Sunday, 28 February 2021

On This Day in Math - February 28

Well David, I have a lot of ideas and throw away the bad ones.
Upon being asked how he had so many good ideas by David Harker, his student.
— Linus Pauling

The 59th day of the year; 59 is the center prime number in a 3x3 prime magic square that has the smallest possible total for each row, column and diagonal, 177.
In 1913, English puzzle writer Henry Dudeney gave an order 3 prime magic square that used the number 1. Although is was commonly included as a prime then,  present day convention no longer considers it a prime.

59 divides the smallest composite Euclid number 13# + 1= 13*11*7*5*2 + 1 = 59*509  (the symbol for a primorial,  n#, means the product of all primes from n down to 2)Euclid used numbers of the form n#+1 in his proof  that there are an infinite number of primes.

And at the right is one of the 59 stellations of the icosahedron.

Now for some nice observations from Derek Orr@MathYearRound:
5^59 - 4^59 is prime.
4^59 - 3^59 is prime.
3^59 - 2^59 is prime.
The first 59 digits of 58^57 form a prime.

EVENTS

1678 In a letter to Robert Boyle, Isaac Newton explained his concept of ether. “I suppose that there is diffused through all places an ethereal substance capable of contraction and dilation, strongly elastic and, in a word, much like air in all respects, but far more subtil.” He thought it was in all bodies of matter, but "rarer in the pores than in free spaces." This he suspects is the cause of light being refracted towards the perpendicular. *Rigaud, Letters of Scientiﬁc men, vol. 2, p. 407

1695 Liebniz writes to Johann Bernoulli encouraging him to use the term calculus summatorus which Liebniz used for integration.

*VFR

1825 Cauchy presented to the Acad´emie a paper on integals of complex-valued functions where the limits of integration were allowed to be complex. Previously, he had done much work on such
integrals when the limits were real. [Grattan-Guinness, 1990, p. 766] *VFR

1928 Chandrasekhara Venkata Raman led experiments at the Indian Association for the Cultivation of Science with collaborators, including K. S. Krishnan, on the scattering of light, when he discovered what now is called the Raman effect. Raman would win the Nobel Prize for this work. He was the first (and still the only) Indian scientist to win the Prize while a citizen of India. He was the first Asian and first non-white to receive any Nobel Prize in the sciences. He broke down at the presentation, in his own words because, " I turned round and saw the British Union Jack under which I had been sitting and it was then that I realised that my poor country, India, did not even have a flag of her own - and it was this that triggered off my complete breakdown."
India celebrates National Science Day on 28 February of every year to commemorate the discovery. *Wik

1953 James Watson, from early on this Saturday, spent his time at the Cavendish Laboratory in Cambridge, shuffling cardboard cutout models of the molecules of the DNA bases: adenine (A), guanine (G), cytosine (C) and thymine(T). After a while, in a spark of ingenuity, he discovered their complementary pairing. He realized that A joined with T had a close resemblance to C joined with G, and that each pair could hold together with hydrogen bonds. Such pairs could also neatly fit like rungs meeting at right-angles between two anti-parallel helical sugar-phosphate backbones of DNA wound around a common axis. Such structure was consistent with the known X-ray diffraction pattern evidence. Each separated helix with its half of the pairs could form a template for reproducing the molecule. The secret of life First announcement by Francis Crick and James Watson that they had reached their conclusion about the double helix structure of the DNA molecule. Their paper, A Structure for Deoxyribose Nucleic Acid, was published in the 25 Apr 1953 issue of journal Nature. *TIS

1956 Jay Forrester at MIT is awarded a patent for his coincident current magnetic core memory. Forrester's invention, given Patent No. 2,736,880 for a "multicoordinate digital information storage device," became the standard memory device for digital computers until supplanted by solid state (semiconductor) RAM in the mid-1970s. *CHM

2001 With a length of 350 feet 6.6 inches and currently the World's Longest documented Slide Rule, The Texas Magnum by Skip Solberg and Jay Francis,was demonstrated on February 28, 2001 in the Lockeed-Martin Aircraft Assembly Facility at Air Force Plant 4 in Fort Worth, Texas. The Texas Magnum holds the world's record for the longest linear slide rule. The Texas Magnum was designed as a traditional Mannheim style slide rule. The A, C, D and L scales are included on the slide rule *International Slide Rule Museum

BIRTHS

1552 Joost Bürgi (28 Feb 1552, 31 Jan 1632) Swiss watchmaker and mathematician who invented logarithms independently of the Scottish mathematician John Napier. He was the most skilful, and the most famous, clockmaker of his day. He also made astronomical and practical geometry instruments (notably the proportional compass and a triangulation instrument useful in surveying). This led to becoming an assistant to the German astronomer Johannes Kepler. Bürgi was a major contributor to the development of decimal fractions and exponential notation, but his most notable contribution was published in 1620 as a table of antilogarithms. Napier published his table of logarithms in 1614, but Bürgi had already compiled his table of logarithms at least 10 years before that, and perhaps as early as 1588. *TIS  For more in-depth look at Burgi's life, see this post at the Renaissance Mathematicus

1704 Louis Godin (28 February 1704 Paris – 11 September 1760 Cadiz) was a French astronomer and member of the French Academy of Sciences. He worked in Peru, Spain, Portugal and France.
He was graduated at the College of Louis le Grand, and studied astronomy under Joseph-Nicolas Delisle. His astronomical tables (1724) gave him reputation, and the French Academy of Sciences elected him a pensionary member. He was commissioned to write a continuation of the history of the academy, left uncompleted by Bernard le Bovier de Fontenelle, and was also authorized to submit to the minister, Cardinal André-Hercule de Fleury, the best means of discovering the truth in regard to the figure of the earth, and proposed sending expeditions to the equator and the polar sea. The minister approved the plan and appropriated the necessary means, the academy designating Charles Marie de La Condamine, Pierre Bouguer, and Godin to go to Peru in 1734.
When they had finished their task in 1738, at the invitation of the Viceroy of Peru, Godin accepted the professorship in mathematics in Lima, where he also established a course of astronomical lectures. When in 1746 an earthquake destroyed the greater part of Lima, he took valuable seismological observations, assisted the sufferers, and made plans by the use of which the new buildings would be less exposed to danger from renewed shocks.
In 1751 he returned to Europe, but found that he had been nearly forgotten, and superseded as pensioner of the academy; and, as his fortune had been lost in unfortunate speculations, he accepted the presidency of the college for midshipmen in Cadiz in 1752. During the earthquake of Lisbon, 1755, which was distinctly felt at Cadiz, he took observations and did much to allay the apprehensions of the public, for which he was ennobled by the king of Spain. In 1759 he was called to Paris and reinstated as pensionary member of the academy, but he died on his return to Cadiz. *Wik

1735 Alexandre-Théophile Vandermonde (28 Feb 1735 in Paris, France - 1 Jan 1796 in Paris, France). was a French mathematician best known for his work on determinants. *SAU
In 1772 Vandermonde used [P]n to represent the product of the n factors p(p-1)(p-2)... (p-n+1). With such a notation [P]p would represent what we would now write as p!, but I can imagine this becoming, over time, just [p] (De Morgan would do just such a thing in his 1838 essays on probability). Vandermonde seems to have been the first to consider [p]0 (or 0!) and determined it was (as we now do) equal to one. Vandermonde's notation included a method for skipping numbers, so that [p/3]n would indicate p(p-3)(p-6)... (p-3(n-1)). (this method seems better to me than the present method for factorials which skip terms) It even allowed for negative exponents.

1859 Florian Cajori (born 28 Feb 1859)Swiss-born U.S. educator and mathematician whose works on the history of mathematics were among the most eminent of his time.*TIS at times Cajori's work lacked the scholarship which one would expect of such an eminent scientist, we must not give too negative an impression of this important figure. He almost single-handedly created the history of mathematics as an academic subject in the United States and, particularly with his book on the history of mathematical notation, he is still one of the most quoted historians of mathematics today. *SAU

1878 Pierre Joseph Louis Fatou (28 Feb 1878 in Lorient, France - 10 Aug 1929 in Pornichet, France) was a French mathematician working in the field of complex analytic dynamics. He entered the École Normale Supérieure in Paris in 1898 to study mathematics and graduated in 1901 when he was appointed an astronomy post in the Paris Observatory. Fatou continued his mathematical explorations and studied iterative and recursive processes such as z == z2+C . the Julia set and the Fatou set are two complementary sets defined from a function.
Fatou wrote many papers developing a Fundamental theory of iteration in 1917, which he published in the December 1917 part of Comptes Rendus. His findings were very similar to those of Gaston Maurice Julia, who submitted a paper to the Académie des Sciences in Paris for their 1918 Grand Prix on the subject of iteration from a global point of view. Their work is now commonly referred to as the generalised Fatou–Julia theorem.*Wik  Fatou dust is a term applied to certain iteration sets that have zero area and an infinite number of disconnected components.(see image at top of page)

1901 Linus Carl Pauling (28 Feb 1901; 19 Aug 1994 at age 93) an American chemist, physicist and author who applied quantum mechanics to the study of molecular structures, particularly in connection with chemical bonding. Pauling was awarded the Nobel Prize for Chemistry in 1954 for charting the chemical underpinnings of life itself. Because of his work for nuclear peace, he received the Nobel Prize for Peace in 1962. He is remembered also for his strong belief in the health benefits of large doses of vitamin C.*TIS

1925 Louis Nirenberg (28 February 1925, Hamilton, Ontario, Canada - ) is a Canadian-born American mathematician, and one of the outstanding analysts of the twentieth century. He has made fundamental contributions to linear and nonlinear partial differential equations and their application to complex analysis and geometry.*Wik

1930 Leon N. Cooper (28 Feb 1930 - ) American physicist who shared (with John Bardeen and John Robert Schrieffer) the 1972 Nobel Prize in Physics, for his role in developing the BCS (for their initials) theory of superconductivity. The concept of Cooper electron pairs was named after him.*Wik

1939 Daniel C. Tsui (28 Feb 1939 - ) Chinese-American physicist who shared (with Horst L. Störmer and Robert B. Laughlin) received the 1998 Nobel Prize for Physics for the discovery and explanation that the electrons in a powerful magnetic field at very low temperatures can form a quantum fluid whose particles have fractional electric charges. This effect is known as the fractional quantum. *TIS

1954 Jean Bourgain(28 Feb 1954 - )Belgian mathematician who was awarded the Fields Medal in 1994 for his work in analysis. His achievements in several fields included the problem of determining how large a section of a Banach space of finite dimension n can be found that resembles a Hilbert subspace; a proof of Luis Antonio Santaló's inequality; a new approach to some problems in ergodic theory; results in harmonic analysis and classical operators; and nonlinear partial differential equations. Bourgain's work was noteworthy for the versatility it displayed in applying ideas from wide-ranging mathematical disciplines to the solution of diverse problems. *TIS

DEATHS
1691 Joseph Moxon (8 August 1627 - February 1691 (Royal Society archives state his death date as 28 February; the Oxford Dictionary of National Biography states that he was buried on 15 February???{I hope one of them was wrong}), hydrographer to Charles II, was an English printer of mathematical books and maps, a maker of globes and mathematical instruments, and mathematical lexicographer. He produced the first English language dictionary devoted to mathematics, "Mathematicks made easie, or a mathematical dictionary, explaining the terms of art and difficult phrases used in arithmetick, geometry, astronomy, astrology, and other mathematical sciences". In November 1678, he became the first tradesman to be elected as a Fellow of the Royal Society. *Wik Thony Christie has written that he was one of the first English Printers to print tables of Logarithms.

1742 Willem's Gravesande (26 September 1688 – 28 February 1742)was a Dutch mathematician who expounded Newton's philosophy in Europe. In 1717 he became professor in physics and astronomy in Leiden, and introduced the works of his friend Newton in the Netherlands.
His main work is Physices elementa mathematica, experimentis confirmata, sive introductio ad philosophiam Newtonianam or Mathematical Elements of Natural Philosophy, Confirm'd by Experiments (Leiden 1720), in which he laid the foundations for teaching physics. Voltaire and Albrecht von Haller were in his audience, Frederic the Great invited him in 1737 to come to Berlin.
His chief contribution to physics involved an experiment in which brass balls were dropped with varying velocity onto a soft clay surface. His results were that a ball with twice the velocity of another would leave an indentation four times as deep, that three times the velocity yielded nine times the depth, and so on. He shared these results with Émilie du Châtelet, who subsequently corrected Newton's formula E = mv to E = mv2. (Note that though we now add a factor of 1/2 to this formula to make it work with coherent systems of units, the formula as expressed is correct if you choose units to fit it.) *Wik

1863 Jakob Philipp Kulik (1 May 1793 in Lemberg, Austrian Empire (now Lviv, Ukraine) - 28 Feb 1863 in Prague, Czech Republic) Austrian mathematician known for his construction of a massive factor tables.
Kulik was born in Lemberg, which was part of the Austrian empire, and is now Lviv located in Ukraine.In 1825, Kulik mentioned a table of factors up to 30 millions, but this table does no longer seem to exist. It is also not clear if it had really been completed.
From about 1825 until 1863 Kulik produced a factor table of numbers up to 100330200 (except for numbers divisible by 2, 3, or 5). This table basically had the same format that the table to 30 millions and it is therefore most likely that the work on the "Magnus canon divisorum" spanned from the mid 1820s to Kulik's death, at which time the tables were still unfinished. These tables fill eight volumes totaling 4212 pages, and are kept in the archives of the Academy of Sciences in Vienna. Volume II of the 8 volume set has been lost.*Wik

1956 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

2013 Donald A. Glaser (21 Sep 1926, 28 Feb 2013) American physicist, who was awarded the Nobel Prize for Physics in 1960 for his invention of the bubble chamber in which the behaviour of subatomic particles can be observed by the tracks they leave. A flash photograph records the particle's path. Glaser's chamber contains a superheated liquid maintained in a superheated, unstable state without boiling. A piston causing a rapid decrease in pressure creates a tendency to boil at the slightest disturbance in the liquid. Then any atomic particle passing through the chamber leaves a track of small gas bubbles caused by an instantaneous boiling along its path where the ions it creates act as bubble-development centers.*TIS  With the freedom that accompanies a Nobel Prize, he soon began to explore the new field of molecular biology, and in 1971 joined two friends, Ronald E. Cape and Peter Farley, to found the first biotechnology company, Cetus Corp., to exploit new discoveries for the benefit of medicine and agriculture. The company developed interleukin and interferon as cancer therapies, but was best known for producing a powerful genetic tool, the polymerase chain reaction, to amplify DNA. In 1991, Cetus was sold to Chiron Corp., now part of Novartis. Glaser died in his sleep Thursday morning, Feb. 28, at his home in Berkeley. He was 86. *Philosopy of Science Portal

1923 Freeman (John) Dyson (15 Dec 1923, Feb 28, 2020  ) is an English-born American physicist and educator best known for his speculative work on extraterrestrial civilizations. As an imaginative scientist he proposed that a highly advanced technological civilization would ultimately completely surround its host star with a huge shell to capture 100% of the useful radiant energy. This "Dyson shell", would have a gigantic cluster of artificial planetoids ("Dyson cloud") with billions of billions of inhabitants who would make use of the energy captured by the Dyson shell. He also made the intriguing speculation that a Dyson shell viewed from other galaxies would have a highly distinctive, unnatural light. He suggests astronomers search for such tell-tale colored stars, which should signify advanced, intelligent life. *TIS (One of Dyson's earliest memories of his calculating power was at a time when he was still being put down for naps. He set about summing the fractions 1+1/2 + 1/4 ... and realized that they added up to two. At a time when most of us were still trying to figure out what fractions were, Dyson summed an infinite converging sequence.)
I came across another beautiful anecdote about Dyson's incredible mental computational ability on the Math Frolic blog Posted by "Shecky Riemann":
Freeman Dyson sitting around a table with a bunch of scientists where the question arises, is there an integer such that by moving the last digit to the front (say 1234 to 4123) you can arrive at a result such that the new integer is exactly double the value of the original integer? In a matter of seconds, Dyson essentially responds (to a stunned group), “Oh, that’s not difficult, but of course the smallest such number is 18 digits long.” AND, he was right! If you don't want to track it down by yourself, the smaller number is at the bottom of this post.
He died in a Hospital near Princton, where he was an emeritus professor.

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

I'm calling this Dyson's Number, 105,263,157,894,736,842