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.

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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

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

*VFR

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1825 Cauchy presented to the Acad´emie a paper on integrals 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

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1905 Lise Meitner had entered the University of Vienna in October 1901. She was particularly inspired by Boltzmann, and was said to often speak with contagious enthusiasm of his lectures. Her dissertation was supervised by Franz Exner and his assistant Hans Benndorf. Her thesis, titled Prüfung einer Formel Maxwells ("Examination of a Maxwell Formula"), was submitted on 20 November 1905 and approved on 28 November. She was examined orally by Exner and Boltzmann on 19 December, and her doctorate was awarded on 1 February 1906.

 She became the second woman to earn a doctoral degree in physics at the University of Vienna, after Olga Steindler who had received her degree in 1903; the third was Selma Freud, who worked in the same laboratory as Meitner, and received her doctorate later in 1906.Freud is also known as  founder of the first official Salvation Army corps in Vienna.

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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

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1935  On this day in 1935, the opera: The Necklace of the Sun : A Mayan Drama by the number theorist Derrick Norman Lehmer had its premiere at the Scottish Rite Auditorium, Oakland. It was also performed in San Francisco.*SAU  This was his second opera, he wrote The Harvest in 1933.

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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

DNA model built by Crick and Watson in 1953, on display in the Science Museum, London

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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

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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

A little over two decades later I ran across the smallest slide rule I have ever seen in an Antique shop in Cadiz, Ky.  It was a sterling silver tie clip with a working center bar and slide, two inches long.

  And on a tip from Ted Courant, I found these even smaller cuff link working slide rules, 1.125" long

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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.  In clock-making circles, Burgi is renowned for inventing the cross-beat escapement. 

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

astronomical clock by Burgi is in Stockholm. 

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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

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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. *PB

Vandermonde was a violinist, and became engaged with mathematics only around 1770. In Mémoire sur la résolution des équations (1771) he reported on symmetric functions and solution of cyclotomic polynomials; this paper anticipated later Galois theory. In Remarques sur des problèmes de situation (1771) he studied knight's tours, and presaged the development of knot theory by explicitly noting the importance of topological features when discussing the properties of knots:

"Whatever the twists and turns of a system of threads in space, one can always obtain an expression for the calculation of its dimensions, but this expression will be of little use in practice. The craftsman who fashions a braid, a net, or some knots will be concerned, not with questions of measurement, but with those of position: what he sees there is the manner in which the threads are interlaced"

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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

On my second copy of Cajori's A History of Mathematical Notation after wearing the first ragged.*PB

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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.

Julia sets for 𝑧^2+0.7885 𝑒^(𝑖𝑎) ,where a ranges from 0 to 2𝜋

*Wik

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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

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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

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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

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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

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1948  Steven Chu FREng ForMemRS HonFInstP (born February 28, 1948) is an American physicist and former government official. He is a Nobel laureate and was the 12th U.S. secretary of energy. He is currently the William R. Kenan Jr. Professor of Physics and Professor of Molecular and Cellular Physiology at Stanford University. He is known for his research at the University of California, Berkeley, and his research at Bell Laboratories and Stanford University regarding the cooling and trapping of atoms with laser light, for which he shared the 1997 Nobel Prize in Physics with Claude Cohen-Tannoudji and William Daniel Phillips.

Chu served as U.S. Secretary of Energy under the administration of President Barack Obama from 2009 to 2013. At the time of his appointment as Energy Secretary, Chu was a professor of physics and molecular and cellular biology at the University of California, Berkeley, and the director of the Lawrence Berkeley National Laboratory, where his research was concerned primarily with the study of biological systems at the single molecule level. Chu resigned as energy secretary on April 22, 2013. He returned to Stanford as Professor of Physics and Professor of Molecular & Cellular Physiology

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1954 Jean Bourgain(28 Feb 1954 - 22 Dec, 2018)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

*Wik

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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.

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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

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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 no longer seems 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

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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

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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. *Philosophy of Science Portal

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1925 Cecilia Berdichevsky or Berdichevski (née Tuwjasz) (Mar 30, 1925 – Feb 28,2010) was a pioneering Argentine computer scientist and began her work in 1961 using the first Ferranti Mercury computer in that country.

She was born Mirjam Tuwjasz  in Vidzy, at that time part of Poland, now Belarus.

Because of growing hostilities toward the Jewish community,first her father and then her mother Hoda[2] and her emigrated to Argentina when she was four years old, where she adopted the name Cecilia, and she spent her childhood years in Avellaneda, south of the Buenos Aires suburbs. Her father died within a few years of arriving in their new home and her mother remarried a rich man.

Cecilia married Mario Berdichevsky, a physician from Avellaneda, in 1951. Despite having a good job as a practicing accountant for ten years, she was not happy there having experienced many frustrations. A friend, computer scientist Rebeca Guber, convinced her to go back to school, which changed her life.

At the age of 31, Berdichevsky began her studies of mathematics at the University of Buenos Aires with Manuel Sadosky. There she had her first experience programming the new Ferranti Mercury computer, which became known by the nickname "Clementina" after someone programmed it to play the American song, "My darling Clementine." In 1961, when it arrived in Buenos Aires from England, Clementina was the most powerful computer in the country, cost $300,000 and measured 18 metres (59 ft) in length. It was the first large computer used for scientific purposes in the country (in that same year, an IBM 1401 was installed in Buenos Aires for business uses).

The newly graduated Berdichevsky studied computing from the visiting English software engineer Cicely Popplewell (famous for having worked with Alan Turing in Manchester) and with the Spanish mathematician Ernesto García Camarero. A photoelectric device read a punched paper ribbon that was used to submit the data and Clementina produced the desired result in only seconds.

Berdichevsky worked with Sadosky's institute until an Argentine coup d'état that installed a military dictatorship, which imposed government control over the workings of the previously autonomous state universities. . Many academics, including Sadosky, were forced into exile.

In 1984, Berdichevsky became Deputy General Manager of the Argentine savings bank Caja de Ahorro in charge of its computer center. She was also named the representative at the International Federation for Information Processing.

After her retirement, she continued to work as a computer consultant and participated in important international projects and organizations such as United Nations Development Program.Cecilia Berdichevsky died in Avellaneda, Argentina, 28 February 2010

Typical paper tapes showing holes punched to input data to early computers.Both five hole and eight hole were common.

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2010 Owen Chamberlain (July 10, 1920 – February 28, 2006) was an American physicist who shared with Emilio Segrè the Nobel Prize in Physics for the discovery of the antiproton, a sub-atomic antiparticle.

In 1948, having completed his experimental work, Chamberlain returned to Berkeley as a member of its faculty. There he, Segrè, and other physicists investigated proton-proton scattering. In 1955, a series of proton scattering experiments at Berkeley's Bevatron led to the discovery of the anti-proton, a particle like a proton but negatively charged. Chamberlain's later research work included the time projection chamber (TPC), and work at the Stanford Linear Accelerator Center (SLAC).

Chamberlain was politically active on issues of peace and social justice, and outspoken against the Vietnam War. He was a member of Scientists for Sakharov, Orlov, and Shcharansky, three physicists of the former Soviet Union imprisoned for their political beliefs. In the 1980s, he helped found the nuclear freeze movement. In 2003 he was one of 22 Nobel Laureates who signed the Humanist Manifesto.

Chamberlain was diagnosed with Parkinson's disease in 1985, and retired from teaching in 1989. He died of complications from the disease on February 28, 2006, in Berkeley at the age of 85. *Wik

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2020 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 Princeton, where he was an emeritus professor.

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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

On This Day in Math - February 27

 

Andromeda Galaxy which Hubble measured to be 300,000 parsecs away.

Mathematical Knowledge adds a manly Vigour to the Mind, frees it from Prejudice, Credulity, and Superstition.
~John Arbuthnot

The 58th day of the year; 58 is  the sum of the first seven prime numbers.

It is the fourth smallest Smith Number. (Find the first three. A Smith number is a composite number for which the sum of its digits equals the sum of the digits in its prime factorization, including repetition. 58 = 2*29, and 5+8= 2+2+9.) Smith numbers were named by Albert Wilansky of Lehigh University. He noticed the property in the phone number (493-7775) of his brother-in-law Harold Smith.

If you take the number 2, square it, and continue to take the sum of the squares of the digits of the previous answer, you get the sequence 2, 4, 16, 37, 58, 89, 145, 42, 20, 4, and then it repeats.  See what happens if you start with other values than 2, and see if you can find one that doesn't produce 58.  

The Greeks knew 220 and 284 were Amicable in 300 BCE. By 1638 two more pairs had been added. Then, in two papers in 1747 and 1750 in a single paper, Euler added 58 more.  He, and everyone else, missed the second smallest, (1184, 1210), was discovered in 1867 by 16-year-old B. Nicolò I. Paganini.

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EVENTS

425 "University" or Pandidakterion of Constantinople Founded on this date by Theodosius II. It is described as "the first deliberate effort of the Byzantine state to impose its control on matters relating to higher education." *Wik *Medieval History ‏@medievalhistory

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1477 Founding of the University of Uppsala. A research university in Uppsala, Sweden, and is the oldest university in Sweden and Northern Europe. It ranks among the best universities in Northern Europe and is generally considered one of the most prestigious institutions of higher learning in Europe. Prominent students include Carolus Linnaeus , the father of taxonomy; Anders Celsius, inventor of the centigrade scale, and Niklas Zennström, co-founder of KaZaA and Skype. *Wik

The University celebrates the 300th anniversary of its reopening in 1893.

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In 1611, Johannes Fabricius, a Dutch astronomer, observed the rising sun through his telescope, and observed several dark spots on it. This was one of the earliest observation of sunspots through a telescope. (Harriot, Galileo, and Christoph Scheiner all observed sunspots in the 1610-1611 period) . He called his father to investigate this new phenomenon with him. The brightness of the Sun's center was very painful, and the two quickly switched to a projection method by means of a camera obscura. Johannes was the first to publish information on such observations. He did so in his Narratio de maculis in sole observatis et apparente earum cum sole conversione. ("Narration on Spots Observed on the Sun and their Apparent Rotation with the Sun"), the dedication of which was dated 13 Jun 1611. *TIS  "One irony of the history of astronomy is that Kepler, the only person to acknowledge Johann’s priority in publication had himself observed a large sunspot in 1607 with a camera obscura, a name that he coined, but mistakenly thought he was observing a transit of Mercury." *The Renaissance Mathematicus, Thony Christie 

monument  churchyard at Osteel

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1665 Huygens writes letter to Robert Moray at the Royal Society asking him to pass on his "miraculous" observation of a synchronizing of his pendulum clocks. *Steven Strogatz, Synch

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1753 James Sadler (Baptized 27 Feb 1753; died 26 Mar 1828 at age 75.)British balloonist, self educated pastry chef, and chemist who was the first English aeronaut, whose first successful ascent was on 4 Oct 1784, in a hot-air balloon, from Christ Church Meadow, Oxford. He rose to an estimated 3600 feet and travelled six miles. He made a 20-minute hydrogen balloon flight the next month, on 12 Nov 1784. By the time he attempted a crossing of St. George's Channel from Ireland, on 1 Oct 1812, he had made about sixty ascents. Almost reaching land, success eluded him when due to a change of wind he ditched in the sea off Liverpool. After some time in the water, he was rescued by a fishing boat. His two sons, John and Wyndham also took up ballooning. Wyndham successfully made the Irish Sea crossing from Dublin to Holyhead on 22 Jul 1817. (He fell from his balloon 29 Sep 1824, and died the next day.) *TIS

A view of the balloon of Mr. Sadler's ascending. Print illustrating Sadler's ascent on 12 August 1811.

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1851 George Merriweather gave a nearly three-hour essay to members of the Philosophical Society entitled "Essay explanatory of the Tempest Prognosticator." The tempest prognosticator, also known as the leech barometer, is a 19th-century invention by Merryweather in which leeches are used in a barometer. The twelve leeches are kept in small bottles inside the device; when they become agitated by an approaching storm they attempt to climb out of the bottles and trigger a small hammer which strikes a bell. The likelihood of a storm is indicated by the number of times the bell is struck.
Merriweather was inspired by two lines from Edward Jenner's poem Signs of Rain: "The leech disturbed is newly risen; Quite to the summit of his prison." Merryweather spent much of 1850 developing his ideas and came up with six designs, the most expensive design, which took inspiration from the architecture of Indian temples, was made by local craftsmen and shown in the 1851 Great Exhibition at The Crystal Palace in London. Merryweather stated in his essay the great success that he had had with the device. It was never very popular, although on its centennial there was a brief rush of renewed interest. *Wik

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1890 Dedekind’s second letter to Keferstein. Hans Keferstein had published a paper on the notion of number with comments and suggestions for change of Dedekind's 1888 book. Dedekind first responded on February 9, and on February 14 and announced that he would push the publication by the "Society". It was in the letter of February 27 that Dedekind gives what is called, "a brilliant presentation of the development of his ideas on the notion of natural number." *Jean Van Heijenoort, From Frege to Gödel: a source book in mathematical logic, 1879-1931, pg 98 The text of the letter is available on-line at Google Books

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1919  Ramanujan sailed to India on 27 February 1919 arriving on 13 March. However his health was very poor and, despite medical treatment, he died there the following year.

 Ramanujan had sailed from India on 17 March 1914. It was a calm voyage except for three days on which Ramanujan was seasick. Ramanujan fell seriously ill in 1917 and his doctors feared that he would die. He did improve a little by September but spent most of his time in various nursing homes. After a brief improvement, his illness rebounded and it was decided to return to India.  Not quite five years in England.  *MacTutor

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1924, Harlow Shapley replied to a letter from Edwin Hubble which presented the measurement of 300,000 parsecs as the distance to the Andromeda nebula. That was the first proof that the nebula was far outside the Milky Way, in fact, a separate galaxy. When Shapley had debated Heber Curtis on 26 Apr 1920, he presented his firm, life-long conviction that all the Milky Way represented the known universe (and, for instance, the Andromeda nebula was part of the Milky Way.) On receipt of the letter, Shapley told Payne-Gaposchkin and said “Here is the letter that has destroyed my universe.” In his reply, Shapley said sarcastically that Hubble's letter was “the most entertaining piece of literature I have seen for a long time.” Hubble sent more data in a paper to the AAS meeting, read on 1 Jan 1925. *TIS

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1936 France issued a stamp with a portrait (by Louis Boilly) of Andr´e-Marie Amp`ere (1775–1836) to honor the centenary of his death. [Scott #306] *VFR

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1940 Carbon-14 was discovered on 27 February 1940, by Martin Kamen and Sam Ruben at the University of California Radiation Laboratory in Berkeley, California. Its existence had been suggested by Franz Kurie in 1934. There are three naturally occurring isotopes of carbon on Earth: 99% of the carbon is carbon-12, 1% is carbon-13, and carbon-14 occurs in trace amounts, i.e., making up about 1 or 1.5 atoms per 1012 atoms of the carbon in the atmosphere. The half-life of carbon-14 is 5,730±40 years.
Radiocarbon dating is a radiometric dating method that uses (14C) to determine the age of carbonaceous materials up to about 60,000 years old. The technique was developed by Willard Libby and his colleagues in 1949. Wik

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1942, J.S. Hey discovered radio emissions from the Sun. *TIS Several prior attempts were made to detect radio emission from the Sun by experimenters such as Nikola Tesla and Oliver Lodge, but those attempts were unable to detect any emission due to technical limitations of their instruments. Jansky first thought the radio signals he picked up from space were from the sun. *Wik

Hey used radar to track the paths of V-2 rockets approaching London at about 100 miles high, aiming to be able to predict their point of impact. He noticed spasmodic transient radar echoes at heights of about 60 miles, arriving at a rate of five to 10 per hour. When the V-2 attacks ceased, the echoes did not; Hey concluded that meteor trails were responsible and that radar could be used to track meteor streams, and could of course do so by day as well as by night. When he tried to increase the sensitivity of his radar in order to track V-2s from a greater distance, he rediscovered the cosmic radio noise that Karl Jansky and Grote Reber had found in the 1930s.

Hey's results of 1942 and 1944 could not be published until after the war. From 1945 to 1947, Hey used AORG's radars in Richmond Park to research his wartime radio astronomical discoveries further. The Richmond Park installation thus effectively became the first radio observatory in Britain.

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1989 In a review of Einstein–Bessso correspondence in the New Yorker, Jeremy Bernstein wrote: “In 1909, Einstein accepted a job as an associate professor at the University of Zurich, ... Einstein makes a familiar academic complaint—that because of his teaching duties he has less free time than when he was examining patents for eight hours a day.” *VFR

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BIRTHS

1547 Baha' ad-Din al-Amili (27 Feb 1547 in Baalbek, now in Lebanon - 30 Aug 1621 in Isfahan, Iran) was a Lebanese-born mathematician who wrote influential works on arithmetic, astronomy and grammar. Perhaps his most famous mathematical work was Quintessence of Calculation which was a treatise in ten sections, strongly influenced by The Key to Arithmetic (1427) by Jamshid al-Kashi. *SAU

Manuscript of The Summa of Arithmetics

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1881 L(uitzen) E(gbertus) J(an) Brouwer (27 Feb 1881, 2 Dec 1966) was a Dutch mathematician who founded mathematical Intuitionism (a doctrine that views the nature of mathematics as mental constructions governed by self-evident laws). He founded modern topology by establishing, for example, the topological invariance of dimension and the fixpoint theorem. (Topology is the study of the most basic properties of geometric surfaces and configurations.) The Brouwer fixed point theorem is named in his honor. He proved the simplicial approximation theorem in the foundations of algebraic topology, which justifies the reduction to combinatorial terms, after sufficient subdivision of simplicial complexes, the treatment of general continuous mappings. *TIS He denies the law of the excluded middle. *VFR

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1897 Bernard(-Ferdinand) Lyot (27 Feb 1897; 2 Apr 1952 at age 55) French astronomer who invented the coronagraph (1930), an instrument which allows the observation of the solar corona when the Sun is not in eclipse. Earlier, using his expertise in optics, Lyot made a very sensitive polariscope to study polarization of light reflected from planets. Observing from the Pic du Midi Observatory, he determined that the lunar surface behaves like volcanic dust, that Mars has sandstorms, and other results on the atmospheres of the other planets. Modifications to his polarimeter created the coronagraph, with which he photographed the Sun's corona and its analyzed its spectrum. He found new spectral lines in the corona, and he made (1939) the first motion pictures of solar prominences.*TIS

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1910 Joseph Doob (27 Feb 1910 in Cincinnati, Ohio, USA - 7 June 2004 in Clark-Lindsey Village, Urbana, Illinois, USA) American mathematician who worked in probability and measure theory. *SAU After writing a series of papers on the foundations of probability and stochastic processes including martingales, Markov processes, and stationary processes, Doob realized that there was a real need for a book showing what is known about the various types of stochastic processes. So he wrote his famous "Stochastic Processes" book. It was published in 1953 and soon became one of the most influential books in the development of modern probability theory. *Wik

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1910 Clarence "Kelly" Johnson, (February 27, 1910 – December 21, 1990) an American aeronautical engineer, was born Feb. 27, 1910.  Johnson came to head up the "Skunk Works" installation and design team at Lockheed, which was given great autonomy in designing cutting-edge aircraft.  Johnson is given most of the credit for designing many of Lockheed's famous aircraft, including the SR-71 Blackbird, between 1937 and his retirement in 1975. 

Fresh out of the University of Michigan in 1933, he was asked by Lockheed to do wind-tunnel tests on their new twin-engine Model 10 Electra, the first all-metal aircraft (second image).  Johnson found the aircraft unstable and recommended that a double-tail be substituted.  Surprisingly, Lockheed agreed, and Johnson’s career was off and running. In 1937, Amelia Earhart posed with Johnson and then took off in her twin-tailed Electra for her ill-fated flight around the world. The crash and disappearance of her plane is believed to be the result of fuel shortage and unrelated to the aircraft’s design.

Johnson's first real challenge came in 1937 when he was asked to design a fighter aircraft for the U.S. Army Air Corps, with the war impending.  The first Lockheed P-38 Lightning rolled off the lines in 1939, with twin booms and twin stabilizers, the two engines on the booms and the crew and the guns in a separate nacelle between. With this unusual configuration, the P-38 proved adept as a fighter, a fighter bomber, and an aerial reconnaissance aircraft. Over 10,000 were built before the end of the War in 1945.

Another superlative aircraft that Johnson designed was the Lockheed P-104, soon relabeled the F-104 Starfighter.  Introduced in 1958, it was intended to be more worthy rival for the Soviet MIG-15, and it was.  The F-104, powered by a single turbojet engine, was highly maneuverable and capable of reaching extreme altitude and supersonic speeds.  It is also a beautiful machine.  Lockheed built more than 2500 of them for a dozen different air forces.  Many are still flying.

The most famous aircraft that Johnson designed were the U-2 and the SR-71.  The U-2 was designed for just one purpose - to cruise at 70,000 feet, where no aircraft has any business flying, and take pictures.  To achieve this, many sacrifices were made, so that the aircraft was very difficult to fly, especially at lower altitudes, and safety margins were very slim.  But it was a great spy plane, until Gary Powers and his U-2 were shot down over the Soviet Union in 1960.  Lockheed continued producing U-2s until 1989, and they are still flying.  Or so they tell me.

 Lockheed SR-71 Blackbird is, in most expert's opinion, the finest design of Johnson's career, and perhaps of anyone’s career.  Even it if didn't fly at all, it would be spectacular, because it looks like it is doing Mach 2 just sitting on the runway.  The SR-71 was a reconnaissance aircraft, capable of flying at high altitude, but unlike the U-2, it was supersonic and maneuverable.  You couldn’t shoot it down, even if you could find it on radar, because it could outrun anything you fired at it.  To many aficionados, it is the Jaguar XK-E of aircraft – the most beautiful airplane ever built. Johnson must have had considerable chutzpah, for he decided to build the SR-71 out of titanium, a rare metal, of which Russia had almost all of the world’s supply. Somehow, he made that work. *Linda Hall Org

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1942 Robert (Bob) Howard Grubbs (b. 27 February 1942 near Possum Trot, Kentucky, – December 19, 2021) ) is an American chemist and Nobel laureate. Grubbs's many awards have included: Alfred P. Sloan Fellow (1974–76), Camille and Henry Dreyfus Teacher-Scholar Award (1975–78), Alexander von Humboldt Fellowship (1975), ACS Benjamin Franklin Medal in Chemistry (2000), ACS Herman F. Mark Polymer Chemistry Award (2000), ACS Herbert C. Brown Award for Creative Research in Synthetic Methods (2001), the Tolman Medal (2002), and the Nobel Prize in Chemistry (2005). He was elected to the National Academy of Sciences in 1989 and a fellowship in the American Academy of Arts and Sciences in 1994. Grubbs received the 2005 Nobel Prize in Chemistry, along with Richard R. Schrock and Yves Chauvin, for his work in the field of olefin metathesis. *Wik

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1943 Steven Alan Orszag (February 27, 1943 – May 1, 2011) was an American mathematician.  In 1962, at the age of 19, he graduated with a B.S. in Mathematics from the Massachusetts Institute of Technology where he was a member of the Pi Lambda Phi fraternity.  He did post graduate study at Cambridge University and in 1966 graduated with a Ph.D. in astrophysics from Princeton University. His thesis adviser was Martin David Kruskal. In 1967, Orszag was appointed as a professor of applied mathematics at the Massachusetts Institute of Technology, where he collaborated with Carl M. Bender, and was a Member of the Institute for Advanced Study. In 1984, he was appointed Forrest E Hamrick Professor of Engineering at Princeton University. In 1988, he accepted a position at Yale University and in 2000, he was named the Percey F. Smith Professor of Mathematics at Yale University from 2000 until his death in 2011.

Orszag has won numerous awards including Sloan Fellowship and Guggenheim Fellowship, the American Institute of Aeronautics and Astronautics Fluid and Plasmadynamics Award, the Otto Laporte Award of the American Physical Society, and the Society of Engineering Science's G. I. Taylor Medal.

Orszag specialized in fluid dynamics, especially turbulence, computational physics and mathematics, electronic chip manufacturing, computer storage system design, and other topics in scientific computing. His work included the development of spectral methods, pseudo-spectral methods, direct numerical simulations, renormalization group methods for turbulence, and very-large-eddy simulations. He was the founder of and/or chief scientific adviser to a number of companies, including Flow Research, Ibrix (now part of HPQ), Vector Technologies, and Exa Corp. 

With Carl M. Bender he wrote Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory, a standard text on mathematical methods for scientists. Orszag has been listed as an ISI Highly Cited Author in Engineering by the ISI Web of Knowledge, Thomson Scientific Company.

 At MIT he was a colleague of Carl M Bender and together they collaborated on a graduate level mathematics course for seven years. Bender said: [The course] was so popular that a lot of students from Harvard came to take it as well. A course that good really wasn't offered at Harvard.

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DEATHS

1735 John Arbuthnot (baptized 29 Apr 1667, 27 Feb 1735 at age 67), fellow of the Royal College of Physicians. In 1710, his paper “An argument for divine providence taken form the constant regularity observ’s in the bith of both sexes” gave the first example of statistical inference. In his day he was famous for his political satires, from which we still know the character John Bull. *VFR
He inspired both Jonathan Swift's Gulliver's Travels book III and Alexander Pope's Peri Bathous, Or the Art of Sinking in Poetry, Memoirs of Martin Scriblerus. He also translated Huygens' "De ratiociniis in ludo aleae " in 1692 and extended it by adding a few further games of chance. This was the first work on probability published in English.*SAU A nice blog about Arbuthnot and his work is at this post by *RMAT.

"It is impossible for a Die, with such determin'd force and direction, not to fall on such determin'd side, only I don't know the force and direction which makes it fall on such determin'd side, and therefore I call it Chance, which is nothing but the want of art ... ."

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1867 James Dunwoody Brownson DeBow (1820 – February 27, 1867) was an American publisher and statistician, best known for his influential magazine DeBow's Review, who also served as head of the U.S. Census from 1853-1857.*Wik

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1906 Samuel Pierpont Langley, (22 Aug 1834; 27 Feb 1906)American astronomer, physicist, and aeronautics pioneer who built the first heavier-than-air flying machine to achieve sustained flight. He launched his Aerodrome No.5 on 6 May 1896 using a spring-actuated catapult mounted on top of a houseboat on the Potomac River, near Quantico, Virginia. He also researched the relationship of solar phenomena to meteorology. *TIS

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1915 Nikolay Yakovlevich Sonin (February 22, 1849 – February 27, 1915) was a Russian mathematician.
Sonin worked on special functions, in particular cylindrical functions. He also worked on the Euler–Maclaurin summation formula. Other topics Sonin studied include Bernoulli polynomials and approximate computation of definite integrals, continuing Chebyshev's work on numerical integration. Together with Andrey Markov, Sonin prepared a two volume edition of Chebyshev's works in French and Russian. He died in St. Petersburg.*Wik

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1975 Hyman Levy (28 Feb 1889 in Edinburgh, Scotland - 27 Feb 1975 in Wimbledon, London, England )graduated from Edinburgh and went on to study in Göttingen. He was forced to leave Germany on the outbreak of World War II and returned to work at Oxford and at the National Physical Laboratory. He held various posts in Imperial College London, finishing as Head of the Mathematics department. His main work was in the numerical solution of differential equations. he published Numerical Studies in Differential Equations (1934), Elements of the Theory of Probability (1936), and Finite Difference Equations (1958). However, Levy was more than a mathematician. He was a philosopher of science and also a political activist. *SAU

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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