## Wednesday 3 July 2024

### On This Day in Math - July 3

Music is the pleasure the human mind experiences from counting
without being aware that it is counting.

~Gottfried Leibniz

The 184th day of the year; 184 = 23 * 23 (concatenation of the first two primes).

The smallest number that can be written as q * pq + r * p r, where p, q and r are distinct primes (184 = 3 * 23 + 5 * 25). *Prime Curios

25^2-21^2 = 184, and the sum of three squares 12^2 + 6^2 + 2^2 and of four squares, 10^2 + 8^2+4^2 + 2^2

On a 5x5 lattice (square grid of dots) there are 184 paths from one corner to the opposite corner touching each lattice point exactly once.

The concatenation of 183 and 184, 183184 is a perfect square. There are no smaller numbers for which the concatenation of two consecutive numbers is square. (Students might seek the next such pair of numbers. They are small enough to be year dates)

EVENTS

1822 Charles Babbage described his ideas for a “difference engine” to the Royal Society. *VFR

1841, John Couch Adams decided to determine the position of an unknown planet by the irregularities it causes in the motion of Uranus. He entered in his journal; "Formed a design in the beginning of this week in investigating, as soon as possible after taking my degree, the irregularities in the motion of Uranus... in order to find out whether they may be attributed to the action of an undiscovered planet beyond it..." In Sep 1845 he gave James Challis, director of the Cambridge Observatory, accurate information on where the new planet, as yet unobserved, could be found; but unfortunately the planet (Neptune) was not recognized at Cambridge until much later, after its discovery at the Berlin Observatory on 23 Sep 1846. *TIS

Using predictions made by Urbain Le Verrier, Johann Galle discovered the planet in 1846. The planet is named after the Roman god of the sea, as suggested by Le Verrier.

It turned out that several astronomers, starting with Galileo Galilei in 1612, had observed Neptune too, but because of its slow motion relative to the background stars. did not recognize it as a planet.

 *NASA

-------------------------------------------------------------------------------------------------------------
1886 Karl Benz officially unveils the Benz Patent-Motorwagen, the first purpose-built automobile. *
the painter flynn

2011  Astronomers using the Hubble Space Telescope discovered a fourth moon orbiting the icy dwarf planet Pluto. The tiny, new satellite – temporarily designated P4 -- was uncovered in a Hubble survey searching for rings around the dwarf planet.

Two labeled images of the Pluto system taken by the Hubble Space Telescope's Wide Field Camera 3 ultraviolet visible instrument with newly discovered fourth moon P4 circled. The image on the left was taken on June 28, 2011. The image of the right was taken on July 3, 2011. Credit: NASA, ESA, and M. Showalter (SETI institute)

BIRTHS

1820 Ernest de Jonquières (3 July 1820 Carpentras, France – 12 Aug 1901 Mousans-Sartoux, France) was a French naval officer who discovered many results in geometry. After his introduction to advanced mathematics by Chasles it is not surprising that his main interests were geometry throughout his life. He made many contributions many of them extending the work of Poncelet and Chasles. An early work, the treatise Mélanges de géométrie pure (1856) contains: an amplifications of Chasles' ideas on the geometric properties of an infinitely small movement of a free body in space; a commentary on Chasles' work on conic sections; the principle of homographic correspondence; and constructions relating to curves of the third order. In a final section de Jonquières presented a French translation of Maclaurin's work on curves. *SAU

1849 Prosper-René Blondlot (3 July 1849 – 24 November 1930) was a French physicist, best remembered for his mistaken "discovery" of N rays, a phenomenon that subsequently proved to be illusory.
In order to demonstrate that a Kerr cell responds to an applied electric field in a few tens of microseconds, Blondlot, in collaboration with Ernest Bichat, adapted the rotating-mirror method that Léon Foucault had applied to measure the speed of light. He further developed the rotating mirror to measure the speed of electricity in a conductor, photographing the sparks emitted from two conductors, one 1.8 km longer than the other and measuring the relative displacement of their images. He thus established that the speed of electricity in a conductor is very close to that of light.
In 1891, he made the first measurement of the speed of radio waves, by measuring the wavelength using Lecher lines. He used 13 different frequencies between 10 and 30 MHz and obtained an average value of 297,600 km/s, which is within 1% of the current value for the speed of light. This was an important confirmation of James Clerk Maxwell's theory that light was an electromagnetic wave like radio waves.
In 1903, Blondlot announced that he had discovered N rays, a new species of radiation. The "discovery" attracted much attention over the following year until Robert W. Wood showed that the phenomena were purely subjective with no physical origin. The French Academy of Sciences awarded the Prix Leconte (₣50,000) for 1904 to Blondot, although they hedged on the reason, citing the totality of his work rather than the discovery of N-rays.
Little is known about Blondlot's later years. William Seabrook stated in his Wood biography Doctor Wood, that Blondlot went insane and died, supposedly as a result of the exposure of the N ray debacle: "This tragic exposure eventually led to Blondlot's madness and death." Using an almost identical wording this statement was repeated later by Martin Gardner, possibly without having investigated into the subject: "Wood's exposure led to Blondlot's madness and death." However, Blondlot continued to work as a university professor in Nancy until his early retirement in 1910. He died at the age of 81; at the time of the N-ray affair he was nearly 60 years old. *Wik

1866 Henry Frederick Baker FRS (3 July 1866 – 17 March 1956) was a British mathematician, working mainly in algebraic geometry, but also remembered for contributions to partial differential equations (related to what would become known as solitons), and Lie groups.
Baker was born in Cambridge, England and educated at The Perse School before winning a scholarship to St John's College, Cambridge in October 1884. Baker graduated as Senior Wrangler in 1887, bracketed with 3 others.
Baker was elected Fellow of St John's in 1888 where he remained for 68 years.
In June, 1898 he was elected a Fellow of the Royal Society. In 1911, he gave the presidential address to the London Mathematical Society.
In January 1914 he was appointed Lowndean Professor of Astronomy. *Wik
In the 1930s before the war Baker's graduate students would meet at what they called Professor Baker’s "Tea Party", who met once a week to discuss the areas of research in which we were all interested. It was to one of these meetings that a young Donald Coxeter brought his "Aunt Alice", the 69 year old Alicia Boole, to co-present on the subject of Polytopes in higher dimensions.

1908 Archibald James Macintyre HFRSE (3 July 1908 – 4 August 1967) was a British-born mathematician.

He was born in Sheffield on 3 July 1908, the second child of William Ewart Archibald Macintyre (b.1878) previously of Long Eaton, and his wife, Mary Beatrice Askew. His father was a schoolmaster in Sheffield and his mother was a former teacher.

Archibald was educated at the Central Secondary School in Sheffield (previously known as the High Storrs Grammar School). He left school in 1926 and won a place at Magdalene College, Cambridge studying a Mathematics Tripos under Arthur Stanley Ramsey. Fellow students included Donald Coxeter, Raymond Paley and Harold Davenport. He graduated BA as a Wrangler in 1929 then began research under Dr Edward Collingwood.

In 1930 he became an assistant lecturer in both applied maths and theoretical physics at Cambridge University. He received his doctorate (PhD) in 1933. In 1936 he accepted a post of lecturer at Aberdeen University. Here he stayed for many years, rising to senior lecturer. In 1947 he was elected an Honorary Fellow of the Royal Society of Edinburgh. His proposers were E. M. Wright, Ivor Etherington, Edward Thomas Copson, Edmund Taylor Whittaker and James Cossar.

In 1958 he moved to the University of Cincinnati in the United States, as a visiting professor of mathematics. He was recruited primarily as a reaction to Sputnik. America wanted to increase its role in the sciences and math. His wife stayed in Aberdeen, Scotland where she continued to teach mathematics at King's College. A year later he accepted a permanent position at the University of Cincinnati and sent for his wife who was also given a teaching position as a lecturer in mathematics. They formed a highly unusual husband-wife team.
He died in Cincinnati on 4 August 1967, eight years after his wife died of breast cancer

1910 Antoine Joseph Bernard Brunhes (3 July 1867 – 10 May 1910) was a French geophysicist known for his pioneering work in paleomagnetism, in particular, his 1906 discovery of geomagnetic reversal. The current period of normal polarity, Brunhes Chron, and the Brunhes–Matuyama reversal are named for him.

1897 Jesse Douglas (3 July 1897 – 7 September 1965) born in New York City. He did important work on Plateau’s problem, which asks for the minimal surface connecting a given boundary. For this work he received a Fields medal in 1936, the ﬁrst time that they were given. *VFR ..the Plateau problem... had first been posed by the Italian-French mathematician Joseph-Louis Lagrange in 1760. The Plateau problem is one of finding the surface with minimal area determined by a fixed boundary. Experiments (1849) by the Belgian physicist Joseph Plateau demonstrated that the minimal surface can be obtained by immersing a wire frame, representing the boundaries, into soapy water. Douglas developed what is now called the Douglas functional, so that by minimizing this functional he could prove the existence of the solution to the Plateau problem. Douglas later developed an interest in group theory.*TIS

1933 Frederick Justin Almgren,(July 3, 1933, Birmingham, Alabama–February 5, 1997, Princeton, New Jersey) Almost certainly Almgren's most impressive and important result was only published in 2000, three years after his death. Why was this? The paper was just too long to be accepted by any journal. Brian Cabell White explains the background in a review of the book published in 2000 containing the result:-
By the early 1970s, geometric analysts had made spectacular discoveries about the regularity of mass-minimizing hypersurfaces. (Mass is area counting multiplicity, so that if k sheets of a surface overlap, the overlap region is counted k times.) In particular, the singular set of an m-dimensional mass-minimizing hypersurface was known to have dimension at most m - 7. By contrast, for an m-dimensional mass-minimizing surface of codimension greater than one, the singular set was not even known to have m-measure 0. Around 1974, Almgren started on what would become his most massive project, culminating ten years later in a three-volume, 1700-page preprint containing a proof that the singular set not only has m-dimensional measure 0, but in fact has dimension at most (m - 2). This dimension is optimal, since by an earlier result of H Federer there are examples for which the dimension of the singular set is exactly (m - 2). ... Now, thanks to the efforts of editors Jean Taylor and Vladimir Scheffer, Almgren's three-volume, 1700-page typed preprint has been published as a single, attractively typeset volume of less than 1000 pages.*SAU

1933 William (Bill) Parry FRS (3 July 1934–20 August 2006) was an English mathematician. During his research career, he was highly active in the study of dynamical systems, and, in particular, ergodic theory, and made significant contributions to these fields. He is considered to have been at the forefront of the introduction of ergodic theory to the United Kingdom. He played a founding role in the study of subshifts of finite type, and his work on nilflows was highly regarded.*Wik

1945 Saharon Shelah (July 3, 1945 - ) is an Israeli mathematician. He is a professor of mathematics at the Hebrew University of Jerusalem and Rutgers University in New Jersey. Shelah is one of the most prolific contemporary mathematicians. As of 2009, he has published nearly 900 mathematical papers (together with over 200 co-authors).
His main interests lie in mathematical logic, model theory in particular, and in axiomatic set theory.  In model theory, he developed classification theory, which led him to a solution of Morley's problem. In set theory, he discovered the notion of proper forcing, an important tool in iterated forcing arguments. With PCF theory, he showed that in spite of the undecidability of the most basic questions of cardinal arithmetic (such as the continuum hypothesis), there are still highly nontrivial ZFC theorems about cardinal exponentiation. Shelah constructed a Jónsson group, an uncountable group for which every proper subgroup is countable. He showed that Whitehead's problem is independent of ZFC. He gave the first primitive recursive upper bound to van der Waerden's numbers V(C,N). He extended Arrow's impossibility theorem on voting systems. *Wik

DEATHS

1749 William Jones, FRS (1675 – 3 July 1749) was a Welsh mathematician, most noted for his proposal for the use of the symbol π (the Greek letter pi) to represent the ratio of the circumference of a circle to its diameter. He was a close friend of Sir Isaac Newton and Sir Edmund Halley. In November, 1711 he became a Fellow of the Royal Society, and was later its Vice-President.*Wik

 Jones Pi for C/d *Wik

1789 Jakob Bernoulli II died. *VFR    Born in Basel in 1759 (17 October), the son of Johann (II).  assistant to Daniel in experimental physics
He graduated in Jurisprudence in 1778 but also studied Maths and Physics. In 1782, he applied for Daniel's former chair but was unsuccessful.
He became secretary to an imperial representative in Venice
In 1786 he went to Petersburg, to the Academy of Science (Fuss recommended him to Dashkoff) and in 1788 became ordentlich academy member for mathematics.
He married one of Euler's granddaughters, Charlotte.
At thirty years of age, he drowned in the Neva.  *Brian Daugherty
In St Petersburg he began to write important works on mathematical physics which he presented to the St Petersburg Academy of Sciences. These treatises were on elasticity, hydrostatics and ballistics.

Despite the rather harsh climate, the city of St Petersburg had great attractions for Jacob(II) Bernoulli since his uncle Daniel Bernoulli had worked there with Euler. In fact Jacob(II) married a granddaughter of Euler in St Petersburg but, tragically, the city was to lead to his death.

St Petersburg is located on the delta of the Neva River, at the head of the Gulf of Finland. St Petersburg, built on 42 islands in the Neva River, is a city of waterways and bridges and because of this it is called the "Venice of the North." Bernoulli drowned, while still only 29 years of age, in the Neva River while he was swimming.

1970 Samuel Beatty (Aug 21, 1881– 3 Jul, 1970)  was a Canadian mathematician who was the first person to receive a PhD in mathematics from a Canadian university.
He entered the University of Toronto in 1903 as an undergraduate. He was to spend the rest of his life studying there and working for the University. After obtaining his undergraduate degree from Toronto, Beatty went on the undertake research for a Ph.D. under Fields's supervision. When Beatty was awarded a doctorate in 1915 he became the first to obtain such a degree from a Canadian university. In fact Beatty was the only student who Fields supervised for a doctorate.

Beatty was appointed as a Lecturer at the University of Toronto after studying for his doctorate. When he was appointed, Alfred Baker was his Head of the Mathematics Department, but in 1918 Baker retired and A T DeLury, who had taught Beatty when he was an undergraduate, became Head. Beatty was promoted to Professor, then in 1934 became Head of the Mathematics Department. In 1936, in addition to his role has Head of the Mathematics Department, he was appointed Dean of the Faculty of Arts and, three years later became a founding member of the Committee of Teaching Staff.
He retired from the role of Dean in 1952 and in the following year was elected Chancellor of the University. He held this position until 1959. First let us quote an episode relating to his time as Dean:-
Dean Beatty is remembered for the enormous support he gave to his students, and he earned their deepest appreciation as a result. One of his students, Walter Kohn, who won the 1998 Nobel Prize in Chemistry for his development of the density-functional theory, expressed heartfelt appreciation to the Dean who in 1942 helped Kohn to enrol in the Mathematics Department at the University. Kohn, a young chemist of enormous potential, could not gain access to the chemistry buildings during the war because of his German nationality, and Dean Beatty was instrumental in helping him to continue his studies.

1991 Ernst Witt (June 26, 1911-July 3, 1991) was a German mathematician born on the island of Als (German: Alsen). Shortly after his birth, he and his parents moved to China, and he did not return to Europe until he was nine.
Witt's work was mainly concerned with the theory of quadratic forms and related subjects such as algebraic function fields.
Witt's work has been highly influential. His invention of the Witt vectors clarifies and generalizes the structure of the p-adic numbers. It has become fundamental to p-adic Hodge theory.

Witt was the founder of the theory of quadratic forms over an arbitrary field. He proved several of the key results, including the Witt cancellation theorem. He defined the Witt ring of all quadratic forms over a field, now a central object in the theory.

The Poincaré–Birkhoff–Witt theorem is basic to the study of Lie algebras. In algebraic geometry, the Hasse–Witt matrix of an algebraic curve over a finite field determines the cyclic étale coverings of degree p of a curve in characteristic p.

In the 1970s, Witt claimed that in 1940 he had discovered what would eventually be named the "Leech lattice" many years before John Leech discovered it in 1965, but Witt did not publish his discovery and the details of exactly what he did are unclear.*Wik

1999 Pelageya Yakovlevna Polubarinova-Kochina (13 May 1899[O.S.] – 3 July 1999) was a Soviet and Russian applied mathematician, known for her work on fluid mechanics and hydrodynamics, particularly, the application of Fuchsian equations [ A linear differential equation in which every singular point, including the point at infinity, is a regular singularity], as well as in the history of mathematics. She was elected a corresponding member of the Academy of Sciences of the Soviet Union in 1946 and full member (academician) in 1958.
She studied at a women's high school in Saint Petersburg and went on to Petrograd University (after the Russian Revolution). After her father died in 1918, she started working at the laboratory of geophysics under the supervision of Alexander Friedmann. There she met Nikolai Kochin; they were married in 1925 and had two daughters. The two taught at Petrograd University until 1934, when they moved to Moscow, where Nikolai Kochin took a teaching position at the Moscow University. In Moscow, Polubarinova-Kochina did research at the Steklov Institute until World War II, when she and their daughters were evacuated to Kazan while Kochin stayed in Moscow to work on aiding the military effort. He died before the war was over.

After the war, she edited his lectures and continued to teach applied mathematics. She was later head of the department of theoretical mechanics at the University of Novosibirsk and director of the department of applied hydrodynamics at the Hydrodynamics Institute. She was one of the founders of the Siberian Branch of the Russian Academy of Sciences (then the Academy of Sciences of the Soviet Union) at Novosibirsk.

She was awarded the Stalin Prize in 1946, was made a Hero of Socialist Labour in 1969 and received the Order of Friendship of Peoples in 1979. She died in 1999, a few months after her 100th birthday, and shortly after publishing her last scientific article.*Wik

2022 Robert Floyd Curl Jr. (August 23, 1933 – July 3, 2022) American chemist who with Richard E. Smalley and Sir Harold W. Kroto discovered the first fullerene, a spherical cluster of carbon atoms, in 1985. The discovery opened a new branch of chemistry, and all three men were awarded the 1996 Nobel Prize for Chemistry for their work. In Sep 1985 Curl met with Kroto of the University of Sussex, Eng., and Smalley, a colleague at Rice, and, in 11 days of research, they discovered fullerenes. They announced their findings to the public in the 14 Nov 1985, issue of the journal Nature.*TIS

Born in Alice, Texas, United States, Curl was the son of a Methodist minister. Due to his father's missionary work, his family moved several times within southern and southwestern Texas, and the elder Curl was involved in starting the San Antonio Medical Center's Methodist Hospital.[Curl attributes his interest in chemistry to a chemistry set he received as a nine-year-old, recalling that he ruined the finish on his mother's porcelain stove when nitric acid boiled over onto it.

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