## Wednesday 5 June 2024

### On This Day in Math - June 5

If your ideas are any good,
you'll have to ram them down people's throats.
~Howard Aiken

The 156th day of the year; 156 is the number of graphs with six vertices. *What's So Special About This Number.

$( \pi(1)+\pi(5)+\pi(6)) * (p_1 + p_5 + p_6) = 156$. 156 is the smallest number for which this is true, and the only even number for which it is true. (The symbols $\pi(n)$ and $p_n$ represent the number of primes less than or equal to n, and the nth prime respectively)

The total number of clock chimes in a 24 hour period is 156.

156 is evenly divisible by 12, the sum of its digits. Numbers which are divisible by the sum of their digits are sometimes called Niven Numbers and often called Harshad (Joy-giver) numbers..

Harshad numbers were defined by D. R. Kaprekar (in 1955), a mathematician from India. The word "harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver.

According to an article in the Journal of Recreational Mathematics the origin of the name is as follows. In 1977, Ivan Niven, a famous number theorist presented a talk at a conference in which he mentioned integers which are twice the sum of their digits. Then in an article by Kennedy appearing in 1982, and in honor of Niven, he christened numbers which are divisible by their digital sum “Niven numbers.” One might try to find the smallest strings of consecutive Niven Numbers with more than a single digit. *http://trottermath.net/niven-numbers/

I wonder about the relative order of the classes of numbers which are n times their digit sum for various n. (48 is 4 times its digit sum, 84 is 7 times its digit sum, and 156 is 13 times its digit sum..)

And being divisible by 12 reminds me that 156 is the 6th dodecagonal number.

EVENTS

1661 Newton admitted to Trinity College.  He was admitted as a "sizar", which meant he earned part of the cost of his education by doing menial chores.  His mother was quite wealthy enough to pay his tuition, but was unsure about his prospects at college since he seemed to be such a poor farmer. Mama and Junior seemed to have an unsteady relationship. He once admitted to his diary in a list of sins, "Threatening my father and mother Smith to burn them and the house over them."

1828 The final meeting of the Board of Longitude in Greenwich. This was the 243rd meeting of the Board since it's creation in 1714. John Barrow, Second Secretary of the Admiralty chaired the meeting. On July 15th the Board was dissolved by Parliament.

1833 Ada Lovelace ﬁrst meets Charles Babbage at the home of Mary Sommerville. She is known to have assisted Charles Babbage in the design of an "analytical engine", an early mechanical computing device. She is often credited with writing the first computer program. (many historians of computing disagree with this.  It depends somewhat on your definition of the term. )
Ada's mother, Lady Byron, had intentionally schooled Ada in the Sciences and Mathematics to counteract the "poetic tendencies" she might have inherited from her father. Ada knew Mary Somerville and Augustus de Morgan socially and received some math instruction from both. She died of cancer in the womb in November of 1852, only 36 years of age, and was buried beside Lord Byron, the father she never knew, in the parish church of St. Mary Magdalene, Hucknall in the UK.
In 1980, 165th years after Ada's birth, the US Defense Department announced a powerful new computer language. They named it Ada in honour of the Countess of Lovelace's important role in the history of computing. It may be of interest to students of mathematics and computer science that Ada Lovelace husband,also named William, was the Baron of Ockham (ancestor of 14th century William of Occam, for whom Occam’s Razor is named) in the 19th century.

1873 The term “radian” ﬁrst appeared in print. Some suggest it may have been intended as an abbreviation for "RADIus ANgle".
Here is a quote from Cajori's History of Mathematical Notations, vol 2 (1929) as provided by Julio Cabellion to the Historia-Matematica Newsgroup:
"An isolated matter of interest is the origin of the term 'radian', used with trigonometric functions. It first appeared in print on June 5, 1873, in examination questions set by James Thomson at Queen's College, Belfast. James Thomson was a brother of Lord Kelvin. He used the term as early as 1871, while in 1869 Thomas Muir, then of St. Andrew's University, hesitated between 'rad', 'radial' and 'radian'. In 1874, T. Muir adopted 'radian' after a consultation with James Thomson.+" (+) _Nature_, Vol. 83, pp. 156, 217, 459, 460.
The concept of a radian measure, as opposed to the degree of an angle, but not the term, should probably be credited to Roger Cotes, although it appeared as early as around 1400 by the Persian mathematician al-Khashi. According to a recent post to a math history newsgroup by Bob Stein; "He (Cotes) then calculated this as approximately 57.295 degrees. He had the radian in everything but name, and he recognized its naturalness as a unit of angular measure."

 *Wik

In 1878, liquid air obtained at a temperature of -192ºC was exhibited by Professor James Dewar at the Royal Institution, London. His work followed the small-scale production of liquid air by Raoul Pictet of Geneva (Dec 1877) and Cailletet of Paris (Jan 1878). In March 1893, Dewar produced solid air. He gave six well-illustrated Christmas Lectures on “Air: gaseous and liquid” at the Royal Institution bewteen  28 Dec 1893 and 9 Jan 1894. (Some of the air in the room was liquified in the presence of the audience, and remained so for some time, when enclosed in a vacuum jacket.) He demonstrated several physical properties of liquid air, and produced solid air at the Friday 19 Jan 1894 meeting of the Royal Institution. *Tis

1907 On June 5, 1907, African American jockey James Lee set a record that has never been beaten when he won the entire six-race card at Churchill Downs.

1929 The US Post Office issued a 2 cent stamp commemorating the Golden Jubilee of Edison's electric Lamp. On Dec 31, 1879 Edison gave the first public demonstration of his new incandescent lamp when he lit up a street in Menlo Park, New Jersey. The Pennsylvania Railroad Company ran special trains to Menlo Park on the day of the demonstration in response to public enthusiasm over the event.

Although the first incandescent lamp had been produced 40 years earlier, no inventor had been able to come up with a practical design until Edison embraced the challenge in the late 1870s. His patent would be approved on January 27, 1880. *.history.com

1943 Contract signed to develop ENIAC with the Moore School at the University of Pennsylvania.

1977, first personal computer, the Apple II, went on sale. They were the invention of Steve Wozniak and Steve Jobs. They have the 6502 microprocessor, ability to do Hi-res and Lo-res color graphics, sound, joystick input, and casette tape I/O. They have a total of eight expansion Slots for adding peripherials. Clock speed is 1MHz and, with Apple's Language Card installed, standard memory size is 64kB. (The Apple I designation referred to an earlier computer that was not much more than a board. You had to supply your own keyboard, monitor and case.) The Apple II was one of three prominent personal computers that came out in 1977. Despite its higher price, it quickly pulled ahead of the TRS-80 and the Commodore Pet. *TIS Model pictured must be after 1979 when the floppy disk drive (1978) and spreadsheet program VisiCalc (1979) made it a blockbuster.

1995 The first gaseous condensate was produced by Eric Cornell and Carl Wieman at the University of Colorado at Boulder NIST–JILA lab, using a gas of rubidium atoms cooled to 170 nanokelvin (nK) [6] (1.7×10−7 K). For their achievements Cornell, Wieman, and Wolfgang Ketterle at MIT received the 2001 Nobel Prize in Physics. This Bose–Einstein condensate was first predicted by Satyendra Nath Bose and Albert Einstein in 1924–25. Interestingly, Bose first letter to Einstein was written on June 4,1924 so the discovery was one day over exactly 71 years later. *Wik

BIRTHS

1814  Pierre Laurent Wantzel (5 June 1814 in Paris – 21 May 1848 in Paris) was a French mathematician who proved that several ancient geometric problems were impossible to solve using only compass and straightedge.

In a paper from 1837, Wantzel proved that the problems of doubling the cube, and trisecting the angle are impossible to solve if one uses only compass and straightedge. In the same paper he also solved the problem of determining which regular polygons are constructible: a regular polygon is constructible if and only if the number of its sides is the product of a power of two and any number of distinct Fermat primes (i.e. that the sufficient conditions given by Carl Friedrich Gauss are also necessary)

The solution to these problems had been sought for thousands of years, particularly by the ancient Greeks. However, Wantzel's work was neglected by his contemporaries and essentially forgotten. Indeed, it was only 50 years after its publication that Wantzel's article was mentioned either in a journal article or in a textbook. Before that, it seems to have been mentioned only once, by Julius Petersen, in his doctoral thesis of 1871. It was probably due to an article published about Wantzel by Florian Cajori more than 80 years after the publication of Wantzel's article that his name started to be well-known among mathematicians.

Wantzel was also the first person to prove, in 1843, that if a cubic polynomial with rational coefficients has three real roots but is irreducible in Q[x] (the so-called casus irreducibilis), then the roots cannot be expressed from the coefficients using real radicals alone; that is, complex non-real numbers must be involved if one expresses the roots from the coefficients using radicals. This theorem would be rediscovered decades later by (and sometimes attributed to) Vincenzo Mollame and Otto Hölder.

1819 John Couch Adams (5 June 1819 – 21 January 1892); In 1878 he published his calculation of Euler’s constant (Euler-Mascheronie constant) to 263 decimal places. (he also calculated the Bernoulli numbers up to the 62 nd) *VFR The Euler-Mascheronie constant is the limiting value of the difference between the sum of the first n values in the harmonic series and the natural log of n. (not 263 places, but the approximate value is 0.5772156649015328606065...)
He also predicted the location of the then unkown planet of Neptune, but it seems he failed to convince Airy to search for the planet. Independently, Urbanne LeVerrier predicted its locatin in Germany, and then assisted Galle in the Berlin Observatory in locating the planet on 23 September 1846. As a side note, when he was appointed to a Regius position at St. Andrews in Scotland, he was the last professor ever to have to swear and oath of “abjuration and allegience”, swearing fealty to Queen Victoria, and abjuring the Jacobite succession. The need for the oath was removed by the 1858 Universities Scotland Act. Adams made many other contributions to astronomy, notably his studies of the Leonid meteor shower (1866) where he showed that the orbit of the meteor shower was very similar to that of a comet. He was able to correctly conclude that the meteor shower was associated with the comet.

 *Wik

1883 John Maynard Keynes born. (5 June, 1883–21 April, 1946) a British economist whose ideas have profoundly affected the theory and practice of modern macroeconomics, as well as the economic policies of governments. He greatly refined earlier work on the causes of business cycles, and advocated the use of fiscal and monetary measures to mitigate the adverse effects of economic recessions and depressions. His ideas are the basis for the school of thought known as Keynesian economics, as well as its various offshoots. *Wik In one logic class of Whitehead he was the only student. Keynes worked on the foundations of probability

In the late 1930s and 1940s, economists (notably John Hicks, Franco Modigliani and Paul Samuelson) attempted to interpret and formalise Keynes's writings in terms of formal mathematical models. In what had become known as the neoclassical synthesis, they combined Keynesian analysis with neoclassical economics to produce neo-Keynesian economics, which came to dominate mainstream macroeconomic thought for the next 40 years.

1888 Gregor Michailowitch Fichtenholz, ( 5 June 1888 in Odessa; 25 June 1959 in Leningrad)who was the founder of the Leningrad school of function theory. *VFR
1900 Dennis Gabor (5 Jun 1900, 8 Feb 1979 at age 78) Hungarian-born British electrical engineer who won the Nobel Prize for Physics in 1971 for his invention of holography, a system of lensless, three-dimensional photography that has many applications. He first conceived the idea of holography in 1947 using conventional filtered-light sources. Because such sources had limitations of either too little light or too diffuse, holography was not commercially feasible until the invention of the laser (1960), which amplifies the intensity of light waves. He also did research on high-speed oscilloscopes, communication theory, physical optics, and television. Gabor held more than 100 patents. *TIS

1979 Dennis Gabor (5 Jun 1900, 8 Feb 1979 at age 78)  Hungarian-born British electrical engineer who won the Nobel Prize for Physics in 1971 for his invention of holography, a system of lensless, three-dimensional photography that has many applications. He first conceived the idea of holography in 1947 using conventional filtered-light sources. Because such sources had limitations of either too little light or too diffuse, holography was not commercially feasible until the invention of the laser (1960), which amplifies the intensity of light waves. He also did research on high-speed oscilloscopes, communication theory, physical optics, and television. Gabor held more than 100 patents. *TIS

1904 George McVittie studied at Edinburgh and Cambridge. He then held posts at Leeds, Edinburgh and London and became Professor of Astronomy at the University of Illinois. His main work was in Relativity and Cosmology. *SAU More detail of his life can be found in this obituary.

1907 Sir Rudolf Ernst Peierls, CBE FRS ( 5 June 1907 – 19 September 1995) was a German-born British physicist who played a major role in Tube Alloys, Britain's nuclear weapon programme, as well as the subsequent Manhattan Project, the combined Allied nuclear bomb programme. His 1996 obituary in Physics Today described him as "a major player in the drama of the eruption of nuclear physics into world affairs"

1924 Geoffrey Foucar Chew (June 5, 1924 – April 12, 2019) was an American theoretical physicist. He is known for his bootstrap theory of strong interactions.

Chew worked as a professor of physics at the UC Berkeley since 1957 and was an emeritus since 1991. Chew held a PhD in theoretical particle physics (1944–1946) from the University of Chicago. Between 1950 and 1956, he was a physics faculty member at the University of Illinois. In addition, Chew was a member of the National Academy of Sciences as well as the American Academy of Arts and Sciences. He was also a founding member of the International Center for Transdisciplinary Research (CIRET).

Chew was a student of Enrico Fermi. His students include David Gross, one of the winners of the 2004 Nobel Prize in Physics, and John H. Schwarz, one of the pioneers of string theory.

1926 Claude Jacques Berge (5 June 1926 – 30 June 2002) was a French mathematician, recognized as one of the modern founders of combinatorics and graph theory.

Berge wrote five books, on game theory (1957), graph theory and its applications (1958), topological spaces (1959), principles of combinatorics (1968) and hypergraphs (1970), each being translated in several languages. These books helped bring the subjects of graph theory and combinatorics out of disrepute by highlighting the successful practical applications of the subjects.[6] He is particularly remembered for two conjectures on perfect graphs that he made in the early 1960s but were not proved until significantly later:

A graph is perfect if and only if its complement is perfect, proven by László Lovász in 1972 and now known as the perfect graph theorem,[7] and

A graph is perfect if and only if neither it nor its complement contains an induced cycle of odd length at least five, proven by Maria Chudnovsky, Neil Robertson, Paul Seymour, and Robin Thomas in work published in 2006 and now known as the strong perfect graph theorem.

Games were a passion of Claude Berge throughout his life, whether playing them – as in favorites such as chess, backgammon, and Hex – or exploring more theoretical aspects. This passion governed his interests in mathematics. He began writing on game theory as early as 1951, spent a year at the Institute for Advanced Study in Princeton, New Jersey in 1957, and the same year produced his first major book, Théorie générale des jeux à n personnes. Here, one not only comes across names such as John von Neumann and John Nash, as one would expect, but also names such as Dénes Kőnig, Øystein Ore, and Richardson. Indeed, the book contains much graph theory, namely the graph theory useful for game theory; it also contains much topology, namely the topology of relevance to game theory. Thus, it was natural that Berge quickly followed up on this work with two larger volumes, Théorie des graphes et ses applications and Espaces topologiques, fonctions multivoques. The first one is a masterpiece, with its unique blend of general theory, theorems – easy and difficult, proofs, examples, applications, diagrams. It is a personal manifesto of graph theory, rather than a complete description, as attempted in the book by Kőnig. It would be an interesting project to compare the first two earlier books on graph theory, by André Sainte-Laguë and Kőnig, respectively, with the book by Berge. It is clear that Berge's book is more leisurely and playful than Kőnig's, in particular. It is governed by the taste of Berge and might well be subtitled 'seduction into graph theory' (to use the words of Gian-Carlo Rota from the preface to the English translation of Berge's book). Among the main topics in this book are factorization, matchings, and alternating paths. Here Berge relies on the fundamental paper of Tibor Gallai. Gallai was one of the greatest graph theorists – he was to some degree overlooked – but not by Berge. Gallai was among the first to emphasize min-max theorems and LP-duality in combinatorics.*Wik

DEATHS

Grégoire de Saint-Vincent  (8 September 1584 Bruges – 5 June 1667 Ghent) was a Flemish Jesuit and mathematician. He is remembered for his work on quadrature of the hyperbola.

Grégoire gave the "clearest early account of the summation of geometric series."  He also resolved Zeno's paradox by showing that the time intervals involved formed a geometric progression and thus had a finite sum.

Saint-Vincent found that the area under a rectangular hyperbola (i.e. a curve given by xy=k is the same over

[a,b]} as over  [c,d]} when  a/b=c/d. This observation led to the hyperbolic logarithm.

Frontispiece to Saint-Vincent's Opus Geometricum

===============================================================

1716 Roger Cotes (10 July 1682 — 5 June 1716) died at age 33 of a violent fever. Sir Isaac Newton, speaking of Mr. Cotes, said, “If he had lived we might have known something.” See Ronald Gowing’s Roger Cotes, Natural Philosopher, pp. 136 and 142. *VFR
A really nice bio about Cotes is at the Renaissance Mathematicus blog by Thony Christie.
Cotes's major original work was in mathematics, especially in the fields of integral calculus, logarithms, and numerical analysis. He published only one scientific paper in his lifetime, titled Logometria, in which he successfully constructs the logarithmic spiral. After his death, many of Cotes's mathematical papers were edited by his cousin Robert Smith and published in a book, Harmonia mensurarum. Cotes's additional works were later published in Thomas Simpson's The Doctrine and Application of Fluxions. Although Cotes's style was somewhat obscure, his systematic approach to integration and mathematical theory was highly regarded by his peers.[citation needed] Cotes discovered an important theorem on the n-th roots of unity, foresaw the method of least squares, and discovered a method for integrating rational fractions with binomial denominators. He was also praised for his efforts in numerical methods, especially in interpolation methods and his table construction techniques. He was regarded as one of the few British mathematicians capable of following the powerful work of Sir Isaac Newton.

1940 Augustus Edward Hough Love (17 April 1863, Weston-super-Mare – 5 June 1940, Oxford), British geophysicist and mathematician who discovered a major type of earthquake wave that was subsequently named for him. Love assumed that the Earth consists of concentric layers that differ in density and postulated the occurrence of a seismic wave confined to the surface layer (crust) of the Earth which propagated between the crust and underlying mantle. His prediction was confirmed by recordings of the behaviour of waves in the surface layer of the Earth. He proposed a method, based on measurements of Love waves, to measure the thickness of the Earth's crust. In addition to his work on geophysical theory, Love studied elasticity and wrote A Treatise on the Mathematical Theory of Elasticity, 2 vol. (1892-93). *TIS

1965 Tadashi Nakayama or Tadasi Nakayama (July 26, 1912 – June 5, 1964) was a mathematician who made important contributions to representation theory. He received his degrees from Tokyo University and Osaka University and held permanent positions at Osaka University and Nagoya University. He had visiting positions at Princeton University, Illinois University, and Hamburg University. Nakayama's lemma and Nakayama algebras and Nakayama's conjecture are named after him. *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