She was appointed as Professor of Mathematics at the University of Wisconsin in 1971.  The two resided in Madison, Wisconsin, in the eponymous Walter Rudin House, a home designed by architect Frank Lloyd Wright. They had four children. *Wik

1928 Jacques-Louis Lions (2 May 1928 in Grasse, Alpes-Maritimes, France - 17 May 2001 in Paris, France) French mathematician who made contributions to the theory of partial differential equations and to stochastic control, among other areas. He received the SIAM's John Von Neumann prize in 1986. *Wik

1939 Sumio Iijima (May 2, 1939, )is a Japanese physicist, often cited as the discoverer of carbon nanotubes. Although carbon nanotubes had been observed prior to his "discovery"1, Iijima's 1991 paper generated unprecedented interest in the carbon nanostructures and has since fueled intense research in the area of nanotechnology. For this and other work Sumio Iijima was awarded, together with Louis Brus, the inaugural Kavli Prize for Nanoscience in 2008. *Wik (Quotes of Sumio Iijma by Arjen Dijksman)


1519 Leonardo da Vinci (15 Apr 1452, 2 May 1519 at age 67) Italian painter, draftsman, sculptor, architect, and engineer. Da Vinci was a great engineer and inventor who designed buildings, bridges, canals, forts and war machines. He kept huge notebooks sketching his ideas. Among these, he was fascinated by birds and flying and his sketches include such fantastic designs as flying machines. These drawings demonstrate a genius for mechanical invention and insight into scientific inquiry, truly centuries ahead of their time. His greater fame lies in being one of the greatest painters of all times, best known for such paintings as the Mona Lisa and The Last Supper.*TIS

1925 Johann Palisa (6 Dec 1848, 2 May 1925 at age 76)Austrian astronomer who was a prolific discoverer of asteroids, 122 in all, beginning with Asteroid 136 Austria (on 18 Mar 1874, using a 6" refractor) to Asteroid 1073 Gellivara in 1923 - all by visual observation, without the aid of photography. In 1883, he joined the expedition of the French academy to observe the total solar eclipse on May 6 of that year. During the eclipse, he searched for the putative planet Vulcan, which was supposed to circle the sun within the orbit of Mercury. In addition to observing the eclipse, Palisa collected insects for the Natural History Museum in Vienna. He also prepared two catalogs containing the positions of almost 4,700 stars. He remains the most successful visual discoverer in the history of minor planet research.*TIS

1967 Robert Daniel Carmichael (1 March 1879 in Goodwater, Coosa County, Alabama, USA - 2 May 1967 in Merriam, Northeast Johnson County, Kansas, USA) Carmichael is known for his mathematical research in what are now called the Carmichael numbers (numbers satisfying properties of primes described by Fermat's Little Theorem although they are not primes- see below), Carmichael's theorem, and the Carmichael function, all significant in number theory and in the study of the prime numbers. Carmichael might have been the first to describe the Steiner system S(5,8,24), a structure often attributed to Ernst Witt. While at Indiana University Carmichael was involved with special theory of relativity. *Wik Fermat had proved that if n is prime then x^n-1 = 1 mod n for every x coprime to n. A 'Carmichael number' is a non-prime n satisfying this condition for any x coprime to n. It was given this name since Carmichael discovered the first such number, 561, in 1910 (there are several base ten Carmichael numbers below 561 for the interested student to search for). For many years it was an open problem as to whether there were infinitely many Carmichael numbers, but this was settled in 1994 by W R Alford, A Granville, and C Pomerance in their paper There are infinitely many Carmichael numbers. *SAU

1981 David Wechsler (12 Jan 1896, 2 May 1981 at age 85) U.S. psychologist and inventor of several widely used intelligence tests for adults and children. During WW I, while assisting Edwin Garrigues Boring (1886-1968) in testing army recruits, Wechsler realized the inadequacies of the Army Alpha Tests (designed to measure abilities of conscripts and match them to suitable military jobs). He concluded that academically defined "intelligence" did not apply to "real life" situations. After leaving the military and more years of research, he developed the Wechsler Adult Intelligence Scale, and introduced deviation scores in intelligence tests. He developed the Wechsler Memory Scale in 1945, Wechsler Intelligence Scale for Children (1949), and Wechsler Preschool and Primary Scale of Intelligence (1967). *TIS

1982 Salomon Bochner (20 Aug 1899, 2 May 1982 at age 82) Galician-born American mathematician and educator responsible for the development of the Bochner theorem of positive-definite functions and the Bochner integral.*TIS
In 1925 he started work in the area of almost periodic functions, simplifying the approach of Harald Bohr by use of compactness and approximate identity arguments. In 1933 he defined the Bochner integral, as it is now called, for vector-valued functions. Bochner's theorem on Fourier transforms appeared in a 1932 book. His techniques came into their own as Pontryagin duality and then the representation theory of locally compact groups developed in the following years.
Subsequently he worked on multiple Fourier series, posing the question of the Bochner–Riesz means. This led to results on how the Fourier transform on Euclidean space behaves under rotations.
In differential geometry, Bochner's formula on curvature from 1946 was most influential. Joint work with Kentaro Yano (1912–1993) led to the 1953 book Curvature and Betti Numbers. It had broad consequences, for the Kodaira vanishing theory, representation theory, and spin manifolds.*WIK

For a torus, the first Betti number is b1 = 2 , which can be intuitively thought of as the number of circular "holes"

2004 John Hammersley (21 March 1920-2 May 2004) British mathematician best-known for his foundational work in the theory of self-avoiding walks and percolation theory. *Wik when introduced to guests at Trinity College, Oxford, he would say he did difficult sums". He believed passionately in the importance of mathematics with strong links to real-life situations, and in a system of mathematical education in which the solution of problems takes precedence over the generation of theory. He will be remembered for his work on percolation theory, subadditive stochastic processes, self-avoiding walks, and Monte Carlo methods, and, by those who knew him, for his intellectual integrity and his ability to inspire and to challenge. Quite apart from his extensive research achievements, for which he earned a reputation as an outstanding problem-solver, he was a leader in the movement of the 1950s and 1960s to re-think the content of school mathematics syllabuses. (Center for Mathematical Sciences, Cambridge)
During his lifetime, great changes were made in the teaching of mathematics at schools, a matter on which he held strong and opposed, but by no means reactionary, views. He published widely and gave many lectures critical of soft theory at the expense of problem-solving and beauty in mathematics. His best known work, `On the enfeeblement of mathematical skills by `Modern Mathematics' and by similar soft intellectual trash in schools and universities' (published in the Bulletin of the Institute of Mathematics and its Applications, 1968), is now regarded as a force for good at a crossroads of mathematics education. (from his Independent obituary)

2010 Clive W. Kilmister (1924 – May 2, 2010) was a British Mathematician who specialized in the mathematical foundations of Physics, especially Quantum Mechanics and Relativity and published widely in these fields (see References). He was one of the discoverers of the Combinatorial Hierarchy, along with A. F. Parker-Rhodes, E. W. Bastin, and J.C.Amson. He was strongly influenced by astrophysicist Arthur Eddington and was well known for his elaboration and elucidation of Eddington’s fundamental theory.
Kilmister attended Queen Mary College London for both his under- and postgraduate degrees. His PhD was supervised by cosmologist George McVittie (himself a student of Eddington), and his dissertation was entitled ‘’The Use of Quaternions in Wave-Tensor Calculus’’ which related to Eddington’s work. Kilmister received his doctoral degree in 1950. His own students included Brian Tupper (1959, King's College London, now professor emeritus of general relativity and cosmology at University of New Brunswick Fredericton [2]), Samuel Edgar (1977, University of London), and Tony Crilly (reader in mathematical sciences at Middlesex University and author of The Big Questions: Mathematics (1981).
Kilmister was elected as a member of the London Mathematical Society during his doctoral studies (March 17, 1949). Upon graduation, he began his career as an Assistant Lecturer in the Mathematics Department of King’s College in 1950. The entirety of his academic career was spent at King’s. In 1954, Kilmister founded the King’s Gravitational Theory Group, in concert with Hermann Bondi and Felix Pirani, which focused on Einstein’s theory of general relativity. At retirement, Kilmister was both a Professor of Mathematics and Head of the King’s College Mathematics Department.
He was Gresham Professor of Geometry, 1972-88. *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

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