Sunday 22 January 2023

On This Day in Math - January 22



Niels & Harald Bohr talking football w/ children (see Deaths 1951)

Prudens interrogatio quasi dimidium sapientiae.
A prudent question is, as it were, one half of wisdom.
~Sir Francis Bacon

The 22nd day of the year; 22 is the smallest Hoax number (the sum of its digits is equal to the sum of the digits of its distinct prime factors). Can you find the next? [these sums that Hoax numbers add up to are an interesting study also]

Arrange the whole numbers from 1 to 22 into pairs so that the sum of the numbers in each pair is a perfect square. (Turns out that you can't, and 22 is the largest even number for which this is true) * Henri Picciotto@hpicciotto

In the "See and Say sequence where 1 is followed by 11 (one one), which is followed by 21 (Two ones)  and that is read as 1211 (one two, one one), Only one number will produce itself, 22. 

22 is also involved in another "almost integer".  \( 22 \pi^4\) is 2143.0000027...

Extra bonus: 22! has exactly 22 digits.   *Mario Livio @Mario_Livio

22 is the smallest number which can be expressed as the sum of two primes in three ways.


1673 Leibniz presents a calculation machine at the Royal Society. Leibniz would complain to Oldenburg that Hooke took an "almost obscene" interest in the machine. Sure enough, by Feb 2 Hooke was actively working on an "arithmetic engine" that he would complete and show to the Royal Society within the month. By the following month his interest waned and he decided that no mechanical device could compare to paper and pencil or "Lord Napier's metal or parchment rods" (Napiers bones)*Stephen Inwood, The Forgotten Genius: The Biography Of Robert Hooke 1635-1703

It was the first calculator that could perform all four arithmetic operations.
Its intricate precision gearwork, however, was somewhat beyond the fabrication technology of the time; mechanical problems, in addition to a design flaw in the carry mechanism, prevented the machines from working reliably.

Two prototypes were built; today only one survives in the National Library of Lower Saxony  *Wik  


1779 The parish register of Madron (the parish church) records ‘Humphry Davy, son of Robert Davy, baptized at Penzance, January 22nd, 1779. Davy was born in Penzance in Cornwall, United Kingdom, on 17 December 1778.

1833 In his notebook, Gauss introduces the linking number of two knots. "Gauss' note presents the first deep incursion into knot theory. *History of Topology edited by Ian Mackenzie James
From the Classic Carl Friedrich Gauss: Titan of Science By Guy Waldo Dunnington, Jeremy Gray, Fritz-Egbert Dohse, a partial translation comments on the developing theory of knots.

1867  It was not until 1867 that Tait verified Helmholtz' theoretical claims regarding two circular vortex rings with experiments with smoke rings. He used two boxes each with a rubber diaphragm which shot out white smoke rings when the diaphragm was struck. Thomson wrote to Helmholtz on 22 January 1867:-
... a few days ago Tait showed me in Edinburgh a magnificent way of producing [vortex rings]. We sometimes can make one ring shoot through another, illustrating perfectly your description; when one ring passes near another, each is much disturbed, and is seen to be in a state of violent vibration for a few seconds, till it settles again into its circular form. ... The vibrations make a beautiful subject for mathematical work. *Mit Edu

1876 The Johns Hopkins University Founded commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States. Johns Hopkins maintains campuses in Maryland, Washington, D.C., Italy, China, and Singapore.
The university was founded on January 22, 1876 and named for its benefactor, the philanthropist Johns Hopkins. Daniel Coit Gilman was inaugurated as first president on February 22, 1876. On his death in 1873, Johns Hopkins, a Quaker entrepreneur and childless bachelor, bequeathed $7 million to fund a hospital and university in Baltimore, Maryland. At that time this fortune, generated primarily from the Baltimore and Ohio Railroad, was the largest philanthropic gift in the history of the United States.*JHU Web page

1879, the English were embroiled in a series of running conflicts in South Africa known as the Zulu War. On Jan. 22, 1879, a numerically superior Zulu force overwhelmed a smaller but technologically more advanced British contingent, in what became known as the Battle of Isandlwana. By coincidence, an annular solar eclipse (where the Moon is visually too small to cover the Sun) occurred around 2:30 p.m. at the tail end of the skirmish. The event would have been a deep partial from the battlefield, and the name “Isandlwana” in Zulu means “the day of the dead moon.” * web page

1889 Oskar Bolza gave his first lecture to a non-German audience. At Johns Hopkins University he gave twenty lectures “on the theory of substitution groups and its application to algebraic equations.” This was the first course on Galois theory in this country. It was published in 1891 in the American Journal of Mathematics.*VFR

1919 Richard Courant married Nina Runge in G¨ottingen. She was the daughter of the mathematician Carl Runge and granddaughter of the physiologist and philosopher of science Emil DuBois-Reymond. This provides another example of mathematical talent being passed from father to son-in-law. [Constance Reid, Courant in G¨ottingen and New York. The Story of an Improbable Mathematician (Springer 1976), p. 75–76] *VFR

In 1980, Soviet dissident physicist Dr. Andrei Sakharov was arrested, stripped of his honors and exiled to Gorky from Moscow. *TIS

1984 Apple Computer Launches the Macintosh, the first successful mouse-driven computer with a graphic user interface, with a single $1.5 million commercial during the Super Bowl. Apple's commercial played on the theme of George Orwell's 1984 and featured the destruction of Big Brother -- a veiled reference to IBM -- with the power of personal computing found in a Macintosh.*CHM Surprise (to most) bit of feminism at the end, wait for it.

In 1997, American Lottie Williams was reportedly the first human to be struck by a remnant of a space vehicle after re-entering the earth's atmosphere. At 3 a.m., while walking in a park in Tulsa, Oklahoma, she saw a light pass over her head. “It looked like a meteor,” she said. Minutes later, she was hit on the shoulder by a six-inch piece of blackened metallic material. The debris that struck Ms. Williams has not been examined to confirm its origin, but a used Delta II rocket, launched nine months earlier, had crashed into the Earth's atmosphere half an hour earlier. NASA scientists believe that Williams was hit by a part of it, making her the only person in the world known to have been hit by man-made space debris. *TIS


1561 Sir Francis Bacon (22 Jan 1561; 9 Apr 1626) English philosopher remembered for his influence promoting a scientific method. He held that the aim of scientific investigation is practical application of the understanding of nature to improve man's condition. He wrote that scientists should concentrate on certain important kinds of experimentally reproducible situations, (which he called "prerogative instances"). After tabulating such phenomena, the investigator should also aim to make a gradual ascent to more and more comprehensive laws, and will acquire greater and greater certainty as he or she moves up the pyramid of laws. At the same time each law that is reached should lead him to new kinds of experiment, that is, to kinds of experiment over and above those that led to the discovery of the law. *TIS He died a month after performing his first scientific experiment. He stuffed a chicken with snow to see if this would cause it to spoil less rapidly. The chill he caught during this experiment led to his death. [A. Hellemans and B. Bunch. The Timetables of Science, p . 32]. *VFR

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

1775 André-Marie Ampère (22 Jan 1775; 10 Jun 1836) French mathematician, physicist and chemist who founded and named the science of electrodynamics, now known as electromagnetism. His interests included mathematics, metaphysics, physics and chemistry. In mathematics he worked on partial differential equations. Ampère made significant contributions to chemistry. In 1811 he suggested that an anhydrous acid prepared two years earlier was a compound of hydrogen with an unknown element, analogous to chlorine, for which he suggested the name fluorine. He produced a classification of elements in 1816. Ampère also worked on the wave theory of light. By the early 1820's, Ampère was working on a combined theory of electricity and magnetism, after hearing about Oersted's experiments. *TIS (It is said that Ampere was capable of intense concentration leading to absent-mindedness. Once walking in Paris he had an insight and pulled a piece of chalk out of his pocket and finding the back of a cab he began to cover the back of the cab with equations, and was then shocked to see his solution begin to pull away and disappear down the street.)

1865 Louis Carl Heinrich Friedrich Paschen (22 Jan 1865; 25 Feb 1947) was a German physicist who was an outstanding experimental spectroscopist. In 1895, in a detailed study of the spectral series of helium, an element then newly discovered on earth, he showed the identical match with the spectral lines of helium as originally found in the solar spectrum by Janssen and Lockyer nearly 40 years earlier. He is remembered for the Paschen Series of spectral lines of hydrogen which he elucidated in 1908. *TIS

1866 Gustav de Vries (22 Jan 1866 in Amsterdam, The Netherlands
- 16 Dec 1934 in Haarlem, The Netherlands) was a Dutch mathematician who introduced the famous Korteweg-de Vries equation which characterizes traveling waves. *SAU

1874 Leonard Eugene Dickson (22 Jan 1874,Independence, Iowa, 17 Jan 1954, Harlingen, Texas)American mathematician who made important contributions to the theory of numbers and the theory of groups. He published 18 books including Linear groups with an exposition of the Galois field theory. The 3-volume History of the Theory of Numbers (1919-23) is another famous work still much consulted today. *TIS

1880 Frigyes Riesz (22 Jan 1880; 28 Feb 1956) Hungarian mathematician and pioneer of functional analysis, which has found important applications to mathematical physics. His theorem, now called the Riesz-Fischer theorem, which he proved in 1907, is fundamental in the Fourier analysis of Hilbert space. It was the mathematical basis for proving that matrix mechanics and wave mechanics were equivalent. This is of fundamental importance in early quantum theory. His book Leçon's d'analyse fonctionnelle (written jointly with his student B Szökefalvi-Nagy) is one of the most readable accounts of functional analysis ever written. Beyond any mere abstraction for the sake of a structure theory, he was always turning back to the applications in some concrete and substantial situation. *TIS

1908 Lev Davidovich Landau (22 Jan 1908; 1 Apr 1968) Soviet physicist who worked in such fields as low-temperature physics, atomic and nuclear physics, and solid-state, stellar-energy, and plasma physics. Several physics terms bear his name. He was awarded the 1962 Nobel Prize for Physics for his theory to explain the peculiar superfluid behaviour of liquid helium at very low temperature (2.18 K). Landau's further contributions are partly reflected in such terms as Landau diamagnetism and Landau levels in solid-state physics, Landau damping in plasma physics, the Landau energy spectrum in low-temperature physics, or Landau cuts in high-energy physics. *TIS

1929 Walter Volodymyr Petryshyn (Vladimir Petryshin) (22 January 1929, Liashky Murovani, Lviv - ) is a famous Ukrainian mathematician. He had commenced his studies in Lviv during World War II, but he became a displaced person at the end of the war and continued his schooling in Germany. In 1950 he emigrated from Germany to the United States and completed his education there, living in Paterson, New Jersey. He studied at Columbia University and was awarded a B.A. in 1953, an M.S. in 1954, and a Ph.D. in 1961. Petryshyn's main achievements are in functional analysis. His major results include the development of the theory of iterative and projective methods for the constructive solution of linear and nonlinear abstract and differential equations.*Wik


1779 Jeremiah Fenwicke Dixon (27 July 1733 – 22 January 1779) was an English surveyor and astronomer who is best known for his work with Charles Mason, from 1763 to 1767, in determining what was later called the Mason-Dixon line.
Dixon was born in Cockfield, near Bishop Auckland, County Durham, the fifth of seven children, to Sir George Fenwick Dixon 5th Bt. and Lady Mary Hunter. His father was a wealthy Quaker coal mine owner and aristocrat. His mother came from Newcastle, and was said to have been "the cleverest woman" to ever marry into the Dixon family. Dixon became interested in astronomy and mathematics during his education at Barnard Castle. Early in life he made acquaintances with the eminent intellectuals of Southern Durham: mathematician William Emerson, and astronomers John Bird and Thomas Wright. In all probability it was John Bird, who was an active Fellow of the Royal Society, who recommended Dixon as a suitable companion to accompany Mason.
Jeremiah Dixon served as assistant to Charles Mason in 1761 when the Royal Society selected Mason to observe the transit of Venus from Sumatra. However, their passage to Sumatra was delayed, and they landed instead at the Cape of Good Hope where the transit was observed on June 6, 1761. Dixon returned to the Cape once again with Nevil Maskelyne's clock to work on experiments with gravity.
Dixon and Mason signed an agreement in 1763 with the proprietors of Pennsylvania and Maryland, Thomas Penn and Frederick Calvert, sixth Baron Baltimore, to assist with resolving a boundary dispute between the two provinces. They arrived in Philadelphia in November 1763 and began work towards the end of the year. The survey was not complete until late 1766, following which they stayed on to measure a degree of Earth's meridian on the Delmarva Peninsula in Maryland, on behalf of the Royal Society. They also made a number of gravity measurements with the same instrument that Dixon had used with Maskelyne in 1761. Before returning to England in 1768, they were both admitted to the American Society for Promoting Useful Knowledge, in Philadelphia.
Dixon sailed to Norway in 1769 with William Bayly to observe another transit of Venus. The two split up, with Dixon at Hammerfest Island and Bayly at North Cape, in order to minimize the possibility of inclement weather obstructing their measurements. Following their return to England in July, Dixon resumed his work as a surveyor in Durham. He died unmarried in Cockfield on 22 January 1779, and was buried in an unmarked grave in the Quaker cemetery in Staindrop.
Although he was recognized as a Quaker, he was not a very good one, dressing in a long red coat and occasionally drinking to excess. *Wik

1904 The Reverend George Salmon (25 September 1819 - 22 January 1904) was, firstly, a mathematician whose publications in algebraic geometry were widely read in the second half of the 19th century. He was also an Anglican theologian who devoted himself mostly to theology for the last forty years of his life. His publications in theology were widely read, too. He spent his entire career at Trinity College Dublin. In 1848 Salmon had published an undergraduate textbook entitled A Treatise on Conic Sections. This text remained in print for over fifty years, going though five updated editions in English, and was translated into German, French and Italian. In the late 1840s and the 1850s Salmon was in regular and frequent communication with Arthur Cayley and J.J. Sylvester. The three of them together with a small number of other mathematicians (including Charles Hermite) were developing a system for dealing with n-dimensional algebra and geometry. During this period Salmon published about 36 papers in journals. In these papers for the most part he solved narrowly defined, concrete problems in algebraic geometry, as opposed to more broadly systematic or foundational questions. But he was an early adopter of the foundational innovations of Cayley and the others. In 1859 he published the book Lessons Introductory to the Modern Higher Algebra (where the word "higher" means n-dimensional). This was for a while simultaneously the state-of-the-art and the standard presentation of the subject, and went through updated and expanded editions in 1866, 1876 and 1885, and was translated into German and French. *Wik

1951 Harald August Bohr (22 Apr 1887, 22 Jan 1951) Danish mathematician who devised a theory that concerned generalizations of functions with periodic properties, the theory of almost periodic functions. His brother was noted physicist Niels Bohr.*TIS Harald was an excellent football(soccer) player in his youth and played for the National team. Niels played also, but not at the same high level. An interesting anecdote about Niels Bohr as an athlete is here.

1921 Marie Georges Humbert (7 Jan 1859 in Paris, France - 22 Jan 1921 in Paris, France) His doctorate extended Clebsch's work on curves. He then studied Abel's work which he developed and put into a geometric setting. It was as a direct consequence of his work on using abelian functions in geometry which won for him the 1892 Académie des Sciences prize for work on Kummer surfaces. As Costabel writes, "He thus enriched analysis and gave the complete solution of the two great questions of the transformation of hyperelliptic functions and of their complex multiplication. "
He also extended work of Hermite considering applications to number theory throughout his life.
Humbert would be better known today if the area of mathematics in which he worked had remained in favor. Since it has now become merely something of an historical curiosity rather than mainstream mathematics, his contribution is less well known. It does, however, indicate the quality of his mathematics that, despite this, his name and results are known today. To some extent this is a consequence of the fact that although he worked in a specialized area he had a remarkably broad knowledge of mathematics and his results form links between areas. *SAU

1922 Camille Jordan (5 Jan 1838, 22 Jan 1922) French mathematician and engineer who prepared a foundation for group theory and built on the prior work of Évariste Galois. As a mathematician, Jordan's interests were diverse, covering topics throughout the aspects of mathematics being studied in his era. The topics in his published works include finite groups, linear and multilinear algebra, the theory of numbers, topology of polyhedra, differential equations, and mechanics.*TIS (His date of death is listed as 22 Jan by *SAU & *Wik but 20 Jan by *TIS)

1936 V Ramaswami Aiyar (1871 in Coimbatore district, India - 22 Jan 1936 in Chittoor, India) was an enthusiastic amateur mathematician who worked as a civil servant in India. He was a founder of the Indian Mathematical Society. *SAU

1981 Rudolf Oskar Robert Williams Geiger (24 Aug 1894, 22 Jan 1981) German meteorologist, one of the founders of microclimatology, the study of the climatic conditions within a few metres of the ground surface. His observations, made above grassy fields or areas of crops and below forest canopies, elucidated the complex and subtle interactions between vegetation and the heat, radiation, and water balances of the air and soil.*TIS

1987 Patrick du Val (March 26, 1903–January 22, 1987) was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity. The concept of Du Val singularity of an algebraic surface is named after him. Du Val's early work before becoming a research student was on relativity, including a paper on the De Sitter model of the universe and Grassmann's tensor calculus. His doctorate was on algebraic geometry and in his thesis he generalised a result of Schoute. He worked on algebraic surfaces and later in his career became interested in elliptic functions.*Wik

1989 Sydney Goldstein (3 Dec 1903 in Hull, England - 22 Jan 1989 in Belmont, Massachusetts, USA) Goldstein's work in fluid dynamics is of major importance. He is described as, "... one of those who most influenced progress in fluid dynamics during the 20th century." He studied numerical solutions to steady-flow laminar boundary-layer equations in 1930. In 1935 he published work on the turbulent resistance to rotation of a disk in a fluid. His work was important in aerodynamics, a subject in which Goldstein was extremely knowledgeable. *SAU

1990 Bill Ferrar graduated from Oxford after an undergraduate career interrupted by World War I. He lectured at Bangor and Edinburgh before moving back to Oxford. He worked in college administration and eventually became Principal of Hertford College. He worked on the convergence of series. *SAU

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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