Saturday, 29 April 2017

On This Day in Math - April 29

Science is built up of facts, as a house is with stones.
But a collection of facts is no more a science
than a heap of stones is a house.
~Henri Poincare

The 119th day of the year; the largest amount of money one can have in coins without being able to make change for a dollar is 119 cents. *Tanya Khovanova, Number Gossip

119 is the product of the first two primes ending with 7

119 is the sum of five consecutive primes (17 + 19 + 23 + 29 + 31).

119 is the order of the largest cyclic subgroups of the Monster group.


In 1699, the French Academy of Sciences held its first public meeting, in the Louvre. *TIS

1756 Benjamin Franklin was elected a Fellow of the Royal Society on April 29, 1756. Under the rules candidates had to be recommended in writing by three or more Fellows acquainted with him “either in person or by his Works,” the recommendation had to be approved by the Council, and the certificate publicly displayed at “ten several ordinary meetings” before balloting. Nothing more was required of foreign fellows. British (including colonial) fellows, however, had to pay an admission fee (five guineas after 1752) and a sum of £21 “for the use of the Society in lieu of Contributions,” or give bond for that amount. Only then was a British subject deemed to be a fellow and entitled to be registered in the Journal-Book and be included in the printed List of Fellows. To attend meetings and vote in elections British fellows had also to sign the obligation to “endeavour to promote the Good of the Royall Society … and to pursue the Ends for which the same was formed.” *Franklin Papers, Natl. Archives

1831 Weber is offered the position of full professor of Physics at Gottingen to fill the position of Tobias Mayer, partially on the recommendation of Gauss.

1832 Evariste Galois released from prison. On (1831)Bastille Day, Galois was at the head of a protest, wearing the uniform of the disbanded artillery, and came heavily armed with several pistols, a rifle, and a dagger. For this, he was again arrested and this time sentenced to six months in prison for illegally wearing a uniform. He was released on April 29, 1832. During his imprisonment, he continued developing his mathematical ideas.*Wik (He will be shot on the morning of May 30, and die the next day, 1832)

1854 Lincoln University, the first university for Blacks, is incorporated. Lincoln University of the Commonwealth of Pennsylvania was chartered in April 1854 as Ashmun Institute. As Horace Mann Bond, '23, the eighth president of Lincoln University, so eloquently cites in the opening chapter of his book, Education for Freedom, this was "the first institution found anywhere in the world to provide a higher education in the arts and sciences for male youth of African descent." The story of Lincoln University goes back to the early years of the 19th century and to the ancestors of its founder, John Miller Dickey, and his wife, Sarah Emlen Cresson. The Institute was re-named Lincoln University in 1866 after President Abraham Lincoln. *Lincoln University web site

1901 Math Blunder succeeds, "But a more recent, a veritably shocking, example is at hand. On April 29, 1901, a Mr. Israel Euclid Eabinovitch submitted to the Board of University Studies of the Johns Hopkins University, in conformity with the requirements for the degree of doctor of philosophy, a dissertation in which, after an introduction full of the most palpable blunders, he proceeds to persuade himself that he proves Euclid's parallel postulate by using the worn-out device of attacking it from space of three dimensions, a device already squeezed dry and discarded by the very creator of non-Euclidean geometry, John Bolyai. And his dissertation was accepted by the referees. (Science Monthly, Vol 67, page 642)

In 1878, “a monument, in memory of the great physicist, Alessandro Volta, was unveiled at Pavia. Most of the Italian Universities, and several foreign scientific societies had sent deputies to Pavia University for this event. The monument is a masterpiece of the sculptor Tantardini of Milan. The ceremony of unveiling was followed by a dignified celebration at the University, and upon that occasion the following gentlemen were elected honorary doctors of the scientific faculty: Professors Clerk Maxwell (Cambridge) and Sir W. Thomson (Glasgow); M. Dumas (Paris), Dr. W. E. Weber (Leipzig); Professors Bunsen (Heidelberg) and Helmholtz (Berlin), Dr. F. H. Neumann (Koenigsberg), and Dr. P. Riess (Berlin).”*TIS

1925 The first woman, F. R. Sabin, is elected to the National Academy of Sciences (Kane, p. 945). *VFR She was a histology professor at Johns Hopkins University. When (who) was the first woman mathematician elected?

1931 Robert Lee Moore elected to the National Academy of Sciences. *VFR


1667 John Arbuthnot (baptised April 29, 1667 – February 27, 1735), 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,m (Wikipedia) 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

1850 William Edward Story (April 29, 1850 in Boston, Massachusetts, U.S. - April 10, 1930 in Worcester, Massachusetts, U.S.) He taught at Johns Hopkins with Sylvester and then moved on to Clark University which was, during the early 1890’s, the strongest mathematics department in the country. In the 1890’s he edited the short lived Mathematical Reviews.*VFR

1854 Jules Henri Poincare (29 April 1854 – 17 July 1912) born in Nancy, France. He did important work in function theory, alge­braic geometry, number theory, algebra, celestial mechanics, differential equations, mathemat­ical physics, algebraic topology, and philosophy of mathematics. There may never be another universal mathematician like Poincar´e. *VFR His Poincaré Conjecture holds that if any loop in a given three-dimensional space can be shrunk to a point, the space is equivalent to a sphere. Its proof remains an unsolved problem in topology. He influenced cosmogony, relativity, and topology. In applied mathematics he also studied optics, electricity, telegraphy, capillarity, elasticity, thermodynamics, potential theory, quantum theory, and cosmology. He is often described as the last universalist in mathematics. He studied the three-body-problem in celestial mechanics, and theories of light and electromagnetic waves. He was a co-discoverer (with Albert Einstein and Hendrik Lorentz) of the special theory of relativity. *TIS

1872 Forest Ray Moulton (29 Apr 1872 (in a log cabin near the small town of Leroy, Michigan); 7 Dec 1952 at age 80) American astronomer who collaborated with Thomas Chamberlin in advancing the planetesimal theory of the origin of the solar system (1904). They suggested filaments of matter were ejected when a star passed close to the Sun, which cooled into tiny solid fragments, “planetesimals.” Over a very long period, grains collided and stuck together. Continued accretion created pebbles, boulders, and eventually larger bodies whose gravitational force of attraction accelerated the formation of protoplanets. (This formation by accretion is still accepted, but not the stellar origin of the planetesimals.) Moulton was first to suggest that the smaller satellites of Jupiter discovered by Nicholson and others in the early 20th century were captured asteroids, now widely accepted. *TIS

1906 Eugène Ehrhart (29 April 1906 Guebwiller – 17 January 2000 Strasbourg) was a French mathematician who introduced Ehrhart polynomials in the 1960s. Ehrhart received his high school diploma at the age of 22. He was a mathematics teacher in several high schools, and did mathematics research on his own time. He started publishing in mathematics in his 40s, and finished his PhD thesis at the age of 60. The theory of Ehrhart polynomials can be seen as a higher-dimensional generalization of Pick's theorem. *Wik

1926 Vera Nikolaevna Maslennikova (29 April 1926, Priluki, Russia - 14 August 2000) Gelfond supervised her diploma work at Moscow and Sobolev directed her Ph.D. at the Steklov Mathematical Institute. She has published more than 80 papers in the theory of partial differential equations, the mathematical hydrodynamics of rotating fluids, and in function spaces.*VFR She has worked in the field of partial differential equations, the mathematical hydrodynamics of rotating fluids, and in function spaces, having published more than one hundred and forty research papers. *Wik

1928 Laszlo Belady,( April 29, 1928 in Budapest - ) 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

1930 Yuan Wang (29 April 1930 in Lanhsi, Zhejiang province, China - )Most of Wang Yuan's research has been in the area of number theory. He looked at sieve methods and applied them to the Goldbach Conjecture. He also applied circle methods to the Goldbach Conjecture. In 1956 he published (in Chinese) On the representation of large even integer as a sum of a prime and a product of at most 4 primes in which he assumed the truth of the Riemann hypothesis and with that assumption proved that every large even integer is the sum of a prime and of a product of at most 4 primes. He also proved that there are infinitely many primes p such that p + 2 is a product of at most 4 primes. In 1957 Wang Yuan published four papers: On sieve methods and some of their applications; On some properties of integral valued polynomials; On the representation of large even number as a sum of two almost-primes; and On sieve methods and some of the related problems.*SAU

1936 Volker Strassen
(April 29, 1936 - ) is a German mathematician, a professor emeritus in the department of mathematics and statistics at the University of Konstanz. Strassen began his researches as a probabilist; his 1964 paper An Invariance Principle for the Law of the Iterated Logarithm defined a functional form of the law of the iterated logarithm, showing a form of scale invariance in random walks. This result, now known as Strassen's invariance principle or as Strassen's law of the iterated logarithm, has been highly cited and led to a 1966 presentation at the International Congress of Mathematicians.
In 1969, Strassen shifted his research efforts towards the analysis of algorithms with a paper on Gaussian elimination, introducing Strassen's algorithm, the first algorithm for performing matrix multiplication faster than the O(n3) time bound that would result from a naive algorithm. In the same paper he also presented an asymptotically-fast algorithm to perform matrix inversion, based on the fast matrix multiplication algorithm. This result was an important theoretical breakthrough, leading to much additional research on fast matrix multiplication, and despite later theoretical improvements it remains a practical method for multiplication of dense matrices of moderate to large sizes. In 1971 Strassen published another paper together with Arnold Schönhage on asymptotically-fast integer multiplication based on the fast Fourier transform; see the Schönhage–Strassen algorithm. Strassen is also known for his 1977 work with Robert M. Solovay on the Solovay–Strassen primality test, the first method to show that testing whether a number is prime can be performed in randomized polynomial time and one of the first results to show the power of randomized algorithms more generally.*Wik


1713 Francis Hauksbee the elder (baptized on 27 May 1660 in Colchester–buried in St Dunstan's-in-the-West, London on 29 April 1713.), also known as Francis Hawksbee, was an 18th-century English scientist best known for his work on electricity and electrostatic repulsion.
Initially apprenticed in 1678 to his elder brother as a draper, Hauksbee became Isaac Newton’s lab assistant. In 1703 he was appointed curator, instrument maker and experimentalist of the Royal Society by Newton, who had recently become president of the society and wished to resurrect the Royal Society’s weekly demonstrations.
Until 1705, most of these experiments were air pump experiments of a mundane nature, but Hauksbee then turned to investigating the luminosity of mercury which was known to emit a glow under barometric vacuum conditions.
By 1705, Hauksbee had discovered that if he placed a small amount of mercury in the glass of his modified version of Otto von Guericke's generator, evacuated the air from it to create a mild vacuum and rubbed the ball in order to build up a charge, a glow was visible if he placed his hand on the outside of the ball. This glow was bright enough to read by. It seemed to be similar to St. Elmo's Fire. This effect later became the basis of the gas-discharge lamp, which led to neon lighting and mercury vapor lamps. In 1706 he produced an 'Influence machine' to generate this effect. He was elected a Fellow of the Royal Society the same year.
Hauksbee continued to experiment with electricity, making numerous observations and developing machines to generate and demonstrate various electrical phenomena. In 1709 he published Physico-Mechanical Experiments on Various Subjects which summarized much of his scientific work.
In 1708, Hauksbee independently discovered Charles' law of gases, which states that, for a given mass of gas at a constant pressure, the volume of the gas is proportional to its temperature.
The Royal Society Hauksbee Awards, awarded in 2010, were given by the Royal Society to the “unsung heroes of science, technology, engineering and mathematics.” *Wik

1862 John Edward Campbell (27 May 1862, Lisburn, Ireland – 1 October 1924, Oxford, Oxfordshire, England) is remembered for the Campbell-Baker-Hausdorff theorem which gives a formula for multiplication of exponentials in Lie algebras. *SAU His 1903 book, Introductory Treatise on Lie's Theory of Finite Continuous Transformation Groups, popularized the ideas of Sophus Lie among British mathematicians.
He was elected a Fellow of the Royal Society in 1905, and served as President of the London Mathematical Society from 1918 to 1920. *Wik  *Renaissance Mathematicus

1864 Charles-Julien Brianchon (19 Dec 1783, 29 Apr 1864 at age 80) French mathematician who published a geometrical theorem (named as Brianchon's theorem) while a student (1806). He showed that in any hexagon formed of six tangents to a conic, the three diagonals meet at a point. (Conics include circles, ellipses, parabolas, and hyperbolas.) In fact, this theorem is simply the dual of Pascal's theorem which was proved in 1639. After graduation, Brianchon became a lieutenant in artillery fighting in Napoleon's army until he left active service in 1813 due to ill health. His last work in mathematics made the first use of the term "nine-point circle." By 1823, Brianchon's interests turned to teaching and to chemistry. *TIS

1872 Jean-Marie-Constant Duhamel (5 Feb 1797, 29 Apr 1872 at age 75) French mathematician and physicist who proposed a theory dealing with the transmission of heat in crystal structures based on the work of the French mathematicians Jean-Baptiste-Joseph Fourier and Siméon-Denis Poisson. *TIS

1894 Giuseppe Battaglini (11 Jan 1826 in Naples, Kingdom of Naples and Sicily (now Italy) - 29 Apr 1894 in Naples, Italy ) Some of Battaglini's results have proved significant. For example, in his doctoral dissertation of 1868, Klein introduced a classification scheme for second-degree line complexes based on Battaglini's earlier work. However, his main importance is his modern approach to mathematics which played a major role in invigorating the Italian university system, particularly in his efforts to bring the non-Euclidean geometry of Lobachevsky and Bolyai to the Italian speaking world. Jules Hoüel played a similar role for non-Euclidean geometry in the French speaking world and the correspondence between the two (see [6]) provides a vivid picture of the reactions of both the French and the Italian mathematical communities against the non-Euclidean geometries. Battaglini and Hoüel also exchanged ideas relating to mathematical education in various European countries. In particular they debated the use of Euclid's Elements as a textbook for teaching elementary geometry in schools. *SAU

1916 – Jørgen Pedersen Gram (June 27, 1850 – April 29, 1916) was a Danish actuary and mathematician who was born in Nustrup, Duchy of Schleswig, Denmark and died in Copenhagen, Denmark.
Important papers of his include On series expansions determined by the methods of least squares, and Investigations of the number of primes less than a given number. The mathematical method that bears his name, the Gram–Schmidt process, was first published in the former paper, in 1883. The Gramian matrix is also named after him.
For number theorists his main fame is the series for the Riemann zeta function (the leading function in Riemann's exact prime-counting function). Instead of using a series of logarithmic integrals, Gram's function uses logarithm powers and the zeta function of positive integers. It has recently been supplanted by a formula of Ramanujan that uses the Bernoulli numbers directly instead of the zeta function.
Gram was the first mathematician to provide a systematic theory of the development of skew frequency curves, showing that the normal symmetric Gaussian error curve was but one special case of a more general class of frequency curves.
He died after being struck by a bicycle.*Wik

1951 Ludwig Josef Johann Wittgenstein (26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947. In his lifetime he published just one book review, one article, a children's dictionary, and the 75-page Tractatus Logico-Philosophicus (1921). In 1999 his posthumously published Philosophical Investigations (1953) was ranked as the most important book of 20th-century philosophy, standing out as "...the one crossover masterpiece in twentieth-century philosophy, appealing across diverse specializations and philosophical orientations". Bertrand Russell described him as "the most perfect example I have ever known of genius as traditionally conceived, passionate, profound, intense, and dominating". *Wik He died three days after his birthday. He is buried in a cemetery off Huntington Road in Cambridge, UK.

1970 Paul Finsler (born 11 April 1894, in Heilbronn, Germany,- 29 April 1970 in Zurich, Switzerland)Finsler did his undergraduate studies at the Technische Hochschule Stuttgart, and his graduate studies at the University of Göttingen, where he received his Ph.D. in 1919 under the supervision of Constantin Carathéodory. He joined the faculty of the University of Zurich in 1927, and was promoted to ordinary professor there in 1944.
Finsler's thesis work concerned differential geometry, and Finsler spaces were named after him by Élie Cartan in 1934. The Hadwiger–Finsler inequality, a relation between the side lengths and area of a triangle in the Euclidean plane, is named after Finsler and his co-author Hugo Hadwiger. Finsler is also known for his work on the foundations of mathematics, developing a non-well-founded set theory with which he hoped to resolve the contradictions implied by Russell's paradox.
In mathematics, the Hadwiger–Finsler inequality is a result on the geometry of triangles in the Euclidean plane, named after the mathematicians Hugo Hadwiger and Paul Finsler. It states that if a triangle in the plane has side lengths a, b and c and area A, then
a^{2} + b^{2} + c^{2} \geq (a - b)^{2} + (b - c)^{2} + (c - a)^{2} + 4 \sqrt{3} A \quad \mbox{(HF)}.
Weitzenböck's inequality is a straightforward corollary of the Hadwiger–Finsler inequality: if a triangle in the plane has side lengths a, b and c and area A, then
a^{2} + b^{2} + c^{2} \geq 4 \sqrt{3} A \quad \mbox{(W)}.
Weitzenböck's inequality can also be proved using Heron's formula, by which route it can be seen that equality holds in (W) if and only if the triangle is an equilateral triangle, i.e. a = b = c.

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

Friday, 28 April 2017

On This Day in Math - April 28

One of the principal objects of theoretical research
in my department of knowledge
is to find the point of view from which
the subject appears in its greatest simplicity.
Willard Gibbs (1839 - 1903)

118 is the smallest n such that the range n, n + 1, ... 4n/3 contains at least one prime from each of these forms: 4x + 1, 4x - 1, 6x + 1 and 6x - 1.

118 is the smallest even number not differing by one or a prime number from one of its prime neighbors.
*Prime Curios


1664 Trinity College, Cambridge awards a scholarship to Isaac Newton to study for his Master's Degree, thus ending his period as a lowly sizar earning his tuition by cleaning up after wealthier students. Within months his formal education would be put on hold as the college closed under the assault of the plague.

1673 Leeuwenhoeck writes his first letter to the Royal Society, which would be published the next month, May 19, in Philosophical Transactions number 94, "A Specimen of Some Observations Made by a Microscope, Contrived by M. Leewenhoeck in Holland, Lately Communicated by Dr. Regnerus de Graaf." Constantijn Huygens, who lived not far from Delft, visited Leeuwenhoek and read the letter. A week before Leeuwenhoek sent it, Huygens sent his own letter to Robert Hooke that acted as a cover letter and recommendation similar to de Graaf's letter in April. Over the rest of Leeuwenhoeck's life, the Society would publish 116 articles containing excerpts from 113 letters. *lensonleeuwenhoek

1686 Newton shows the handwritten copy of his Principia to the Royal Society. *VFR
 28 April 1686 "Dr. Vincent presented a manuscript treatise entitled Philosophiae Naturalis principia mathematica, and dedicated to the Society by Mr. Isaac Newton,..." Minutes of the RS written by Halley clerk to the Society. (It was actually only the manuscript of Book I) *Thony Christie

1693 Leibniz, in a letter to L’Hopital, explains his discovery of determinants. This work was fifty years before that of Cramer who was the real driving force in the development of determinants. Leibniz’s work had no influence because it was not published until 1850 in his Mathematische Schriften. [Smith, Source Book, p. 267] *VFR
Leibniz was convinced that good mathematical notation was the key to progress so he experimented with different notation for coefficient systems. His unpublished manuscripts contain more than 50 different ways of writing coefficient systems which he worked on during a period of 50 years beginning in 1678. Only two publications (1700 and 1710) contain results on coefficient systems and these use the same notation as in his letter to de l'Hôpital mentioned above.
Leibniz used the word 'resultant' for certain combinatorial sums of terms of a determinant. He proved various results on resultants including what is essentially Cramer's rule. He also knew that a determinant could be expanded using any column - what is now called the Laplace expansion. As well as studying coefficient systems of equations which led him to determinants, Leibniz also studied coefficient systems of quadratic forms which led naturally towards matrix theory. In the 1730's Maclaurin wrote Treatise of algebra although it was not published until 1748, two years after his death. It contains the first published results on determinants proving Cramer's rule for 2 cross 2 and 3 cross 3 systems and indicating how the 4 cross 4 case would work. Cramer gave the general rule for n cross n systems in his book Introduction to the analysis of algebraic curves (1750). It arose out of a desire to find the equation of a plane curve passing through a number of given points. The rule appears in an Appendix to the book but no proof is given] *SAU (edited and corrected with suggestions by Dave Renfro)
Dave adds:   a 715 page book (xxiii + 680 + xii pages), which is freely available on the internet. Cramer's rule itself appears in Appendix 2 (pp. 657-676). Cramer's book itself was motivated by Newton's work in classifying cubic curves, and I believe he was one of three mathematicians that devoted an extensive study to Newton's classification in the 1700s. (I don't remember who the other two were, but I believe one of them was Euler.) There is an excellent annotated and translation of Newton's work published in 1860 and freely available on the internet:

"Sir Isaac Newton's Enumeration of Lines of the Third Order, Generation of
Curves by Shadows, Organic Description of Curves, and Construction of
Equations by Curves", Translated from the Latin, with notes and examples,
by C.R.M. Talbot, 1860.
Thanks again to Dave for the corrections.

1817 Gauss wrote the astronomer H. W. M. Olbers, “I am becoming more and more convinced that the necessity of our [Euclidean] geometry cannot be proved, at least not by human intellect nor for the human intellect.” [G. E. Martin, Foundations of Geometry and the Non-Euclidean Plane, p. 306] *VFR

1983 Greece issued a stamp portraying Archimedes and his Hydrostatic Principle

1897 In a letter to Fuchs, Dedekind expressed skepticism of a tale about Gauss attempting to light his pipe with a copy of his DA
Schering in Gottingen in response to a note from Fuchs that he had found materials related to Guass' Disquisitiones Arithmetica in the papers of Dirichlet had described a story that he had shared with Kronecker a decade before,
"The piece of Guass's Disquisitiones Arithmeticiae, which is found among Dirichlet's papers, is probably that portion which, as Dirichlet told me himself, he saved from the hand of Gauss when the latter lit his pipe with his manuscript of the Disquisitiones Arithmeticae on the day of his doctoral jubilee."
Dedekind reasoned, if Guass had saved the paper for fifty years he obviously valued it, and that if the anecdote were true, Dirichlet surely would have shared it with him as well.
*Uta Merzbach, An Early Version of Gauss's Disquisitiones Arithmeticae, Mathematical Perspectives, 1981

2004 At 11:50 AM a paper was submitted electronically to the American Mathematical Monthly which purports to be the shortest journal entry ever, essentially two words," n2 + 2 can". After some correspondence back and forth, (the journal suggested, "a line or two of explanatin might help") the paper was accepted as a "filler" in the January 2005 issue. *

2012 Mountain View, Ca—January 19, 2012—
The Computer History Museum (CHM), the world’s leading institution exploring the history of computing and its ongoing impact on society, today announced its 2012 Fellow Award honorees: Edward A. Feigenbaum, pioneer of artificial intelligence and expert systems; Steve Furber and Sophie Wilson, chief architects of the ARM processor architecture; and Fernando J. Corbató, pioneer of timesharing and the Multics operating system. The four Fellows will be inducted into the Museum’s Hall of Fellows on Saturday, April 28, 2012, at a formal ceremony where Silicon Valley insiders, technology leaders, and Museum supporters will gather to celebrate the accomplishments of the Fellows and their impact on society. This year’s celebration commemorates the 25th Anniversary of the Fellow Awards and will reunite pioneers from more than two decades. *CHM

1765 Sylvestre François Lacroix (April 28, 1765, Paris – May 24, 1843, Paris) was a French mathematician. He displayed a particular talent for mathematics, calculating the motions of the planets by the age of 14. In 1782 at the age of 17 he became an instructor in mathematics at the École Gardes de Marine in Rochefort, France. He returned to Paris and taught courses in astronomy and mathematics at the Lycée. In 1787 he was the co-winner of that year's Grand Prix of the French Académie des Sciences, but was never awarded the prize. The same year the Lycée was abolished and he again moved to the provinces.
In Besançon he taught course in mathematics, physics, and chemistry at the École d'Artillerie. In 1793 he became examiner of the Artillery Corps, replacing Pierre-Simon Laplace in the post. By 1794 he was aiding his old instructor, Gaspard Monge, in creating material for a course on descriptive geometry. In 1799 he was appointed professor at the École Polytechnique. Lacroix produced most of his texts for the sake of improving his courses. The same year he was voted into the newly formed Institut National des Sciences et des Arts. In 1812 he began teaching at the Collège de France, and was appointed chair of mathematics in 1815.
During his career he produced a number of important textbooks in mathematics. Translations of these books into the English language were used in British universities, and the books remained in circulation for nearly 50 years. In 1812 Babbage set up The Analytical Society for the translation of Differential and Integral Calculus and the book was translated into English in 1816 by George Peacock. *Wik He coined the term “analytic geometry.” *VFR

1773 Robert Woodhouse (28 April 1773 – 23 December 1827) was an English mathematician. He was born at Norwich and educated at Caius College, Cambridge, (BA 1795) of which society he was subsequently a fellow. He was elected a Fellow of the Royal Society in December 1802.
His earliest work, entitled the Principles of Analytical Calculation, was published at Cambridge in 1803. In this he explained the differential notation and strongly pressed the employment of it; but he severely criticized the methods used by continental writers, and their constant assumption of non-evident principles. This was followed in 1809 by a trigonometry (plane and spherical), and in 1810 by a historical treatise on the calculus of variations and isoperimetrical problems. He next produced an astronomy; of which the first book (usually bound in two volumes), on practical and descriptive astronomy, was issued in 1812, and the second book, containing an account of the treatment of physical astronomy by Pierre-Simon Laplace and other continental writers, was issued in 1818.
He became the Lucasian Professor of Mathematics in 1820, and subsequently the Plumian professor in the university. As Plumian Professor he was responsible for installing and adjusting the transit instruments and clocks at the Cambridge Observatory. He held that position until his death in 1827.
On his death in Cambridge he was buried in Caius College Chapel.*Wik He was interested in the “metaphysics of the calculus,” i.e., questions such as the proper theoretical foundations of the calculus, the role of geometric and analytic methods, and the importance of notation. *VFR

1774 Francis Baily (28 April 1774 – 30 August 1844) was an English astronomer. He is most famous for his observations of 'Baily's beads' during an eclipse of the Sun. Bailey was also a major figure in the early history of the Royal Astronomical Society, as one of the founders and president four times.
Baily was born at Newbury in Berkshire in 1774 to Richard Baily. After a tour in the unsettled parts of North America in 1796–1797, his journal of which was edited by Augustus de Morgan in 1856, Baily entered the London Stock Exchange in 1799. The successive publication of Tables for the Purchasing and Renewing of Leases (1802), of The Doctrine of Interest and Annuities (1808), and The Doctrine of Life-Annuities and Assurances (1810), earned him a high reputation as a writer on life-contingencies; he amassed a fortune through diligence and integrity and retired from business in 1825, to devote himself wholly to astronomy.
His observations of "Baily's Beads", during an annular eclipse of the sun on 15 May 1836, at Inch Bonney in Roxburghshire, started the modern series of eclipse expeditions. The phenomenon, which depends upon the irregular shape of the moon's limb, was so vividly described by him as to attract an unprecedented amount of attention to the total eclipse of 8 July 1842, observed by Baily himself at Pavia. *Wik

1831 Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist, best known for the seminal energy physics textbook Treatise on Natural Philosophy, which he co-wrote with Kelvin, and his early investigations into knot theory, which contributed to the eventual formation of topology as a mathematical discipline. His name is known in Graph theory mainly for Tait's conjecture.*Wik (His conjecture was proved wrong by counterexample in 1946 by W. T. Tutte. The problem is related to the four color theorem.) He helped develop quaternions, an advanced algebra that gave rise to vector analysis and was instrumental in the development of modern mathematical physics. *TIS
Below is The First Seven Orders of Knottiness"-table compiled by P.G. Tait in 1884 with a big hat-tip to Ben Gross@bhgross144 .

1854 Phoebe Sarah Hertha Ayrton (28 April 1854 – 23 August 1923), was a British engineer, mathematician, physicist, and inventor. Known in adult life as Hertha Ayrton, born Phoebe Sarah Marks, she was awarded the Hughes Medal by the Royal Society for her work on electric arcs and ripples in sand and water.
In 1880, Ayrton passed the Mathematical Tripos, but Cambridge did not grant her an academic degree because, at the time, Cambridge gave only certificates and not full degrees to women. Ayrton passed an external examination at the University of London, which awarded her a Bachelor of Science degree in 1881.
In 1899, she was the first woman ever to read her own paper before the Institution of Electrical Engineers (IEE). Her paper was entitled "The Hissing of the Electric Arc". Shortly thereafter, Ayrton was elected the first female member of the IEE; the next woman to be admitted to the IEE was in 1958. She petitioned to present a paper before the Royal Society but was not allowed because of her sex and "The Mechanism of the Electric Arc" was read by John Perry in her stead in 1901. Ayrton was also the first woman to win a prize from the Society, the Hughes Medal, awarded to her in 1906 in honour of her research on the motion of ripples in sand and water and her work on the electric arc. By the late nineteenth century, Ayrton's work in the field of electrical engineering was recognised more widely, domestically and internationally. At the International Congress of Women held in London in 1899, she presided over the physical science section. Ayrton also spoke at the International Electrical Congress in Paris in 1900. Her success there led the British Association for the Advancement of Science to allow women to serve on general and sectional committees. *Wik

1868 Georgy Fedoseevich Voronoy (also voronoi)(28 April 1868 – 20 November 1908) introduced what are today called Voronoi diagrams or Voronoi tessellations. Today they have wide applications to the analysis of spatially distributed data, so have become important in topics such as geophysics and meteorology. Although known under different names, the notion occurs in condensed matter physics, and in the study of Lie groups. (Two dimensional diagrams of Voronoi type were considered as early at 1644 by René Descartes and were used by Dirichlet (1850) in the investigation of positive quadratic forms. They were also studied by Voronoi (1907), who extended the investigation of Voronoi diagrams to higher dimensions. They find widespread applications in areas such as computer graphics, epidemiology, geophysics, and meteorology. A particularly notable use of a Voronoi diagram was the analysis of the 1854 cholera epidemic in London, in which physician John Snow determined a strong correlation of deaths with proximity to a particular (and infected) water pump on Broad Street. *Mathworld)

1900 Jan Hendrik Oort (28 April 1900 – 5 November 1992) was a Dutch astronomer who made significant contributions to the understanding of the Milky Way and who was a pioneer in the field of radio astronomy. His New York Times obituary called him “one of the century's foremost explorers of the universe;” the European Space Agency website describes him as, “one of the greatest astronomers of the 20th century,” and states that he “revolutionised astronomy through his ground-breaking discoveries.” In 1955, Oort’s name appeared in Life Magazine’s list of the 100 most famous living people. He has been described as “putting the Netherlands in the forefront of postwar astronomy.”

Oort determined that the Milky Way rotates and overturned the idea that the Sun was at its center. He also postulated the existence of the mysterious invisible dark matter in 1932, which is believed to make up roughly 84.5% of the total matter in the Universe and whose gravitational pull causes “the clustering of stars into galaxies and galaxies into connecting strings of galaxies.” He discovered the galactic halo, a group of stars orbiting the Milky Way but outside the main disk. Additionally Oort is responsible for a number of important insights about comets, including the realization that their orbits “implied there was a lot more solar system than the region occupied by the planets.”

The Oort cloud, the Oort constants, and the Asteroid, 1691 Oort, were all named after him. *Wik

1906 Kurt Godel (April 28, 1906 – January 14, 1978) Austrian-born US mathematician, logician, and author of Gödel's proof. He is best known for his proof of Gödel's Incompleteness Theorems (1931) He proved fundamental results about axiomatic systems showing in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system. In particular the consistency of the axioms cannot be proved. This ended a hundred years of attempts to establish axioms to put the whole of mathematics on an axiomatic basis.*TIS

1906 Richard Rado FRS(28 April 1906 – 23 December 1989) was a Jewish German mathematician. He earned two Ph.D.s: in 1933 from the University of Berlin, and in 1935 from the University of Cambridge. He was interviewed in Berlin by Lord Cherwell for a scholarship given by the chemist Sir Robert Mond which provided financial support to study at Cambridge. After he was awarded the scholarship, Rado and his wife left for the UK in 1933. He made contributions in combinatorics and graph theory. He wrote 18 papers with Paul Erdős. In 1964, he discovered the Rado graph (The Rado graph contains all finite and countably infinite graphs as induced subgraphs..)
In 1972, he was awarded the Senior Berwick Prize*Wik

1923 Fritz Joseph Ursell FRS (28 April 1923 – 11 May 2012) was a British mathematician noted for his contributions to fluid mechanics, especially in the area of wave-structure interactions.[5] He held the Beyer Chair of Applied Mathematics at the University of Manchester from 1961–1990, was elected Fellow of the Royal Society in 1972 and retired in 1990.
Ursell came to England as a refugee in 1937 from Germany. From 1941 to 1943 he studied at Trinity College, Cambridge, graduating with a bachelor degree in mathematics. *Wik

1843 William Wallace (23 September 1768, Dysart—28 April 1843, Edinburgh) worked on geometry and discovered the (so-called)
Simson line of a triangle.*SAU In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. The line through these points is the Simson line of P, named for Robert Simson. The concept was first published, however, by William Wallace.*Wik
 Mary Sommerville was one of his students.  He succeeded John Playfair as Math Chair in Edinburgh. He also invented a complicated type of pantograph called the eidograph.

1903 Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American mathematical physicist and chemist known for contributions to vector analysis and as one of the founders of physical chemistry. In 1863, He was awarded Yale University's first engineering doctorate degree. His major work was in developing thermodynamic theory, which brought physical chemistry from an empirical inquiry to a deductive science. In 1873, he published two papers concerning the fundamental nature of entropy of a system, and established the "thermodynamic surface," a geometrical and graphical method for the analysis of the thermodynamic properties of substances. His famous On the Equilibrium of Homogeneous Substances, published in 1876, established the use of "chemical potential," now an important concept in physical chemistry. *TIS
He is buried at the  Grove Street Cemetery in New Haven Connecticut, USA.

1946 Louis Jean-Baptiste Alphonse Bachelier (March 11, 1870 – April 28, 1946) was a French mathematician at the turn of the 20th century. He is credited with being the first person to model the stochastic process now called Brownian motion, which was part of his PhD thesis The Theory of Speculation, (published 1900).
His thesis, which discussed the use of Brownian motion to evaluate stock options, is historically the first paper to use advanced mathematics in the study of finance. Thus, Bachelier is considered a pioneer in the study of financial mathematics and stochastic processes. *Wik Bachelier is now recognised internationally as the father of financial mathematics, but this fame, which he so justly deserved, was a long time coming. The Bachelier Society, named in his honour, is the world-wide financial mathematics society and mathematical finance is now a scientific discipline of its own. The Society held its first World Congress on 2000 in Paris on the hundredth anniversary of Bachelier's celebrated PhD Thesis, Théorie de la Spéculation *SAU

1986 R H Bing (October 20, 1914, Oakwood, Texas – April 28, 1986, Austin, Texas) He wrote papers on general topology, particularly on metrization; planar sets where he examined in particular planar webs, cuttings and planar embeddings. He worked on topological classification of the 2-sphere, the 3-sphere, pseudo arcs, simple closed curves and Hilbert space. He studied partitions and decompositions of locally connected continua. He considered several different aspects of 3-manifolds including decompositions, maps, approximating surfaces, recognizing tameness, triangulation and the Poincaré conjecture. *SAU Oakwood had a population of 471 at the 2000 census.

1991 Paul Ernest Klopsteg (May 30, 1889 – April 28, 1991) was an American physicist. The asteroid 3520 Klopsteg was named after him and the yearly Klopsteg Memorial Award was founded in his memory.
He performed ballistics research during World War I at the US Army's Aberdeen Proving Grounds in Maryland. He applied his knowledge of ballistics to the study of archery.
He was director of research at Northwestern University Technical Institution. From 1951 through 1958 he was an associate director of the National Science Foundation and was president of the American Association for the Advancement of Science from 1958 through 1959.*Wik

1999 Arthur Leonard Schawlow (May 5, 1921 – April 28, 1999) was an American physicist. He is best remembered for his work on lasers, for which he shared the 1981 Nobel Prize in Physics with Nicolaas Bloembergen and Kai Siegbahn.
In 1991 the NEC Corporation and the American Physical Society established a prize: the Arthur L. Schawlow Prize in Laser Science. The prize is awarded annually to "candidates who have made outstanding contributions to basic research using lasers."
In 1951, he married Aurelia Townes, younger sister to physicist Charles Hard Townes, and together they had three children; Arthur Jr., Helen, and Edith. Arthur Jr. was autistic, with very little speech ability.
Schawlow and Professor Robert Hofstadter at Stanford, who also had an autistic child, teamed up to help each other find solutions to the condition. Arthur Jr. was put in a special center for autistic individuals, and later Schawlow put together an institution to care for people with autism in Paradise, California. It was later named the Arthur Schawlow Center in 1999, shortly before his death on the 29th of April 1999.
Schawlow died of leukemia in Palo Alto, California.*Wik

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

Thursday, 27 April 2017

On This Day in Math - April 27

I believe that we do not know anything for certain,
but everything probably.
~ Christiaan Huygens

The 117th day of the year; 117 can be written as the difference of prime squares (112 - 22) or prime cubes (53 - 23). *Prime Curios (Can you find another number which can be expressed as both the difference of squared primes and cubed primes?)

117 is the smallest possible length for the longest side of a Heronian tetrahedron (one whose sides are all integers, and all surface areas and volume are rational). The other edges are 51, 52, 53, 80, & 84. (Are the areas / volume integral?)


1521 In the Philippines, Magellan became involved in a tribal war in which he was killed. His remaining ships returned to Spain in September of 1522 without their leader. *VFR

1657 Christiaan Huygens published De ratiociniis in ludo aleae. *VFR [Download of English version printed in London in pdf]

1740 The French Academie des Sciences announced that their prize on the ebb and flow of the tides would be shared between Leonhard Euler, Daniel Bernoulli, Antoine Cavalleri, one of the last of the Cartesians, and Colin Maclaurin, then Professor of Mathematics at the University of Edinburgh. [Niccol´o Guiciardini, The Development of Newtonian Calculus in Britain 1700–1800 (1989), p. 69.] *VFR

1783 In a letter to A. M. Lorgna, Gian Francesco Malfatti gave the polar equation concerning the squaring of the circle. [DSB 9, 55] Does this refer to the polar equation of the spiral of Archimedes, r = aθ? *VFR

In 1871, the American Museum of Natural History opened to the public in New York City. With a series of exhibits, the Museum's collection Went on view for the first time in the Central Park Arsenal, the Museum's original home, on the eastern side of Central Park. The museum began from the efforts of Albert Smith Bickmore, one-time student of Harvard zoologist Louis Agassiz, who was successful in his proposal to create a natural history museum in Central Park, New York City, with the support of William E. Dodge, Jr., Theodore Roosevelt, Sr., Joseph Choate, and J. Pierpont Morgan. The Governor of New York, John Thompson Hoffman, signed a bill officially creating the American Museum of Natural History on 6 Apr 1869. *TIS

1865 King George V of Hanover visited Gottingen and ordered a commemorative plate placed at the room in which Gauss had died ten years before.

In 1895, Professor Charles F. Marvin, a future chief of the Weather Bureau, began experimenting with kites for routine use in the Bureau. In 1896 he perfected his kite meteorograph, an instrument capable of measuring and recording temperature, pressure and humidity. These measurements were recorded by pens tracings on paper, or on a smoked copper sheet, which was attached to a clock rotated drum. i
n 1898, the first Weather Bureau kite was launched from Topeka, Kansas, and by the end of the year, 16 additional kite stations were attempting daily, early morning, simultaneous observations. The kites were large "box types" with dimensions of 8 feet long, 7 feet wide and 3 feet high. As many as seven kites would be attached to the kite wire during and observation. These kites were placed at regular intervals with the second 1500 feet behind the first, the third 2000 feet behind the second and from there on a spacing of 2500 feet.*TIS

1961 Patent issued for multilayer circuit boards.

1962 The Netherlands issued a stamp showing Christiaan Huygens’ Pendulum
Clock as pictured by van Ceulen. [Scott #B365] *VFR

1994 U.S. Companies Get Aid From Government
The Clinton administration unveils a multimillion-dollar program to aid U.S. companies that make flat-panel display screens as part of an effort to help the industry stay afloat in light of Japanese domination of 95 percent of the industry. The funding comes partly from the Defense Department, for use of flat screens on military equipment. The flat-panel display market had previously been limited to laptop computers. *CHM

2002 The last successful reception of telemetry was received from Pioneer 10 on April 27, 2002; subsequent signals were barely strong enough to detect, and provided no usable data. Pioneer 10 was launched in 1972 . Pioneer 10 crossed the orbit of Saturn in 1976 and the orbit of Uranus in 1979.
On June 13, 1983, Pioneer 10 crossed the orbit of Neptune, the outermost planet at the time, and so became the first man-made object to leave the proximity of the major planets of the solar system. The final, very weak signal from Pioneer 10 was received on January 23, 2003 when it was 12 billion kilometers (80 AU) from Earth. *Wik


1791 Samuel Finley Breese Morse (27 Apr 1791; 2 Apr 1872 at age 81) was an American artist and inventor who is famous for developing the Morse Code (1838) and independently perfecting an electric telegraph (1832-35). He spent the first part of his life as a portrait artist, and did not turn to science until 1832, when he was past his 40th birthday. He was returning to America from a tour of Europe, when he met Charles T. Jackson on the boat, who inspired him about newly discovered electromagnets. From that point, Morse worked to develop apparatus for electrical communications. Backed by Congress, he erected a line spanning 40 miles between Baltimore, Maryland and Washington D.C. which had its first trial on 23 May 1843. It was ready for public use on 1 Apr 1845. *TIS

1837 Paul Albert Gordan,(27 April 1837 – 21 December 1912) king of the invariant theorists, (died: 1912). He found simpler proofs that π and e are transcendental. Emmy Noether, the first woman to get a doctorate in Germany, was his student. *VFR

1843 Felix Muller He compiled the earliest mathematical calendar (that I know of)*VFR. Interests were in the history of mathematical terminology. His advisors were Weierstrass and Kummer.

1875 (6th duke) (Louis-César-Victor-) Maurice de Broglie (27 Apr 1875; died 14 Jul 1960 at age 85.) a French physicist who made many contributions to the study of X rays. While in the navy (1895-1908), he first distinguished himself by installing the first French shipboard wireless. From 1912, his chief interest was X-ray spectroscopy. His “method of the rotating crystal” was an application of Bragg's “focussing effect” to eliminate spurious spectral lines. De Broglie discovered the third L absorption edge (1916), which led to the exploration of “corpuscular spectra.” During 1921-22, he worked with his brother Louis to refine Bohr's specification of the substructure of the various atomic shells. He also did pioneer work in nuclear physics and cosmic radiation.*TIS

1920 Mark Alexandrovich Krasnosel'skii (April 27, 1920, Starokostiantyniv – February 13, 1997, Moscow) was a Soviet, Russian and Ukrainian mathematician renowned for his work on nonlinear functional analysis and its applications. *Wik


1936 Karl Pearson, (27 March 1857 in London, England - 27 April 1936 in Coldharbour, Surrey, England) English mathematician, one of the founders of modern statistics. Pearson's lectures as professor of geometry evolved into The Grammar of Science (1892), his most widely read book and a classic in the philosophy of science. Stimulated by the evolutionary writings of Francis Galton and a personal friendship with Walter F.R. Weldon, Pearson became immersed in the problem of applying statistics to biological problems of heredity and evolution. The methods he developed are essential to every serious application of statistics. From 1893 to 1912 he wrote a series of 18 papers entitled Mathematical Contributions to the Theory of Evolution, which contained much of his most valuable work, including the chi-square test of statistical significance. *TIS l There is a plaque in the church at Crambe in No. Yorkshire where he was born and many of his family are buried. 

1978 Guido Stampacchia (March 26, 1922 - April 27, 1978) was a 20th century mathematician. Stampacchia was active in research and teaching throughout his career. He made key contributions to a number of fields, including calculus of variation and differential equations. In 1967 Stampacchia was elected President of the Unione Matematica Italiana. It was about this time that his research efforts shifted toward the emerging field of variational inequalities, which he modeled after boundary value problems for partial differential equations.
Stampacchia accepted the position of Professor Mathematical Analysis at the University of Rome in 1968 and returned to Pisa in 1970. He suffered a serious heart attack in early 1978 and died of heart arrest on April 27 of that year *Wik

1999 Rolf William Landauer (4 Feb 1927; 27 Apr 1999) German-born American physicist known for his formulation of Landauer's principle concerning the energy used during a computer's operation. Whenever the machine is resetting for another computation, bits are flushed from the computer's memory, and in that electronic operation, a certain amount of energy is lost. Thus, when information is erased, there is an inevitable "thermodynamic cost of forgetting," which governs the development of more energy-efficient computers. While engineers dealt with practical limitations of compacting ever more circuitry onto tiny chips, Landauer considered the theoretical limit, that if technology improved indefinitely, how soon will it run into the insuperable barriers set by nature?*TIS

1999 Mark David Weiser (23 Jul 1952, 27 Apr 1999 at age 46) American computer scientist and visionary who was the chief technology officer at XEROX PARC, and is remembered for developed the pioneering idea for what he referred to as “ubiquitous computing.” He coined that term in 1988 to describe a future in which personal computers will be replaced with tiny computers embedded in everyday “smart” devices (everyday items such as coffeepots and copy machines) and their connection via a network. He said, “First were mainframes, each shared by lots of people. Now we are in the personal computing era, person and machine staring uneasily at each other across the desktop. Next comes ubiquitous computing, or the age of calm technology, when technology recedes into the background of our lives.” He died at age 46, only six weeks after being diagnosed as having gastric cancer. *TIS

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

Wednesday, 26 April 2017

On This Day in Math - April 26

Mathematics is like childhood diseases. The younger you get it, the better.
~Arnold Sommerfeld

The 116th day of the year; 116! + 1 is prime! *Prime Curios (Students might investigate how often n!+1 is prime)
116^2 + 1 is prime

The number 1 appears 116 times in the first 1000 digits of pi. Thanks to *Math Year-Round ‏@MathYearRound

Impress your History teacher, the 100 Years war between France and England..... lasted 116 years.

and Jiroemon Kimura died in 2013 in Japan. He was 116 years old.  Two years later his record was broken by an even older Japanese citizen who died.


1514 Nicolaus Copernicus (1473-1543) made his first observation of Saturn. Copernicus later proposed that the sun is stationary and that the Earth and the planets move in circular orbits around it. * Saturn_Project

1760 Euler was asked to tutor the niece of Frederick the Great, the Princess of Anhalt-Dessau. Euler wrote over 200 letters to her in the early 1760s. On this date he sent the third of these letters. The letter covered the physics of sound and he gave a speed of one thousand feet per second. He closes by telling the Princess that we are incapable of hearing a string vibrating at less than 30 vibrations per second, or one that is more than 7552 vibrations per second.

1766 D’Alembert after writing to Frederick II in praise of Lagrange writes to Lagrange about an offer to move to Berlin:
My dear and illustrious friend, the king of Prussia has charged me to write you that, if you would like to come to Berlin to occupy a place in the Academy, he would give you a pension of 1,500 crowns, which are 6,000 French pounds … Mr Euler, unhappy for reasons of which I do not know the details, but in which I see that everyone thinks him wrong, requests permission to leave and wants to go to St. Petersburg. The king, who was not too anxious to grant it, would definitely give it to him if you accept the proposition that he has made
Frederick II of Prussia had more than once invited both d’Alembert and Lagrange to move to Berlin. The encyclopaedist had declined the offer and suggested the name of his Turinese friend. But Lagrange, even though he was on good terms with Euler, did not relish a "cohabitation" with him in the Berlin Academy. *Mauro ALLEGRANZA, Stack Exchange

1826 The first class of 10 students graduated from Renssalaer Polytechnic Institute on 26 Apr 1826. The Renssalaer School was founded in 1824 in Troy, N.Y., by Stephen van Renssalaer becoming the first engineering college in the U.S. It opened on 3 Jan 1825, with the purpose of instructing persons, who may choose to apply themselves, in the application of science to the common purposes of life." The first director and senior professor was Amos Eaton who served from Nov 1824 - 10 May 1842. The name of Renssalaer Institute was adopted on 26 Apr 1832, and Renssalaer Polytechnic Institute on 8 Apr 1861. *TIS

1861 Richard Owen gives the longest ever discourse at a Royal Institution lecture, ‘On the Scope and Appliances of a National Museum of Natural History’.
Discourse speakers were supposed to aim to speak for exactly one hour but Owen kept talking for two. (It may be coincidence but this is the last discourse he gave.) *Royal Institution web page

In 1882, a perpetual motion machine was patented by John Sutliff in the U.S. (No. 257,103). *TIS (Wouldn't you love to be the guy that approved that one.)

1892 Hermite to Stieltjes: “You state this result and then try to mortify me by saying that it is easy to prove. Since I can’t succeed in doing it I appeal to your good nature to help me out of this difficulty.” [Two Year Journal, 11, 49] *VFR (Boy, haven't we all been there?)

1920 Shapley and Curtis debate the nature of the nebulae. In astronomy, the Great Debate, also called the Shapley–Curtis Debate, was an influential debate between the astronomers Harlow Shapley and Heber Curtis which concerned the nature of spiral nebulae and the size of the universe. more here.

1921 the first U.S. broadcast of the weather was made from St. Louis, Missouri, over station WEW for the federal government. *TIS
Radio Station WEW, the original radio station of Saint Louis University, played an important role in the history of early radio. In 1921 it became only the second radio station in the U.S. and the first station west of the Mississippi River. In 1939 it became the first station to broadcast Sacred Heart Radio, a Catholic religious program which eventually grew to include over a thousand stations around the world. Finally, in 1947 WEW became the first FM radio station in St. Louis.

1962 The UK became the world's third spacefaring country, after the US and the USSR, with the launch of the satellite Ariel 1. It was built by Nasa in collaboration with British scientists to study the properties of the upper atmosphere and cosmic rays, and formed the first of six missions. "The big legacy is that, despite the fact we are a relatively small country, we are a major international player in space research," said Martin Barstow, an astrophysicist and head of the college of science and engineering at the University of Leicester. *The Guardian


1968 Time magazine (p. 41) reports a “Trial by Mathematics” in which a couple was convicted on the basis of mathematical probability. Later the reasoning was found to be incorrect. The discussion there is of interest. See also Journal of Recreational Mathematics, 1(1968), p. 183. *VFR See details here.

1985 A 22-cent commemorative stamp for Public Education in America issued in Boston.

1986 Nuclear reactor number 4 at Chernobyl, USSR, exploded and released a large amount of radioactive material into the atmosphere. [A. Hellemans and B. Bunch. The Timetables of Science, p. 597].


1711 David Hume, (7 May[O.S. 26 April]1711,– 25 August 1776) was a Scottish philosopher, historian, economist, and essayist, known especially for his philosophical empiricism and skepticism. He was one of the most important figures in the history of Western philosophy and the Scottish Enlightenment. Hume is often grouped with John Locke, George Berkeley, and a handful of others as a British Empiricist *Wik

Robert Tucker (26 April 1832 in Walworth, Surrey, England - 29 Jan 1905 in Worthing, England) A major mathematical contribution made by Tucker was his work as editor of William Kingdon Clifford's papers. Fifty-seven of Clifford's papers were collected and edited by Tucker and published in 1882 as Mathematical Papers. Tucker also wrote many biographies including those of Gauss, Sylvester, Chasles, Spottiswoode, and Hirst, all of which appeared in Nature. But, like a number of schoolmaster's at this time, he also made a contribution to research in geometry. He wrote over 40 research papers which were published in leading journals. These papers, although sometimes not of the highest quality, do contain a number of interesting ideas. Hill specially singles out for special mention his work on the Triplicate-Ratio Circle, the group of circles sometimes known as Tucker Circles, and the Harmonic Quadrilateral. *SAU

1874 Edward Vermilye Huntington (April 26 1874, Clinton, New York, USA – November 25, 1952, Cambridge, Massachusetts, USA) . This enthusiastic and innovative teacher was professor of mechanics at Harvard from 1919 to 1941. He made many contributions to the logical foundations of mathematics. His book, The Continuum (1917), was the standard introduction to set theory for many years. In 1928 he recommended the “method of equal proportion” for the apportionment of representatives to Congress; in 1941 this method was adopted by Congress. *VFR (now often called the Huntington-Hill method)

1879 Sir Owen Willans Richardson (26 Apr 1879; 15 Feb 1959 at age 79) English physicist who was awarded the Nobel Prize for Physics in 1928 for “his work on the thermionic phenomenon [electron emission by hot metals] and especially for the discovery of the law named after him.”This effect is why a heated filament in a vacuum tube releases a current of electrons to travel an anode, which was essential for the development of such applications as radio amplifiers or a TV cathode ray tube. Richardson's law mathematically relates how the electron emission increases as the absolute temperature of the metal surface is raised. He also conducted research on photoelectric effects, the gyromagnetic effect, the emission of electrons by chemical reactions, soft X-rays, and the spectrum of hydrogen.*TIS

1889 Ludwig Josef Johann Wittgenstein (26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language.*Wik This noted philosopher introduced the word “tautology” in his Tractatus Logico Philosophicus of 1921. *VFR

1900 Charles Richter(April 26, 1900, Hamilton, Ohio - September 30, 1985, Pasadena, California ) This American seismologist developed the earthquake magnitude scale which bears his name. *VFR The scale is logarithmic (base ten). When an earthquake occurs, the maximum amplitude of the shake is measured on a seismometer and assigned a Richter number. A quake with a value of 5 on the Richter scale is 10 times more powerful than a quake with a value of 4. The choice of a log scale seems to have come from his associate, Beno Gutenberg,

1922 Asger Hartvig Aaboe (April 26, 1922 – January 19, 2007) was a historian of the exact sciences and mathematician who is known for his contributions to the history of ancient Babylonian astronomy. He studied mathematics and astronomy at the University of Copenhagen, and in 1957 obtained a PhD in the History of Science from Brown University, where he studied under Otto Neugebauer, writing a dissertation "On Babylonian Planetary Theories". In 1961 he joined the Department of the History of Science and Medicine at Yale University, serving as chair from 1968 to 1971, and continuing an active career there until retiring in 1992. In his studies of Babylonian astronomy, he went beyond analyses in terms of modern mathematics to seek to understand how the Babylonians conceived their computational schemes.*Wik

1933 Arno Allan Penzias (26 Apr 1933, ) is a German-American astrophysicist who shared one-half of the 1978 Nobel Prize for Physics with Robert Woodrow Wilson for their discovery of a faint electromagnetic radiation throughout the universe. Their detection of this radiation lent strong support to the big-bang model of cosmic evolution. (The other half of the prize was awarded to Pyotr Kapitsa for unrelated research.)*TIS

1938 Manuel Blum (26 April 1938; Caracas, Venezuela -) is a computer scientist who received the Turing Award in 1995 "In recognition of his contributions to the foundations of computational complexity theory and its application to cryptography and program checking".
Blum attended MIT, where he received his bachelor's degree and his master's degree in EECS in 1959 and 1961 respectively, and his Ph.D. in Mathematics in 1964 under professor Marvin Minsky.
He worked as a professor of computer science at the University of California, Berkeley until 1999. In 2002 he was elected to the United States National Academy of Sciences.
He is currently the Bruce Nelson Professor of Computer Science at Carnegie Mellon University, where his wife, Lenore Blum, and son, Avrim Blum, are also professors of Computer Science. *Wik


1600 Cunradus Dasypodius ((c. 1530–1532 – April 26, 1600) whose fame is based on the “construction of an ingeneous and accurate astronomical clock in the cathedral of Strasbourg, installed between 1571 and 1574.” *VFR The Strasbourg astronomical clock is located in the Cathédrale Notre-Dame of Strasbourg, Alsace, France. The current, third clock dates from 1843. Its main features, besides the automata, are a perpetual calendar (including a computus), an orrery (planetary dial), a display of the real position of the Sun and the Moon, and solar and lunar eclipses. The main attraction is the procession of the life-size figures of Christ and the Apostles which occurs every day at 12:30pm,(not sure if I read this right, but that seems to be when the clock reads noon (corrections anyone?))*Wik
[A minor point on language, the "orrery" was proabably not so-named in that period, according to a post at the Univ of Penn Library, "The name Orrery comes from the following train of facts. When George Graham, the celebrated London mechanic and watchmaker, employed one Rowley to construct his planetarium, said Rowley retained a model, and was afterward patronized by Charles Boyle, Earl of Orrery, in making a large machine which, though only representing one or two of the heavenly bodies, was sold to George the First for a thousand guineas. Sir Richard Steele in the work entitled "A New and General Biographical Dictionary", published in 1761, attributed this invention to the Earl of Orrery. Hence compilers of the British Encyclopaedia, which was republished in Philadelphia, followed his lead and such machines have since been known as Orreries. ]

1815 Carsten Niebuhr(March 17, 1733 Lüdingworth – April 26, 1815 Meldorf, Dithmarschen), German mathematician, cartographer, and explorer in the service of Denmark. Niebuhr's first book, Beschreibung von Arabien, was published in Copenhagen in 1772, the Danish government providing subsidies for the engraving and printing of its numerous illustrations. This was followed in 1774 and 1778 by the two volumes of Niebuhr's Reisebeschreibung von Arabien und anderen umliegenden Ländern. These works (particularly the one published in 1778), and most specifically the accurate copies of the cuneiform inscriptions found at Persepolis, were to prove to be extremely important to the decipherment of cuneiform writing. Before Niebuhr's publication, cuneiform inscriptions were often thought to be merely decorations and embellishments, and no accurate decipherments or translations had been made up to that point. Niebuhr demonstrated that the three trilingual inscriptions found at Persepolis were in fact three distinct forms of cuneiform writing (which he termed Class I, Class II, and Class III) to be read from left to right. His accurate copies of the trilingual inscriptions gave Orientalists the key finally crack the cuneiform code, leading to the discovery of Old Persian, Akkadian, and Sumerian. *Wik

1876 Osip Ivanovich Somov (1 June 1815 in Otrada, Moscow gubernia (now oblast), Russia - 26 April 1876 in St Petersburg, Russia) Somov was the first in Russia to develop a geometrical approach to theoretical mechanics. He studied the rotation of a solid body about a point, studying examples arising from the work of Euler, Poinsot, Lagrange and Poisson. Other topics Somov studied included elliptic functions and their application to mechanics. *SAU

1902 Lazarus Immanuel Fuchs (5 May 1833 – 26 April 1902) was a German mathematician who contributed important research in the field of linear differential equations. He was born in Mosina (located in Grand Duchy of Poznań) and died in Berlin, Germany.
He is the eponym of Fuchsian groups and functions, and the Picard–Fuchs equation; Fuchsian differential equations are those with regular singularities. Fuchs is also known for Fuchs's theorem. *Wik

1920 Srinivasa Aaiyangar Ramanujan died at age 32. This self educated mathematician, who was discovered by G. H. Hardy of Cambridge, is remembered for his notebooks crammed with complicated identities. *VFR
Although self-taught, he was one of India's greatest mathematical geniuses. He worked on elliptic functions, continued fractions, and infinite series. His remarkable familiarity with numbers, was shown by the following incident. While Ramanujan was in hospital in England, his Cambridge professor, G. H. Hardy, visited and remarked that he had taken taxi number 1729, a singularly unexceptional number. Ramanujan immediately responded that this number was actually quite remarkable: it is the smallest integer that can be represented in two ways by the sum of two cubes: 1729=13+123=93+103 *TIS
I later learned from a blog at John D. Cooks The Endeavour blog that there is a little more to the story. Here is how John writes it:
This story has become famous, but the rest of the conversation isn’t as well known. Hardy followed up by asking Ramanujan what the corresponding number would be for 4th powers. Ramanujan replied that he did not know, but that such a number must be very large.

Hardy tells this story in his 1937 paper “The Indian Mathematician Ramanujan.” He gives a footnote saying that Euler discovered 635318657 = 158^4 + 59^4 = 134^4 + 133^4 and that this was the smallest number known to be the sum of two fourth powers in two ways. It seems odd now to think of such questions being unresolved. Today we’d ask Hardy “What do you mean 653518657 is the smallest known example? Why didn’t you write a little program to find out whether it really is the smallest?”
His readers seem to find that Euler was correct. No suprise there.

1946 Louis Bachelier, the French mathematician, is now recognized internationally as the father of financial mathematics,..Bachelier was ahead of his time and his work was not appreciated in his lifetime. In the light of the enormous importance of international derivative exchanges (where the pricing is determined by financial mathematics) the remarkable pioneering work of Bachelier can now be appreciated in its proper context and Bachelier can now be given his proper place. *SAU

1951 Arnold (Johannes Wilhelm) Sommerfeld (5 Dec 1868, 26 Apr 1951 at age 82) was a German physicist whose atomic model permitted the explanation of fine-structure spectral lines. His first work was on the theory of the gyroscope (with Klein), and then on wave spreading in wireless telegraphy. More significant was his major contribution to the development of quantum theory, generally, and in its application to spectral lines and the Bohr atomic model. He evolved also a theory of the electron in the metallic state valuable to the study of thermo-electricity.*TIS

1976 Carl Benjamin Boyer (November 3, 1906 – April 26, 1976) was a historian of sciences, and especially mathematics. David Foster Wallace called him the "Gibbon of math history". He wrote the books History of Analytic Geometry, The History of the Calculus and Its Conceptual Development, A History of Mathematics, and The Rainbow: From Myth to Mathematics. He served as book-review editor of Scripta Mathematica. *Wik
His History of analytic Geometry is excellent.

1980 Stanisław Gołąb (July 26, 1902 – April 30, 1980) was a Polish mathematician from Kraków, working in particular on the field of affine geometry.
In 1932, he proved that the perimeter of the unit disc can take any value in between 6 and 8, and that these extremal values are obtained if and only if the unit disc is an affine regular hexagon. *Wik

2006 Yuval Ne'eman (14 May 1925, 26 Apr 2006 at age 80) Israeli theoretical physicist, who worked independently of Gell-Mann but almost simultaneously (1961) devised a method of grouping baryons in such a way that they fell into logical families. Now known as the Eightfold Way (after Buddha's Eightfold Path to Enlightenment and bliss), the scheme grouped mesons and baryons (e.g., protons and neutrons) into multiplets of 1, 8, 10, or 27 members on the basis of various properties. He had served as the head of his Israel's atomic energy commission, and founded the country's space program.*TIS

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