Tuesday 6 February 2024

On This Day in Math - February 6


Newton Statue - Trinity Chapel, Cambridge UK

The feeling of it (pure oxygen) to my lungs was not sensibly different from that of common air; but I fancied that my breast felt peculiarly light and easy for some time afterwards. Who can tell but that, in time, this pure air may become a fashionable article in luxury. Hitherto only two mice and myself have had the privilege of breathing it.~Joseph Priestley

The 37th day of the year; 37 is the only prime with a three digit period for the decimal expansion of its reciprocal, 1/37 = .027027....  But 37has a strange affinity with 27, which also has a three digit period for its reciprocal, .037037...,   The affinity, of course, is due to 27 x 37 = 999

Big Prime:::   n = integer whose digits are (left to right) 6424 copies of 37, followed by units digit of 3, is prime (n = 3737...373 has 12849 digits) *Republic of Math ‏@republicofmath

An amazing reversal: 37 is the 12th prime & 73 is the 21st prime . This enigma is the only known combination.

If you use multiplication and division operations to combine Fibonacci numbers, (for example, 4 = 2^2, 6 = 2·3, 7 = 21/ 3 ,...) you can make almost any other number. Almost, but you can't make 37.  In fact, there are 12 numbers less than 100 that can not be expressed as "Fibonacci Integers" *Carl Pomerance, et al.

Any number divisible by 37 will still be divisible by 37 if you rotate its digits, 148, 481, 1nd 814 are all divisible by 37.  
1672 Newton wrote Henry Oldenburg about his optical theories, (including the phrase, "because that Light is a heterogenous mixture of differently refrangible rays." and Oldenburg published them a few days later in the
Philosophical Transactions. The controversy that followed dissuaded Newton from publishing on optics—and also on the calculus—until 1704 *ISIS, 69, p 134 (*VFR)
But it is requisite, that the prism and lens be placed steady, and that the paper, on which the colours are cast be moved to and fro; for, by such motion, you will not only find, at what distance the whiteness is most perfect but also see, how the colours gradually convene, and vanish into whiteness, and afterwards having crossed one another in that place where they compound whiteness, are again dissipated and severed, and in an inverted order retain the same colours, which they had before they entered the composition. You may also see, that, if any of the colours at the lens be intercepted, the whiteness will be changed into the other colours. And therefore, that the composition of whiteness be perfect, care must be taken, that none of the colours fall besides the lens.
Some of his opponents denied the truth of his experiments, refusing to believe in the existence of the spectrum. Others criticized the experiments, saying that the length of the spectrum was never more than three and a half times the breadth, whereas Newton found it to be five times the breadth. It appears that Newton made the mistake of supposing that all prisms would give a spectrum of exactly the same length;

1766 Just a few months before he returns to St. Petersburg, Euler reads his paper (E401) “A New Method for Comparing the Observation of the Moon to Theory” to the Berlin Academy. The paper proposes numerical techniques for approximating a body's velocity and acceleration. Sandifer suggests that the paper had great influence on LaGrange’s foundational program for the Calculus. *Ed Sandifer, How Euler Did It, MAA

1828 George Biddell Airy appointed Plumian professor of astronomy at Cambridge at a salary of £500 per annum. He was appointed even after he raised a row that the previous salary of £300 was inadequate. For the previous two years he held the Lucasian professorship—the post Newton held—at a salary of £99. *VFR

1930 Kurt G¨odel received his Ph.D. from the University of Vienna for a dissertation, directed by Hans Hahn, that showed the completeness of first order logic (every valid first-order formula is provable). *VFR

 the board game Monopoly went on sale under its present day name for the first time.  Prior to being purchased by Parker Brothers, the game had been developed by Elizabeth Magie under the name, “The Landlord’s Game.”  Magie intended the game to give an economic lesson about land value tax. Parker Brothers initially rejected the game, claiming that it was too complicated and took too long to finish, but later changed their opinion based on the game’s popularity in Pennsylvania.

Monopoly has grown into one of Parker Brothers’ most successful board game franchises. 
*Famous Daily

1959 Kilby Files Patent For Integrated Circuit.
Jack Kilby of Texas Instruments files a patent application called "miniaturized electronic circuits" for his work on a multi-transistor device. The patent was only one of 60 that Kilby holds. While Kilby has the earliest patent on the "integrated circuit," it was Robert Noyce, later co-founder of Intel, whose parallel work resulted in a practical device. Kilby's device had several transistors connected by flying wires while Noyce devised the idea of interconnection via a layer of metal conductors. Noyce also adapted Jean Hoerni's planar technique for making transistors to the manufacture of more complex circuits. *CHM
Two drawings from Kilby's first IC patent *haverford.edu

1465 Scipione del Ferro (6 February 1465 – 5 November 1526) born in Bologna, Italy. Around 1515 he solved the cubic equations x3+px = q and x3= px + q when p and q are positive. His methods are unknown. This information was passed on to his son-in-law Annibale dalla Nave who was tricked into revealing it to Cardano, who published it in his Ars magna of 1545.*VFR
There are no surviving scripts from del Ferro. This is in large part due to his resistance to communicating his works. Instead of publishing his ideas, he would only show them to a small, select group of friends and students. It is suspected that this is due to the practice of mathematicians at the time of publicly challenging one another. When a mathematician accepted another's challenge, each mathematician needed to solve the other's problems. The loser in a challenge often lost funding or his university position. Del Ferro was fearful of being challenged and likely kept his greatest work secret so that he could use it to defend himself in the event of a challenge.
Despite this secrecy, he had a notebook where he recorded all his important discoveries. After his death in 1526, this notebook was inherited by his son-in-law Hannival Nave, who was married to del Ferro's daughter, Filippa. Nave was also a mathematician and a former student of del Ferro's, and he replaced del Ferro at the University of Bologna after his death. In 1543, Gerolamo Cardano and Lodovico Ferrari (one of Cardano's students) travelled to Bologna to meet Nave and learn about his late father-in-law's notebook, where the solution to the depressed cubic equation appeared.
Del Ferro also made other important contributions to the rationalization of fractions with denominators containing sums of cube roots.
He also investigated geometry problems with a compass set at a fixed angle, but little is known about his work in this area. *Wik (Teachers may need to explain to students how suppression of the squared term allows this to solve general cubics.)
Four years before del Ferro died, the brilliant mind that would solve the quartic (fourth power) equation was born.  His name was  Lodovico Ferrari.

1695 Nicolaus II Bernoulli (February 6, 1695, Basel, Switzerland – July 31, 1726, St. Petersburg, Russia) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. Nicolaus worked mostly on curves, differential equations, and probability. He was a contemporary of Leonhard Euler. He also contributed to fluid dynamics.*Wik He was the oldest and favorite of three sons of Johann Bernoulli. He made important mathematical contributions to the problem of trajectories while working on the mathematical arguments behind the dispute between Newton and Leibniz.*SAU When the father was asked to come to St. Petersburg to join the Academy, he declined because of his age. He suggested that they take his son Nikolaus, but, so that he not be lonely, they should also take another son Daniel. Unfortunately, Nikolaus II drowned in 1726, only eight months after going to St. Petersburg. His professorship was succeeded in 1727 by Leonhard Euler, whom the Bernoulli brothers had recommended.

1802 Sir Charles Wheatstone, (6 Feb 1802, 19 Oct 1875) English physicist who popularized the Wheatstone bridge, a device that accurately measured electrical resistance and became widely used in laboratories. He didn't actually invent the "Wheatstone Bridge". His contemporary, Samuel Hunter Christie, came up with the idea of the bridge circuit, but Wheatstone set the precedent for using it in the way in which it has been most commonly used. Over time, the device became associated with him and took on his name. He did, however, invent the concertina (1829), the stereoscope (1838), and an early form of the telegraph. He also developed a chronoscope (1842) to determine the velocity of projectiles at an English gunnery.*TIS (For students of discrete math, or interested in codes, Wheatstone was also the creator of the Playfair Cipher.) {Wheatstone's work was so diverse that after a lecture at the Science Conference in South Kensington (London) by Prof. W. G. Adams on Wheatstone's acoustical discoveries, William Spottiswoode commented, "It must have struck all those in science... that when they fancied they had found something new, they find it was done by Sir Charles Wheatstone years ago." *Knowledge and Scientific News, Jan 1908, pg 7

1824 William Huggins (7 February 1824 – 12 May 1910) was an English amateur astronomer. He built his own private observatory, called Tulse Hill, in London in 1856, and when spectroscopy was established as a scientific field of inquiry in 1859, Huggins jumped at the chance to apply it to astronomy. He said he felt like a parched man spying water in the desert. In the early 1860s, he examined the light of several nebulae and found that the spectral lines were those of a gas, not stars , and suggested that at least some nebulae were gaseous in nature (at the time, no one knew what nebulae were, except that they were nebulous).

In 1868, Huggins discovered that the spectral lines of the star Sirius are shifted slightly to the red end of the spectrum, which he recognized as a indication that Sirius is moving away from us, and he even measured its speed of recession. Huggins's wife was his close collaborator throughout his career, and just before he died, he and Lady Huggins republished all his scientific papers in a beautiful volume, The Scientific Papers of Sir William Huggins (1909) *Linda Hall Org

1848 Adam Wilhelm Siegmund Günther (6 Feb 1848 in Nuremberg, Germany - 3 Feb 1923 in Munich, Germany) Günther's contributions to mathematics include a treatise on the theory of determinants (1875), hyperbolic functions (1881), and the parabolic logarithm and parabolic trigonometry (1882). He also wrote numerous books and journal articles [which] encompass both pure mathematics and its history and physics physics, geophysics, meteorology, geography, and astronomy. The individual works on the history of science, worth reading even today, bear witness to a thorough study, a remarkable knowledge of the relevant secondary literature, and a superior descriptive ability. *SAU

1900 Rosalind Cecilia Hildegard Tanner (née Young) (5 February 1900 – 24 November 1992) was a mathematician and historian of mathematics. She was the eldest daughter of the mathematicians Grace and William Young. She was born and lived in Göttingen in Germany (where her parents worked at the university) until 1908. During her life she used the name Cecily.

Cecily joined the University of Lausanne in 1917. She also helped her father's research between 1919 and 1921 at the University College Wales in Aberystwyth, and worked with Edward Collingwood, also of Aberystwyth, on a translation of Georges Valiron's course on Integral Functions.[3] She received a L-És-sc (a bachelor's degree) from Lausanne in 1925.

She then studied at Girton College, Cambridge, gaining a PhD in 1929 under the supervision of Professor E. W. Hobson for research on Stieltjes integration. She accepted a teaching post at Imperial College, London where she worked until 1967.

After 1936, most of her research was in the history of mathematics, and she had a particular interest in Thomas Harriot, an Elizabethan mathematician. She set up the Harriot Seminars in Oxford and Durham. Rosalind married William Tanner in 1953; however, he died a few months after their marriage.

In 1972 she and Ivor Grattan-Guinness published a second edition of her parents' book The Theory of Sets of Points, originally published in 1906.
Mrs. R. C. H. Young (left, upper) at the ICM 1932

1916 John Crank (6 February 1916 – 3 October 2006) was a mathematical physicist, best known for his work on the numerical solution of partial differential equations.
He worked on ballistics during the Second World War, and was then a mathematical physicist at Courtaulds Fundamental Research Laboratory from 1945 to 1957. In 1957, he was appointed as the first Head of Department of Mathematics at Brunel College in Acton. He served two terms of office as Vice-Principal of Brunel before his retirement in 1981, when he was granted the title of Professor Emeritus.
Crank's main work was on the numerical solution of partial differential equations and, in particular, the solution of heat-conduction problems. He is best known for his work with Phyllis Nicolson on the heat equation, which resulted in the Crank–Nicolson method.*Wik


1612 Christopher Clavius (March 25, 1538 – February 6, 1612 {some sources give Feb 12 for the date of death}), the Euclid of the sixteenth-century, born in the German town of Bamberg, the see of the prince-bishop of Franconia. He was also the leader of the Gregorian calendar reform. Perhaps his greatest contribution was as an educational reformer. *Renaissance Mathematicus He was a German Jesuit mathematician and astronomer who was the main architect of the modern Gregorian calendar. In his last years he was probably the most respected astronomer in Europe and his textbooks were used for astronomical education for over fifty years in Europe and even in more remote lands (on account of being used by missionaries). As an astronomer Clavius held strictly to the geocentric model of the solar system, in which all the heavens rotate about the Earth. Though he opposed the heliocentric model of Copernicus, he recognized problems with the orthodox model. He was treated with great respect by Galileo, who visited him in 1611 and discussed the new observations being made with the telescope; Clavius had by that time accepted the new discoveries as genuine, though he retained doubts about the reality of the mountains on the Moon. Later, a large crater on the Moon was named in his honour. *Wik

Stephen Gray (December 1666 – 7 February 1736) was an English dyer and astronomer who was the first to systematically experiment with electrical conduction. Until his work in 1729 the emphasis had been on the simple generation of static charges and investigations of the static phenomena (electric shocks, plasma glows, etc.). Gray showed that electricity can be conducted through metals and that it appeared on the surfaces of insulators.
Gray went on to make more electrical discoveries, the most noticeable being electrical induction (creating an electrical charge in a suspended object without contact). In 1729 Gray showed that the "Electrik Vertue" of a glass tube can be conducted via a metal to another body. This was the first evidence that electricity was not a property of the glass tube but some kind of fluid. That same year Gray create two oaken cubes, one solid and one hollow; observing that these had the same electrical properties demonstrated that electricity was a surface rather than a bulk character.

This experiment was widely celebrated around Europe as the famous "Flying Boy" demonstration: a boy was suspended on silk cords, and then charged by Gray bringing his rubbed tube (static electric generator) close to the boy's feet, but without touching. Gray showed that the boy's face and hands still attracted the chaff, paper and other materials. Gray noted the crackling of 'electric virtue' resembled lightning (as did other experimenters), foreshadowing the great discoveries of Benjamin Franklin nearly a century later.
Stephan Gray's “electric boy” experiment, in which a boy hanging from insulating silk ropes is given an electric charge. A group are gathered around. A woman is encouraged to bend forward and poke the boy's nose, to get an electric shock.*Wik

1804 Joseph Priestley (13 Mar 1733, 6 Feb 1804) English chemist, clergyman and political theorist who discovered the element oxygen. His early scientific interest was electricity, but he is remembered for his later work in chemistry, especially gases. He investigated the "fixed air" (carbon dioxide) found in a layer above the liquid in beer brewery fermentation vats. Although known by different names at the time, he also discovered sulphur dioxide, ammonia, nitrogen oxides, carbon monoxide and silicon fluoride. Priestley is remembered for his invention of a way of making soda-water (1772), the pneumatic trough, and recognizing that green plants in light released oxygen. His political opinions and support of the French Revolution, were unpopular. After his home and laboratory were set afire (1791), he sailed for America, arriving at New York on 4 Jun 1794 *TIS He died on the morning of 6 February 1804 and was buried at Riverview Cemetery in Northumberland, Pennsylvania.

Priestley's epitaph reads:
Return unto thy rest, O my soul, for the
Lord hath dealt bountifully with thee.
I will lay me down in peace and sleep till
I awake in the morning of the resurrection. *Wik

1923 Edward Emerson Barnard (16 Dec 1857; 6 Feb 1923) astronomer who pioneered in celestial photography, specializing in wide-field photography. From the time he began observing in 1881, his skill and keen eyesight combined to make him one of the greatest observers. Barnard came to prominence as an astronomer through the discovery of numerous comets. In the 1880s, a patron of astronomy in Rochester, N.Y. awarded $200 per new comet was found. Barnard discovered eight - enough to build a "comet house" for his bride. At Lick Observatory (1888-95) he made the first photographic discovery of a comet; photographed the Milky Way; and discovered the fifth moon of Jupiter. Then he joined Yerkes Observatory, making his Photographic Atlas of Selected Regions of the Milky Way.*TIS The faint Barnard's Star is named for Edward Barnard after he discovered in 1916 that it had a very large proper motion, relative to other stars. This is the second nearest star system to the Sun, second only to the Alpha Centauri system. *Wik

1965 Ernst Erich Jacobsthal (16 October 1882, Berlin – 6 February 1965, Überlingen) was a German mathematician, and brother to the archaeologist Paul Jacobsthal.
In 1906, he earned his PhD at the University of Berlin, where he was a student of Georg Frobenius, Hermann Schwarz and Issai Schur; his dissertation, Anwendung einer Formel aus der Theorie der quadratischen Reste (Application of a Formula from the Theory of Quadratic Remainders), provided a proof that prime numbers of the form 4n + 1 are the sum of two square numbers. *Wik The theory was first conjectured by Fermat and proved by Euler.

1973 Ira Sprague Bowen (21 Dec 1898; 6 Feb 1973) was an American astrophysicist. His investigation of the ultraviolet spectra of highly ionized atoms led to his explanation of the unidentified strong green spectral lines of gaseous nebulae (clouds of rarefied gas) as forbidden lines of ionized oxygen and nitrogen. This emission, appearing to match no known element, had formerly been suggested to be due to a hypothetical element, "nebulium." Bowen was able to show, that in reality, the emission lines exactly matched those calculated to be the "forbidden lines" of ionized oxygen and nitrogen under extremely low pressure. This made a major advance in the knowledge of celestial composition. He was director of the Mt. Wilson and Palomar Observatories from 1948-64.*TIS
Ira Bowen (right) in the lab with Robert Millikan.

1992 Caius Jacob (29 March 1912 , Arad - 6 February 1992 , Bucharest ) was a Romanian mathematician and member of the Romanian Academy. He made ​​contributions in the fields of fluid mechanics and mathematical analysis , in particular vigilance in plane movements of incompressible fluids, speeds of movement at subsonic and supersonic , approximate solutions in gas dynamics and the old problem of potential theory. His most important publishing was Mathematical introduction to the mechanics of fluids. *Wik

2017 Raymond Merrill Smullyan ( May 25, 1919 -February 6, 2017) is an American mathematician, concert pianist, logician, Taoist philosopher, and magician. His first career (like Persi Diaconis a generation later) was stage magic. He then earned a BSc from the University of Chicago in 1955 and his Ph.D. from Princeton University in 1959. He is one of many logicians to have studied under Alonzo Church. Smullyan is the author of many books on recreational mathematics, recreational logic, etc. Most notably, one is titled "What Is the Name of This Book?". *Wik For example the book is described on the cover as follows:"Beginning with fun-filled monkey tricks and classic brain-teasers with devilish new twists, Professor Smullyan spins a logical labyrinth of even more complex and challenging problems as he delves into some of the deepest paradoxes of logic and set theory, including Gödel's revolutionary theorem of undecidability."
Martin Gardner described this book in Scientific American as:"The most original, most profound and most humorous collection of recreational logic and mathematics problems ever written."

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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