Some History of a Weighty Problem (repost from 2012)

  A while back my blog got a nice mention on Gary Antonick’s “Numberplay” in the New York Times. That seems only fair as I was in the process of writing this post about one of the problems in his column which relates back to a nice old recreational problem from way back.

Gary’s version of the problem reads like this:

You have a balance scale and a single chain with thirteen links.

Each link of the chain weighs one ounce. How many links of the chain

do you need to break in order to be able to weigh items from 1 to 13 ounces

in 1-ounce increments?

This is a complication of the ancient problem in two ways, first by having to divide up the chain to get links, but also because it does not say how the weighing is to be performed.

In recreational history such “balance scale” problems have two basic forms, one in which all the weights have to go on one side to balance the unknown object, and a more clever approach (my bias) that allows known weights to be on both pans of the balance. In the end Gary’s solution goes for the both-sides solution which allows the chain to be cleverly cut in only one place (producing three sections of one, three, and nine lengths) allowing the weighing of any integer weight as requested.(Cut the fourth link and remove it for the one, leaving three on one end of it, and nine on the other)

Searching for older versions of the problem, I quickly found a post in the Problem of the Week section of a 1961 Popular Science.

This one particularly allows the weights to be placed on both pans of the balance.

The solution a month later not only provides the same solution approach as Gary’s column, but also gives a bit of (not quite correct) history of the problem.

The credits to Tartaglia and Bachet are not wrong, they are just not complete. This is understandable because the attributions probably came from one of the outstanding recreational mathematics books of the early 20th century, Mathematical Recreations and Essays by W.W.Rouse BALL, in which he also credits Bachet and Tartaglia:

Both solutions were given over three hundred years earlier than Tartaglia, by Leonardo of Pisa, often known now as Fibonacci. From Sigler’s translation of the famous Liber Abaci I find:

Fibonacci also posted a version avoiding the use of weights in both pans by requiring that the total weight for each increment must be presented on a given day, in this case where each ounce was represented in a valuable metal, requiring the powers of two solution.

From David Singmaster's notes on the Chronology of Recreational Mathematics I found an earlier reference, but do could find no more about the subject named there

"c1075 Tabar_: Mift_h al-mu`_mal_t - first Use of 1,3,9,... as Weights."

If some reader knowledgeable about this source can provide more information I would be very grateful.

Even among those whose historical education has fully informed them of the earlier usages, the use of Bachet’s name is still common, as illustrated in a relatively new article which suggests a newer version of the problem from Edwin O’Shea’s BACHET’S PROBLEM: AS FEW WEIGHTS TO WEIGH THEM ALL

The generalized Bachet’s problem that we will explore here is that of finding appropriate weights when one replaces 40 with any positive integer. The full generalization, due to Park and studied further by Rødseth, not only tells us the minimum number of parts needed when 40 is replaced by any m but all possible ways to accordingly break up a given m. Furthermore, we can also count the number of distinct ways to break up such an m. For example, when we replace 40 by m = 25 we’ll still need no more than four parts but there are now nine ways to break up 25 to solve Bachet’s problem. Written as partitions with four parts, these are:

25 = 1 + 3 + 9 + 12 = 1 + 3 + 8 + 13 = 1 + 3 + 7 + 14

= 1 + 3 + 6 + 15 = 1 + 3 + 5 + 16 = 1 + 3 + 4 + 17

= 1 + 2 + 7 + 15 = 1 + 2 + 6 + 16 = 1 + 2 + 5 + 17

This brings us back to the NY Times version of the problem, but we might ask, how would you split the 13 link chain if you had to be able to pay any amount from 1 to 13 ounces of gold on a given day, as in the Fibonacci's second version of the problem?

On This Day in Math - November 7

  

I am one of those who think, like Nobel, that humanity will draw more good than evil from new discoveries.

~Marie Curie

The 311th day of the year; 311 not only prime, but is a prime under any permutation of its digits (113, 131, 311) (students might search for the next smaller, or larger number which is also a permutable prime)

Also, 311 is prime, and is also the sum  of three, five, seven, and eleven consecutive primes and the sum of its digits is prime.  *PB

and the smallest three-digit prime that is the sum of three different three-digit primes. (101 + 103 +  107 = 311).  *Prime Curios

It is the first of six consecutive primes for which eliminating the first digit (3) leaves a prime.



EVENTS

1631 Transit of Mercury across the sun, the first observation of a transit of a planet, observed by Pierre Gassendi. This had been predicted by Kepler in 1629. [Scott, Works of Wallis, p. 191, had 1621] *VFR  When Gassendi observed the dot of Mercury passing across the face of the Sun, he was surprised - it seemed far too small, according to ancient conceptions of  the relative sizes of heavenly objects. With a Galilean telescope he observed the transit by projecting the sun's image on a screen of paper. He recorded this in Mercurius in sole visus (1632; Mercury in the Face of the Sun) as support for the new astronomy of Johannes Kepler. His instrument was not strong enough, however, to disclose the occultations and transits of Jupiter's satellites. *TIS Gassendi unsuccessfully attempted to observe the transit of Venus just one month later, but due to inaccurate astronomical tables he did not realize that it was not visible from most of Europe, including Paris. A transit of Venus was not observed until 1639, by Jeremiah Horrocks. (for more on the march to accepting a heliocentric system, see this blog by The Renaissance Mathematicus.)

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1725   Nicolaus II and Daniel Bernoulli arrived in St. Petersburg on October 27, 1725 (OS)  Nov 7 (NS)

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1749 Benjamin Franklin enters in his notebook a list of 12 ways in which lightening and electrical fluid agree, from 1) "giving light", to 12) "sulphurous smell". He then considers whether lightning will be as equally attracted to "points" and lays out the framework for an experiment. *A history of physics in its elementary branches By Florian Cajori

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1763  Maskelyne arrives in Barbados during Longitude test. The Princess Louise sailed for Barbados on 23 September. During the voyage Maskelyne and Charles Green took many lunar-distance observations (with Maskelyne later claiming that his final observation was within half of degree of the truth) and struggled a couple of times with the marine chair. Maskelyne’s conclusion was that the Jupiter’s satellites method of finding longitude would simply never work at sea because the telescope magnification required was far too high for use in a moving ship.
On 29 December 1763 he wrote his brother Edmund, reporting his safe arrival on 7 November after “an agreeable passage of 6 weeks”. He noted that he had been “very sufficiently employed in making the observations recommended to me by the Commissioners of Longitude” and that it was at times “rather too fatiguing”. *Board of Longitude project, Greenwich

Marine Chair

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1782  Published in Philosophical Transactions, as 'A letter from William Herschel, Esq. F. R. S' (to Joseph Banks) and 'On the diameter and magnitude of the Georgium Sidus; with a description of the dark and lucid disk and periphery micrometers'  *Royal Society Org. 

 The planet would eventually be named Uranus, the Greek deity of the sky.Like the classical planets, Uranus is visible to the naked eye, but it was never recognized as a planet by ancient observers because of its dimness and slow orbit. Sir William Herschel first observed Uranus on 13 March 1781, first reported as a comet.  Consensus on the name was not reached until almost 70 years after the planet's discovery.

The first page of the letter begins  "By the observation of the most eminent Astronomers in Europe it appears that the new star, which I had the honour of pointing out to them in March 1781, is a Primary Planet of our Solar System."  

*Royal Society Org. 

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1849 The official opening of Queen’s College in Cork, Ireland. George Boole was the professor of mathematics—the only university post he ever applied for. [MacHale, George Boole, His Life and Work, p 88].

Queen's College, Cork, was founded by the provisions of an act which enabled Queen Victoria to endow new colleges for the "Advancement of Learning in Ireland". Under the powers of this act, the three colleges of Belfast, Cork and Galway were incorporated on 30 December 1845.

Queen's College, Cork is now known as University College Cork (UCC),

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In 1908, Prof. Ernest Rutherford announced in London that he had isolated a single atom of matter. *TIS

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1915 In connection with the celebration of the centenary of Weierstrass' birth (31 October 1815), a memorial tablet was unvieled at his birthplace, Osterfelde, near Warendorf in Westphalia. It reads” “An dieser St¨att wurde am 31•X•1815 Karl Weierstrass, der grosse Mathematiker, eine Leuchte der Berliner Universit¨at, geboren.” *VFR

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1917 The “October Revolution” of the Bosheviks broke out in Russia. It is now celebrated on 7 November as the Gregorian calendar was not adopted there until 1918. *VFR Most Americans don't know that US sent ships and ground troops in aide of the White side, Almost all Russians know. The United States withheld diplomatic recognition of the Soviet Union until 1933.

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1918  Jeannette Rankin (born June 11, 1880, near Missoula, Montana, U.S.—died May 18, 1973, Carmel, California) was the first woman member of the U.S. Congress, representing Montana in the House of Representatives (1917–19, 1941–43). Rankin was a vigorous feminist and a lifetime pacifist and crusader for social and electoral reform. 

Rankin graduated from the University of Montana in 1902. She subsequently attended the New York School of Philanthropy (later the New York, then the Columbia, School of Social Work) before embarking on a career of social work in Seattle, Washington, in 1909. Caught up in the rising tide of sentiment for woman suffrage, she campaigned effectively for the next five years in Washington, California, and Montana on behalf of the cause. In 1914 she became legislative secretary of the National American Woman Suffrage Association, and in that same year she led a successful campaign for woman suffrage in her native Montana.

In 1916 Rankin, a Republican, was elected to the U.S. House of Representatives, and after taking office the following year, she became the first woman to hold a seat in either chamber. She introduced the first bill that would have allowed women citizenship independent of their husbands and also supported government-sponsored hygiene instruction in maternity and infancy. Reflecting a deep-seated pacifism, she became an outspoken isolationist and was one of 49 members of Congress to vote against declaring war on Germany in 1917 *Britannica

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1935 The Mysterious Number 137 was the title of a lecture that Max Born delivered to the South Indian Science Association in Bangalore on 7 November 1935. Called the fine structure constant α, 137 is a dimensionless entity (its value is actually its reciprocal 1/137), calculated using the charge of an electron, Planck’s constant and the speed of light. Since the early 1900s, some physicists have suggested that this number could be at the heart of a Grand Unified Theory because it combines electromagnetism, gravity and quantum mechanics.

The talk was among over 30 lectures that Born gave, both within and outside the Institute, in his capacity as a Reader in Theoretical Physics at IISc, a position he held for six months. The Institute’s 1935-36 Annual Report states that his presence provided great stimulus to the work in the Physics Department, which had just been established by IISc’s Director CV Raman. 

Image: Quantum pioneer Max Born in Bangalore, India, at the invitation of fellow Nobel Laureate Chandrasekhara Venkata Raman (left).

Born (center) delivered a lecture about the 'mysterious number 137' the approximate inverse of the fine structure constant:

Robert Matthews commented:

“Born wasn't the only world-class physicist who tried to work out the numerical value of FSC (lecture available at https://www.ias.ac.in/article/fulltext/seca/002/06/0533-0561 p557 et seq). Pauli obsessed about it, and Eddington devoted a lot of effort to working out the value of the FSC from first principles and in 1929 published his answer...1/136. 

Joking apart, it is kind-of interesting that the true value is so close to being 1 over an integer. It's a bit like Dirac's integer value of exactly 2 for the (similarly dimensionless) g-factor of the electron, which in reality is just a tiny bit greater due to messy loop corrections.  “

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1937 Ernest O. Lawrence appeared on the cover of Time for November 7, 1937, on the occasion of his winning the Comstock Prize of the National Academy of Sciences. The caption under his name says "He creates and destroys."

*aip.org/history

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1940 at approximately 11:00 am, the first Tacoma Narrows suspension bridge collapsed due to wind-induced vibrations. Situated on the Tacoma Narrows in Puget Sound, near the city of Tacoma, Washington, the bridge had only been open for traffic a few months. *TIS “Galloping Gertie,” suspension bridge over the Narrows of Puget Sound, Tacoma, Washington, breaks up from a torsional oscillation of steadily increasing amplitude caused by the wind known as the von Karman vortice street. The film is instructive for classes in Differential Equations.

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2004  

William Herschel discovered the small moon Mimas, Saturns smallest and innermost moon in 1789.  The name of this, and the other six known moons of Saturn was suggested by William's son John in 1847.  All were named for mythological giants of Greek literature.  The large crater, now named for William Herschel was not observed until photographed by the Cassinni probe on November 7, 2004.  

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2013 The Bank of Canada began circulating a new $5 note emblazoned with the orbiting outpost's Canadarm2 robotic arm seven months after debuting the space-inspired design aboard the space station.

*space.com

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BIRTHS

1660 Thomas Fantet de Lagny (7 Nov 1660 in Lyon, France - 11 April 1734 in Paris, France) De Lagny is well known for his contributions to computational mathematics, calculating π to 120 places and also making useful comments on the convergence of the series he was using. In about 1690 he developed a method of giving approximate solutions of algebraic equations and, in 1694, Halley published a twelve page paper in the Philosophical Transactions of the Royal Society giving his method of solving polynomial equations by successive approximation which is essentially the same as that given by Lagny a few years earlier. One should note that although methods based on the differential calculus were being developed at this time, neither Lagny not Halley used these new ideas. Lagny's publications on this topic are Méthodes nouvelle infiniment générale et infiniment abrégée pour l'extraction des racines quarrées, cubique (1691) and Méthodes nouvelles et abrégée pour l'extraction et l'approximation des racines (1692).
Lagny constructed trigonometric tables and used binary arithmetic in his text Trigonométrie française ou reformée published in Rochefort in 1703. In 1733 he examined the continued fraction expansion of the quotient of two integers and, as an example, considered adjacent Fibonacci numbers as the worst case expansion for the Euclidean algorithm in his paper Analyse générale ou Méthodes nouvelles pour résoudre les problèmes de tous les genres et de tous les degrés à l'infini.*SAU

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1687 William Stukeley FRS, FRCP, FSA (7 November 1687 – 3 March 1765) was an English antiquarian who pioneered the archaeological investigation of the prehistoric monuments of Stonehenge and Avebury, work for which he has been remembered as "probably... the most important of the early forerunners of the discipline of archaeology". Stukeley was also one of the first biographers of Isaac Newton. Stukeley was a friend of Isaac Newton and wrote a memoir of his life in 1752. This is one of the earliest sources for the story of the falling apple that inspired Newton's formulation of the theory of gravitation.
Becoming involved in the newly fashionable organization of Freemasonry, he also began to describe himself as a "druid", and incorrectly believed that the prehistoric megalithic monuments were a part of the druidic religion. However, despite this he has been noted as being a significant figure in the early development of the modern movement known as Neo-Druidry. *Wik

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1799 Karl Gräffe (7 November 1799, Brunswick, Germany- 2 December 1873 , Zurich, Switzerland) Gräffe is best remembered for his "root-squaring" method of numerical solution of algebraic equations, developed to answer a prize question posed by the Berlin Academy of Sciences..*SAU

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1867 Marie Marja Sklodowska Curie (7 Nov 1867; 4 Jul 1934) was a Polish-born French chemist and physicist. In 1898, her celebrated experiments on uranium minerals led to discovery of two new elements. First she separated polonium, and then radium a few months later. The quantity of radon in radioactive equilibrium with a gram of radium was named a curie (subsequently redefined as the emission of 3.7 x 1010 alpha particles per sec.) With Henri Becquerel and her husband, Pierre Curie, she was awarded the 1903 Nobel Prize for Physics. She was then sole winner of a second Nobel Prize in 1911, this time in Chemistry. Her family won five Nobel awards in two generations. She died of radiation poisoning from her pioneering work before the need for protection was known. *TIS

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1878 Lise Meitner (7 Nov 1878; 27 Oct 1968)  Austrian physicist who shared the Enrico Fermi Award (1966) with the chemists Otto Hahn and Fritz Strassmann for their joint research beginning in 1934 that led to the discovery of uranium fission. She refused to work on the atom bomb. In 1917, with Hahn, she had discovered the new radioactive element protactinium. She was the first to describe the emission of Auger electrons. In 1935, she found evidence of four other radioactive elements corresponding to atomic numbers 93-96. In 1938, she was forced to leave Nazi Germany, and went to a post in Sweden. Her other work in the field of nuclear physics includes study of beta rays, and study of the three main disintegration series. Later, she used the cyclotron as a tool. *TIS

It happened that Meitner’s nephew, Otto Frisch, also a physicist, was visiting Meitner in Sweden for the holidays, and as the two strolled in the snow in those days after Christmas, they came to understand that, in Hahn's bombardment experiment, uranium atoms must have split into two lighter by-products, one of which was barium.  Hahn had split the atom, only he didn't know it.  Meitner and Frisch figured out how and why a nucleus could divide, and they also understood that such a reaction would produce a prodigious amount of energy, and they immediately sent off a paper to Nature, a paper that was published on Feb. 11, 1939, with the title "Disintegration of uranium by neutrons: a new type of nuclear reaction."  They called the new reaction: "fission."  The Pandora's Box of atomic energy had suddenly been opened.

In 1945, Hahn received the Nobel Prize in Chemistry (for 1944) for his discovery of fission.  Meitner and Frisch were not so honored, or even mentioned in the citation. Now that the records of the prize committee’s deliberations have been unsealed, it appears that the committee was not prepared to consider the possibility that a pair of physicists might have made an important contribution to a discovery that was essentially chemical.  Meitner was very gracious about the omission in her later years, but there are many people who feel that a share of that Nobel Prize should have been hers. *Linda Hal Org  (She  was nominated for the Nobel Prize 49 times - 19 for Chemistry and 30 for Physics - but never won.)

in 1939 during the Fifth Washington Conference on Theoretical Physics at the George Washington University, Nobel Laureate Niels Bohr publicly announced the splitting of the uranium atom. The resulting “fission,” with its release of two hundred million electron volts of energy, heralded the beginning of the atomic age.

The announcement came just weeks after Otto Hahn and Fritz Strassmann, two of Bohr’s colleagues at Copenhagen, reported that they had discovered the element barium after bombarding uranium with neutrons. After receiving the news in a letter, physicist Lise Meitner and her cousin, Otto Frisch, correctly interpreted the results as evidence of nuclear fission. Frisch confirmed this experimentally on January 13, 1939. *atomicheritage.org

Addendum:

In Lise Meitner,  Ruth Lewin Sime tells a story that may shed some light on Meitner's early interest in experimentation:"When Lise was still very young, her grandmother warned her never to sow on the Sabbath, or the heavens would come tumbling downLise was doing some embroidery at the time and decided to make a test. Placing her needle on the embroidery, she stuck just the tip of it in and glanced nervously at the sky, took a stitch, waited again, and then, satisfied that there would be no objections from above, contentedly went on with her work."

With Hahn in Laboratory

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1888 Sir Chandrasekhara Venkata Raman (7 Nov 1888; 21 Nov 1970) Indian physicist whose work was influential in the growth of science in India. He was the recipient of the 1930 Nobel Prize for Physics for the 1928 discovery now called Raman scattering: a change in frequency observed when light is scattered in a transparent material. When monochromatic or laser light is passed through a transparent gas, liquid, or solid and is observed with the spectroscope, the normal spectral line has associated with it lines of longer and of shorter wavelength, called the Raman spectrum. Such lines, caused by photons losing or gaining energy in elastic collisions with the molecules of the substance, vary with the substance. Thus the Raman effect is applied in spectrographic chemical analysis and in the determination of molecular structure. *TIS He was the first Asian and first non-white to receive any Nobel Prize in the sciences.*Wik

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1906  Jean Leray (7 Nov 1906 in Chantenay, near Nantes, Loire-Inférieure, France

- 10 Nov 1998 in La Baule, Loire-Atlantique, France) was a French mathematician, who worked on both partial differential equations and algebraic topology.

He was born in Chantenay-sur-Loire (today part of Nantes). He studied at École Normale Supérieure from 1926 to 1929. He received his Ph.D. in 1933. In 1934 Leray published an important paper that founded the study of weak solutions of the Navier–Stokes equations. In the same year, he and Juliusz Schauder discovered a topological invariant, now called the Leray–Schauder degree, which they applied to prove the existence of solutions for partial differential equations lacking uniqueness.

From 1938 to 1939 he was professor at the University of Nancy. He did not join the Bourbaki group, although he was close with its founders.

His main work in topology was carried out while he was a prisoner of war in a camp in Edelbach, Austria from 1940 to 1945. He concealed his expertise on differential equations, fearing that its connections with applied mathematics could lead him to be asked to aid the German war effort.

Leray's work of this period proved seminal to the development of spectral sequences and sheaves. These were subsequently developed by many others, each separately becoming an important tool in homological algebra.

He returned to work on partial differential equations from about 1950.

He was professor at the University of Paris from 1945 to 1947, and then at the Collège de France until 1978.

He was awarded the Malaxa Prize (Romania, 1938), the Grand Prix in mathematical sciences (French Academy of Sciences, 1940), the Feltrinelli Prize (Accademia dei Lincei, 1971), the Wolf Prize in Mathematics (Israel, 1979), and the Lomonosov Gold Medal (Moscow, 1988). He was elected to the American Academy of Arts and Sciences and the American Philosophical Society in 1959 and the United States National Academy of Sciences in 1965.

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DEATHS

Painting by G. H. Tweedale

1633 Cornelis Jacobszoon Drebbel (1572 – 7 November 1633) was the Dutch builder of the first navigable submarine in 1620. Drebbel was an innovator who contributed to the development of measurement and control systems, optics and chemistry.  Drebbel became famous for his invention in 1621 of a microscope with two convex lenses. Several authors, including Christiaan Huygens assign the invention of the compound microscope to Drebbel. However, a Neapolitan, named Fontana, claimed the discovery for himself in 1618. Other sources attribute the invention of the compound microscope directly to Hans Jansen and his son Zacharias around 1595.
He also built the first navigable submarine in 1620 while working for the English Royal Navy. Using William Bourne's design from 1578, he manufactured a steerable submarine with a leather-covered wooden frame. Between 1620 and 1624 Drebbel successfully built and tested two more submarines, each one bigger than the last. The final (third) model had 6 oars and could carry 16 passengers. This model was demonstrated to King James I in person and several thousand Londoners. The submarine stayed submerged for three hours and could travel from Westminster to Greenwich and back, cruising at a depth of from 12 to 15 feet (4 to 5 metres). Drebbel even took James in this submarine on a test dive beneath the Thames, making James I the first monarch to travel underwater. This submarine was tested many times in the Thames, but it couldn't attract enough enthusiasm from the Admiralty and was never used in combat. (More recently it has been suggested that the contemporary accounts of the craft contained significant elements of exaggeration and it was at most a semi-submersible that was able to travel down the Thames by the force of the current)
He has also been credited by some authors with the invention of the thermometer; while others credit Robert Fludd, Galileo Galilei or Santorio Santorio. Whether or not he invented the thermometer, it seems he invented one of the first known temperature regulators:  "about 1620 Cornelis Drebbel (1572-1633), a Dutch engineer in the service of King James I of Britain. To maintain constant temperatures in chemical furnaces and in incubators (Figure 88), he connected a thermoscope with a damper so that it would, at excessive temperatures, reduce the oxygen supply to the fire."* (F. M. Gibbs, "The Furnaces and Thermometers of Cornelis Drebbel," Annals of Science 6(1948):32-43.)
While at the court of James I Drebbel demonstrated a number of his inventions. He was most famed for his perpetual motion machine, which told the time, date, and season, and was mounted in a globe on pillars. The invention became so famous that Rudolf II, Holy Roman Emperor, invited Drebbel to Prague in 1610 and 1619. Turbulent imperial politics saw him arrested on both occasions and it was only royal interventions from England that ensured his release.
A small lunar crater has been named after him. *Wik

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1872 Rudolf Friedrich Alfred Clebsch (19 January 1833 – 7 November 1872) was a German mathematician who made important contributions to algebraic geometry and invariant theory. He attended the University of Königsberg and was habilitated at Berlin. He subsequently taught in Berlin and Karlsruhe. His collaboration with Paul Gordan in Giessen led to the introduction of Clebsch–Gordan coefficients for spherical harmonics, which are now widely used in quantum mechanics.
Together with Carl Neumann at Göttingen, he founded the mathematical research journal Mathematische Annalen in 1868. *Wik

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1913 Alfred Russel Wallace (8 Jan 1823, 7 Nov 1913) British naturalist, and biogeographer (who studies the distribution of organisms). He was the first westerner to describe some of the most interesting natural habitats in the tropics. He is best known for devising a theory of the origin of species through natural selection made independently of Darwin. Between 1854 and 1862, Wallace assembled evidence in the Malay Archipelago, sending his conclusions to Darwin in England. Their findings were presented to the Linnaean Society in 1858. Wallace found that Australian species were more primitive, in evolutionary terms, than those of Asia, and that this reflected the stage at which the two continents had become separated. He proposed an imaginary line (now known as Wallace's line) dividing the fauna of the two regions.*TIS

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1918 Artemas Martin (August 3, 1835; Steuben County, New York - November 7, 1918; Washington, DC, United States) was a self-educated American mathematician.
Martin grew up in Venango County, Pennsylvania. He was home-schooled until the age of 14, when he began studying mathematics at the local school, later moving to the Franklin Select School a few miles away and then to the Franklin Academy, finishing his formal education at age approximately 20. He worked as a farmer, oil driller, and schoolteacher.
Martin was a prolific contributor of problems and solutions to mathematical puzzle columns in popular magazines beginning at the age of 18 in the Pittsburgh Almanac and the Philadelphia Saturday Evening Post. From 1870 to 1875, he was editor of the "Stairway Department" of Clark's School Visitor, one of the magazines to which he had previously contributed. From 1875 to 1876 Martin moved to the Normal Monthly, where he published 16 articles on diophantine analysis. He subsequently became editor of the Mathematical Visitor in 1877 and of the Mathematical Magazine in 1882.
In 1881, he declined an invitation to become a professor of mathematics at the Normal School in Missouri. In 1885, he became the librarian for the Survey Office of the United States Coast Guard, and in 1898 he became a computer in the Division of Tides.
In 1877 Martin was given an honorary M.A. from Yale University. In 1882 he was awarded another honorary degree, a Ph.D. from Rutgers University, and his third honorary degree, an LL.D., was given to him in 1885 by Hillsdale College. He was elected to the London Mathematical Society in 1878, the Société Mathématique de France in 1884, the Edinburgh Mathematical Society in 1885, the Philosophical Society of Washington in 1886, the American Association for the Advancement of Science in 1890, and the New York Mathematical Society in 1891. He was also a member of the American Mathematical Society, the Circolo Matematico di Palermo, the Mathematical Association of England, and the Deutsche Mathematiker-Vereinigung.
He died on November 7, 1918.
Martin maintained an extensive mathematical library, now in the collections of American University.  *Wik

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1936 Gury Vasilievich Kolosov   (25 August 1867; Ust, Novgorod guberniya, Russia
- 7 November 1936 ; Leningrad (now St Petersburg), Russia) was a Russian mathematician who worked on the theory of elasticity.  In 1907 Kolosov derived the solution for stresses around an elliptical hole. It showed that the concentration of stress could become far greater, as the radius of curvature at an end of the hole becomes small compared with the overall length of the hole. *SAU

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1968 Aleksandr Osipovich Gelfond (24 Oct 1906, 7 Nov 1968) Russian mathematician who originated basic techniques in the study of transcendental numbers (numbers that cannot be expressed as the root or solution of an algebraic equation with rational coefficients). He profoundly advanced transcendental-number theory, and the theory of interpolation and approximation of complex-variable functions. He established the transcendental character of any number of the form ab, where a is an algebraic number different from 0 or 1 and b is any irrational algebraic number, which is now known as Gelfond's theorem. This statement solved the seventh of 23 famous problems that had been posed by the German mathematician David Hilbert in 1900. *TIS

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2003 Donald Redfield Griffin (August 3, 1915 – November 7, 2003) was an American professor of zoology at various universities who conducted seminal research in animal behavior, animal navigation, acoustic orientation and sensory biophysics. In 1938, while an undergraduate at Harvard University, he began studying the navigational method of bats, which he identified as animal echolocation in 1944. In The Question of Animal Awareness (1976), he argued that animals are conscious like humans. Griffin was the originator of the concept of mentophobia: the denial of the consciousness of other animals by scientists. *Wik

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Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*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 

#31 Loxodrom, Rhumb Line.....History and Etymology of Math Terms

    Loxodrome

The shortest path between two points on the surface of the Earth is along a great circle arc, but this path is often not possible for ships. One reason is that a great circle arc takes constant changes of compass heading. Because it is not much longer in the middle latitudes, ships often sail a path of constant compass heading, called a loxodrome (and sometimes a rhumb line). Loxodrome comes from the Greek roots loxos for slanted, and drome which means path or course. The word rhumb was derived from the old Spanish term rumb for room or space, and the "h" seems to have crept in over confusion with the word rhombus. The first person to study the rhumb lines, and realize that they were not the shortest path between two points on the globe, was Pedro Nunez, the Portugese mathematician. In 1537, Nunez, the Royal Cosmographer of Portugal published his studies in Tratado da Sphera. In 1541 Gerard Mercator published the first globe with rhumb lines marked on it. The Globe was also the largest globe made up to that time. Today one of the globes may be found at the National Maritime Museum in Greenwich in Great Britain. Another is at the Harvard University Map Collection. You can view selected images of the globe at this web link.

The term "loxodrome" first appears in Tiphys batavus in 1624 by the Dutch Scientist Willebrord van Roijen Snell who is also known for his optical law of refraction.

Until the middle of the 18th century, finding a ships longitude at sea was nearly impossible. This forced seamen to try to navigate along a constant direction and use their estimated speed to "dead reckon" their position. It was 1569, almost 28 years after Mercator's use of rhumb lines on a globe, that he hit upon his most marvelous creation, a flat map in a new projection that would make navigation much easier, the type of map we now call a Mercator or cylindrical projection (at right). A straight line drawn on a Mercator projection map is a loxodrome.

The word loxodrome is also sometimes used for a logarithmic spiral because it always cuts a line through the origin with the same angle. A true complete loxodromic spiral on a sphere will endlessly circle the poles without reaching them. For that reason, the loxodrome is also called a spherical spiral.One of the first to show this was true was the English Mathematician Thomas Harriot. "He exhibited the logarithmic spiral as the stereographic projection of a loxodrome on a sphere, a projection he proved to be conformal." [St Andrews Univ math history web site

On This Day in Math - November 6

 

I have made this letter longer than usual, because I lack the time to make it short.
~ Blaise Pascal, (my favorite Pascal Quote)


The 310th day of the year; 310 = 1234 in base six. In base 2 it repeats one period, 100,110,110

(1!)²+(2!)²+...+(310!)² is prime. *Math Year-Round ‏@MathYearRound

The four possible 3 digit permutations of 310 all use the same digits in their squares as well, 130² = 16900, 310² = 96100, 103² = 10609,and 301² = 90601. (Are there numbers with a digit greater than three for which this is true? With or without a 0.)

310 is a magnanimous number. A number (which we assume of at least 2 digits) such that the sum obtained inserting a "+" among its digit in any position gives a prime.  31+0 is prime and 3+10 is prime

EVENTS
1500 Nicholas Copernicus observes a deep (85%) partial eclipse of the Moon from Rome. *David Dickinson ‏@Astroguyz 4m:

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1572, a supernova was first noted by Wolfgang Schuler of Wittenberg in the W-shaped constellation of Cassiopeia but was seen by many observers throughout Europe and in the Far East. It appeared as a new star, adjacent to the fainter star seen just northwest of the middle of the "W." Tycho Brahe first noticed this new star on 11 Nov 1572, and he began to meticulously record its appearance. Although he was not the first to see it, he gained fame from his book Stella Nova (Latin: "new star"). For two weeks it was brighter than any other star in the sky and visible in daytime. By month's end, it began to fade and change color, from bright white to yellow and orange to faint reddish light. It was visible to the naked eye for about 16 months until Mar 1574 *TIS

De Stella Nova opened to display image with the Supernova located in the foot of the serpent bearer

*Wik

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1766 Lagrange welcomed, at age 30, to the Berlin Academy by Frederick the Great. “The greatest king in Europe” wished to have at his court “the greatest mathematician of Europe.” *VFR 

By March 1766 d'Alembert knew that Euler was returning to St Petersburg and wrote again to Lagrange to encourage him to accept a post in Berlin. Full details of the generous offer were sent to him by Frederick II in April, and Lagrange finally accepted. Leaving Turin in August, he visited d'Alembert in Paris, then Caraccioli in London before arriving in Berlin in October. Lagrange succeeded Euler as Director of Mathematics at the Berlin Academy on 6 November 1766.

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1780 Aloisio Galvani discovers the famous "twitch" in a frog's leg. *A history of physics in its elementary branches By Florian Cajori 
During the 1780's, biologist Luigi Galvani performed experiments at the University of Bologna involving frogs. While cutting a frog’s leg, Galvani's steel scalpel touched a brass hook that was holding the leg inplace. The leg twitched. Further experiments confirmed this effect, and Galvani was convinced that he was seeing the effects of what he called animal electricity. *batteryfacts

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1869 The first game of intercollegiate "football" between two colleges from the United States was an unfamiliar ancestor of today's college football, as it was played under 99-year-old soccer-style Association rules. The game was played between teams from Rutgers University and Princeton University, which was called the College of New Jersey at the time. It took place on November 6, 1869 at College Field, which is now the site of the College Avenue Gymnasium at Rutgers University in New Brunswick, New Jersey. Rutgers won by a score of 6 "runs" to Princeton's 4 *Wik

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1936 Problem number 153 was entered into the Scottish Book by Stanislaw Mazur. The problem asked (although not in these words) about the existence of Schauder bases in separable Banach spaces. As with many of the problems in the Scottish Book the proposer would offer a prize for their solution. Prizes offered included wine, spirits, or a meal in Cambridge but Mazur offered a live goose as the prize for this particular problem. Per Enflo showed in 1972 that the problem had a negative solution and, while in Warsaw lecturing on his solution, Mazur presented him with his prize, the live goose! The ceremony was broadcast throughout Poland. *SAU

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1960 The New York Times picked up an Associated Press story about a Catholic Church near Cologne, Germany which had decided to put a modern touch to the new church bell, so they ordered Einstein's famous equation to be engraved on the bell. Unfortunately, someone miss engraved the bell, replacing the C with an R. Unfortunately, when the story ran in the press, another adjustment to the Professor's great equation had occurred... read it for yourself.

*J F PTAK

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1980 Microsoft signs a contract with IBM to create an operating system for the new IBM PC. The PC ignited the personal computer market, making home computers popular among more than just hobbyists. Microsoft cofounders Bill Gates and Paul Allen developed the Microsoft Disk Operating System, commonly known as MS-DOS, using existing software from a Seattle company as a foundation. *CHM

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2002 A group of Australian scientists published a paper in Applied Ergonomics with the title, "An Analysis of the Forces Required to Drag Sheep over Various Surfaces." *sciencedirect abstract

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BIRTHS
1638 James Gregory (6 Nov 1638; Oct 1675) Scottish mathematician, astronomer and inventor of a type of reflecting telescope, born in Aberdeen. He was the first to investigate converging number series, which have an infinite number of terms but a finite sum.

 Gregory published Vera Circuli et Hyperbolae Quadratura (1667) in which he approximated the areas of the circle and hyperbola with convergent series:

[James Gregory] cannot be denied the authorship of many curious theorems on the relation of the circle to inscribed and circumscribed polygons, and their relation to each other. By means of these theorems he gives with infinitely less trouble than by the usual calculations, … the measure of the circle and hyperbola (and consequently the construction of logarithms) to more than twenty decimal places. Following the example of Huygens, he also gave constructions of straight lines equal to the arcs of the circle, and whose error is still less.

"The first proof of the fundamental theorem of calculus and the discovery of the Taylor series can both be attributed to him.

 He made important contributions to the development of the calculus, although some of his best work remained virtually unknown until long after his death. In 1660 he published his Optica Promota, in which he described the first practical reflecting ("Gregorian") telescope. Light reflected from a concave elliptical secondary mirror is brought to a focus just behind a hole in the primary mirror. It was superceded by the Newtonian and Cassegrain telescopes. Gregory also introduced estimation of stellar distances by photometric methods. *TIS  (For more on the origin of reflecting telescopes see this blog by the Renaissance Mathematicus.)

*Wik

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1781 Giovanni Antonio Amedeo Plana (6 November 1781 – 20 January 1864) was an Italian astronomer and mathematician. In 1800 he entered the École Polytechnique, and was one of the students of Joseph Lagrange. Jean Fourier, impressed by Plana's abilities, managed to have him appointed to the chair of mathematics in a school of artillery in Piedmont in 1803, which came under the control of the French in 1805. In 1811 he was appointed to the chair of astronomy at the University of Turin thanks to the influence of Lagrange. He spent the remainder of his life teaching at that institution.
His contributions included work on the motions of the Moon, as well as integrals, elliptic functions, heat, electrostatics, and geodesy. In 1820 he was one of the winners of a prize awarded by the Académie des Sciences in Paris based on the construction of lunar tables using the law of gravity. In 1832 he published the Théorie du mouvement de la lune. In 1834 he was awarded with the Copley Medal by the Royal Society for his studies on lunar motion. He became astronomer royal, and then in 1844 a Baron. At the age of 80 he was granted membership in the prestigious Académie des Sciences. He died in Turin. He is considered one of the premiere Italian scientists of his age. *Wik

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1899, James Packard and his brother, William Doud Packard, had finished building a car of their own design, and gave it a road test on the streets of Warren, Ohio. As a mechanical engineer, when he was dissatisfied the Winton car he had had bought, and gave his criticsms to the manufacturer, it is said that Alexander Winton gave him a curt reply suggesting that he build his own, if he thought he could do better. It took fourteen months for the Packard brothers, with two men hired from Winton, to produce what became known as the Packard Model A. It had high wire wheels, was steered by a tiller rather than a wheel, and was powered by a single-cylinder engine under the seat. Packard had invented the automatic spark advance as an improvement. He sold the car for $1250, and thus began in business.. *TIS

Though it has rested in a glass case in Lehigh University’s engineering building for the last 85 years, Old Number One—the vehicle considered to be the very first Packard ever built—hasn’t exactly sat idle that whole time. Students over the years got to take it on jaunts around town, and it seems every time some dignitary came by, Lehigh officials would pull it out for a photo op. With Lehigh installing a new permanent enclosure for it, however, Old Number One’s cruising days may very well have come to an end.

No tombstone grille adorns the front of Old Number One, and technically it’s not even a Packard—it was built as an Ohio Model A four years before the automotive division of the New York and Ohio Company in Warren, Ohio, changed its name to Packard—but Packard enthusiasts and historians embrace it as one of their own nonetheless. James Ward Packard, his brother, William Doud Packard, and two former Winton employees, George Weiss and William Hatcher, built the car in 1899 as the first of five Model A’s, conceived after James Ward Packard took his troublesome Winton back to the factory in Cleveland one too many times with suggestions for improvements.

Completed on November 6, 1899, the Model A featured a number of innovations, including a pedal for throttle control, automatic spark advance, a float-feed carburetor and a recirculating water pump for the cooling system. It still remained rather primitive in other aspects, however, with a tiller steering system, a total-loss oiling system, a buggy-type body built by carriage-maker Morgan and Williams, and a 9 horsepower single-cylinder suction-intake engine driving through a four-speed planetary transmission and chain drive to the rear axle.*Hemmings Motor Club

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1906 Emma Markovna Lehmer (née Trotskaia) (November 6, 1906 – May 7, 2007) was a mathematician known for her work on reciprocity laws in algebraic number theory. She preferred to deal with complex number fields and integers, rather than the more abstract aspects of the theory. At UC Berkeley, she started out in engineering in 1924, but found her niche in mathematics. One of her professors was Derrick N. Lehmer, the number theorist well known for his work on prime number tables and factorizations. While working for him at Berkeley finding pseudosquares, she met her future husband Derrick H. Lehmer. Upon her graduation summa cum laude with a B.A. in Mathematics (1928), Emma married the younger Lehmer. They moved to Brown University, where Emma received her M.Sc., and Derrick his Ph.D., both in 1930. Emma did not obtain a Ph.D. herself. Most universities had nepotism rules which prevented husband and wife from both holding teaching positions, although Emma claimed there were many advantages to not holding a Ph.D.
The Lehmers had two children, Laura (1932) and Donald (1934). Emma did independent mathematical work, including a translation from Russian to English of Pontryagin's book Topological Groups. She worked closely with her husband on many projects; 21 of her 60-some publications were joint work with him. Her publications were mainly in number theory and computation, with emphasis on reciprocity laws, special primes, and congruences. *Wik

Photo by Paul Halmos

*SAU

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1960 Amir D. Aczel (November 6, 1950 – November 26, 2015) was an Israeli-born American lecturer in mathematics and the history of mathematics and science, and an author of popular books on mathematics and science.
Aczel was born in Haifa, Israel. Aczel's father was the captain of a passenger ship that sailed primarily in the Mediterranean Sea. When he was ten, Aczel's father taught his son how to steer a ship and navigate. This inspired Aczel's book The Riddle of the Compass.
When Aczel was 21 he studied at the University of California, Berkeley. He graduated with a BA in mathematics in 1975, and received a Master of Science in 1976. Several years later Aczel earned a Ph.D. in statistics from the University of Oregon.
Aczel taught mathematics at universities in California, Alaska, Massachusetts, Italy, and Greece. He married his wife Debra in 1984 and has one daughter, Miriam, and one stepdaughter. He accepted a professorship at Bentley College in Massachusetts where he taught classes on the history of science and the history of mathematics. While teaching at Bentley, Aczel wrote several non-technical books on mathematics and science, as well as two textbooks. His book, Fermat's Last Theorem (ISBN 978-1-56858-077-7), was a United States bestseller and was nominated for a Los Angeles Times Book Prize. Aczel appeared on CNN, CNBC, The History Channel, and Nightline. Aczel was a 2004 Fellow of the John Simon Guggenheim Memorial Foundation and Visiting Scholar in the History of Science at Harvard University (2007). In 2003 he became a research fellow at the Boston University Center for Philosophy and History of Science, and in Fall 2011 was teaching mathematics courses at University of Massachusetts Boston.
He died of cancer on Nov. 26, 2015 in Nîmes, in the south of France. He was 65. *Wik, *Obit
His most recent book was Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers

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1966 Laurent Lafforgue (born 6 November 1966, in Antony, Hauts-de-Seine) is a French mathematician.
He won 2 silver medals at International Mathematical Olympiad (IMO) in 1984 and 1985. He entered the École Normale Supérieure in 1986. In 1994 he received his Ph.D. under the direction of Gérard Laumon in the Arithmetic and Algebraic Geometry team at the Université de Paris-Sud. Currently he is a research director of CNRS, detached as permanent professor of mathematics at the Institut des Hautes Études Scientifiques (I.H.E.S.) in Bures-sur-Yvette, France.
In 2002 at the 24th International Congress of Mathematicians in Beijing, China he received the Fields Medal together with Vladimir Voevodsky. Lafforgue made outstanding contributions to Langlands' program in the fields of number theory and analysis, and in particular proved the Langlands conjectures for GLn of a function field. The crucial contribution by Lafforgue to solve this question is the construction of compactifications of certain moduli stacks of shtukas. The monumental proof is the result of more than six years of concentrated efforts.
He received the Clay Research Award in 2000. His younger brother Vincent Lafforgue is also a notable mathematician.*Wik

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DEATHS
1656 Jean-Baptiste Morin (February 23, 1583 – November 6, 1656) was a French astrologer and astronomer who attempted to solve the longitude problem using lunar observations. He was certainly not the first to propose the method but he did add one important new piece of understanding, namely he took lunar parallax into account.
Since Morin put forward his method for a longitude prize, a committee was set up by Cardinal Richelieu​ to evaluate it. Étienne Pascal, Mydorge, Beaugrand, Hérigone, J C Boulenger and L de la Porte served on the committee and they were in dispute with Morin for the five years after he made his proposal.
Morin realized that instruments had to be improved, improved methods of solving spherical triangles had to be found and better lunar tables were needed. He made some advances in these areas but his method, although theoretically sound, could not achieve either the computational or observational accuracy to succeed. Morin refused to listen to objections to his proposal.
Even while the dispute was going on, in 1638, Morin attacked Descartes saying that he had realized as soon as they met how bad his philosophy was. These disputes alienated Morin from the scientific community. He was to spend the latter part of his life isolated from other scientists although Cardinal Richelieu's successor Cardinal Mazarin did award him a pension for his work on the longitude in 1645. *SAU

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1790 James Bowdoin (7 Aug 1726, 6 Nov 1790) American founder and first president of the American Academy of Arts and Sciences (1780). He was a scientist prominent in physics and astronomy, and wrote several papers including one on electricity with Benjamin Franklin, a close friend. In one of his letters to Franklin, Bowdoin suggested the theory, since generally accepted, that the phosphorescence of the sea, under certain conditions, is due to the presence of minute animals. Bowdoin was also a political leader in Massachusetts during the American revolution (1775-83), and governor of Massachusetts (1785-87). His remarkable library of 1,200 volumes, ranged from science and math to philosophy, religion, poetry, and fiction. He left it in his will to the Academy.*TIS

Among his bequests was a gift to Harvard College for awards that are now known as the Bowdoin Prizes. His son James III donated lands from the family estate in Brunswick, Maine, as well as funds and books, to establish Bowdoin College in his honor.

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1880 Giusto Bellavitis (22 Nov 1803 in Bassano, Vicenza, Italy - 6 Nov 1880 in Tezze (near Bassano) Italy ) Bellavitis solved various mechanical problems by original methods, among them Hamilton's quaternions. He developed very personal critical observations about the calculus of probabilities and the theory of errors. He also explored physics, especially optics and electrology, and chemistry. As a young man, Bellavitis weighted the problem of a universal scientific language and published a paper on this subject in 1863. He also devoted time to the history of mathematics and, among other things, he vindicated Cataldi by attributing the invention of continued fractions to him. *SAU

Bellavitis anticipated the idea of a Euclidean vector with his notion of equipollence. Two line segments AB and CD are equipollent if they are parallel and have the same length and direction. The relation is denoted  In modern terminology, this relation between line segments is an example of an equivalence relation. The concept of vector addition was written by Bellavitis as: According to Laissant, Bellavitis published works in "arithmetic, algebra, geometry, infinitesimal calculus, probability, mechanics, physics, astronomy, chemistry, mineralogy, geodesy, geography, telegraphy, social science, philosophy, and literature.   *Wik

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1913 Sir William Henry Preece (15 Feb 1834, 6 Nov 1913) Welsh electrical engineer who was a major figure in the development and introduction of wireless telegraphy and the telephone in Great Britain. Preece's interest in applied electricity and telegraphic engineering was developed as a graduate student under Michael Faraday. For 29 years, from 1870, he was an engineer with the Post Office telegraphic system and contributed many inventions and improvements, including a railroad signaling system that increased railway safety. An early pioneer in wireless telegraphy, he originated his own system in 1892. He encouraged Guglielmo Marconi by obtaining assistance from the Post Office for his work. Preece also introduced into Great Britain the first Bell telephones. Preece was knighted in 1899. *TIS

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1946 Dunham Jackson (July 24, 1888, Bridgewater, Massachusetts – November 6, 1946) was a mathematician who worked within approximation theory, notably with trigonometrical and orthogonal polynomials. He is known for Jackson's inequality. He was awarded the Chauvenet Prize in 1935. His book Fourier Series and Orthogonal Polynomials (dated 1941) was reprinted in 2004.
Harold Bacon recalls that Jackson was an inspired writer of limericks. When Bacon purchased Jackson's "The Theory of Approximations" he took it to Jackson's office and requested he sign it, suggesting a limerick. Without any visible prethought Jackson wrote on the flyleaf:

There was a young fellow named Bacon
Whose judgement of books was mistaken
In a moment too rash
He relinquished some cash
And his faith in the Author was shaken

*Steven Krantz, Mathematical Apocrypha Redux

*Wik

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1966 Frieda Nugel (18 June 1884 in Cottbus, Brandenburg, Germany
- 6 Nov 1966 in Bad Godesberg, Bonn, Germany) was a German mathematician who was one of the first women to receive a doctorate in Germany. *SAU

She earned her PhD at Martin Luther University of Halle-Wittenberg in 1912, under the supervision of August Gutzmer.  

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1975  Samuel Stephens Kistler (March 26, 1900  – November 6, 1975) was an American scientist and chemical engineer, best known as the inventor of aerogels, one of the lightest known solid materials.

The exact circumstances of the creation of the first aerogels are not well recorded. A popular story is that they resulted from a competition between Kistler and one Charles Learned "to see if they could replace the liquid inside of a jelly jar without causing any shrinkage". Whether these experiments were performed at the College of the Pacific, still with limited facilities following the move in 1923 to the new Stockton campus, or at Stanford, where Kistler began pursuing a doctorate in 1927, is a source of some confusion. Either way, in 1931 Kistler published a paper in Nature (vol. 127, p. 741) titled "Coherent Expanded Aerogels and Jellies".

He died in Salt Lake City in November 1975, shortly before the resurgence of interest in aerogels caused by the discovery of a less time-consuming method of manufacture by researchers led by Stanislaus Teichner in France.

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1979 Alexander Weinstein (21 Jan 1897 in Saratov, Russia
- 6 Nov 1979 in Washington DC, USA)Weinstein's research covered a wide range of topics. He is famed for solving a variety of boundary value problems. For example he solved Helmholtz's problem for jets, giving the first uniqueness and existence theorems for free jets in a series of papers from 1923 to 1929. He examined boundary problems in an infinite strip, giving hydrodynamic and electromagnetic applications.
Weinstein's method was developed to give accurate bounds for eigenvalues of plates and membranes. In examining singular partial differential equations he introduced a new branch of potential theory and applied the results to many different situations including flow about a wedge, flow around lenses and flow around spindles. *SAU

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2010 Zofia Szmydt (29 July 1923 – 26 November 2010) was a Polish mathematician working in the areas of differential equations, potential theory and the theory of distributions. She was the first woman winner of the Stefan Banach Prize for mathematics in 1956.

In 1946, Szmydt graduated in mathematics from the Jagiellonian University. She defended her doctoral thesis in 1949, written under the direction of Tadeusz Ważewski.

Until 1952, Szmydt worked at the Jagiellonian University. She was a member of the Mathematical Institute of the Polish Academy of Sciences between 1949 and 1971. In 1971, she joined the University of Warsaw where she became a professor in 1984. She retired in 1993.

In her 1951 paper, Sur l’allure asymptotique des intégrales des équations différentielles ordinaires, Szmydt applied the topological method by Ważewski to generalizations of Perron's classic results on the asymptotics of systems of solutions of ordinary differential equations.

Szmydt's work on hyperbolic differential equations Sur un problème concernant un systèmes d’équations différentielles hyperboliques d’ordre arbitraire à deux variables indépendantes (1957) proposed a generalised solution for the functional differential equation, which subsumed the Darboux, Cauchy, Picard and Goursat problems as special cases. This was in later literature referred to as the Szmydt problem.

Szmydt's textbook Fourier Transformation and Linear Differential Equations (1971) was the first on the topic to be published in the Polish language. Her motivation was to present the basics of the theory of partial differential equations with a particular emphasis on distributions in limit problems of the classical equations (the heat equation, Schrödinger equation, and the Laplace and Poisson equations).

In Paley–Wiener theorems for the Mellin transformations (1990), Szmydt gave a full characterization of the space of multipliers for Mellin's distribution in terms of the Mellin transform (equivalent to the Paley–Wiener theorem) and established relationships between Schwartz and Mellin distribution spaces.

In 1956, Szmydt won the Stefan Banach Prize of the Polish Mathematical Society for her research into topological methods in nonlinear ordinary differential equations.[2] In 1973, she awarded the Commander's Cross of the Order of Polonia Restituta for her services to mathematical education.

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2021 Laszlo Belady,( April 29, 1928 in Budapest - November 6, 2021) creator of the Belady algorithm (used in optimizing the performance of computers), is born. Belady worked at IBM for 23 years in software engineering before joining the Mitsubishi Electronics Research Laboratory in the mid-1980s. He wins numerous awards, including the J.D. Warnier Prize for Excellence in Information and an IEEE fellowship. *CHM

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Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*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