On two occasions I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.
~ Charles Babbage
The 13th day of the year; there are 13 Archimedean Solids. (different from the Platonic solids, which have only one type of polygon meeting in identical vertices)
If you wrote , e, and one under another, the first digit they are all alike is the 13th digit, a nine in each number.
Heronian triangles (integer sides and area) with sides of three consecutive numbers include the 3-4-5, which is the only such triangle that is a right triangle. The smallest of the rest has a smallest side of length 13.
The 13th palindromic prime is 373 and has a digit sum of 13. 13 is smallest n for which digit sum of nth palindromic prime =n.
Another 13 palindrome, The longest word in the English language that is a palindrome in Morse code is .. -. - .-. .- -. ... .. --. . -. -.-. . (translation left to the reader, if your coding is rusty try copy and paste to http://morsecode.scphillips.com/translator.html)
Tip for Twin Prime Hunters. Primes ending in 3 can not be part of a twin prime pair unless p = 13 (mod 30). HT *Gary W. Croft.
There are only three known primes in the sequence, 13 is the largest that is a year day
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| *Fermat's Library |
1404, English alchemists were forbidden to use their knowledge to create precious metals. Since the time of Roger Bacon, it had fascinated the imagination of many ardent men in England. During the reign of Henry IV, the Act of Multipliers was passed by the Parliament, declaring the use of transmutation to "multiply" gold and silver to be felony. Great alarm was felt at that time lest any alchemist should succeed in his projects, and perhaps bring ruin upon the state, by furnishing boundless wealth to some designing tyrant, who would make use of it to enslave his country. In 1689, Robert Boyle lobbied for repeal of the Act.*TIS
It was repealed in 1689, and according to Isaac Newton this repeal was initiated by Robert Boyle. In fact both Newton and Boyle worked very hard at alchemy in their later years; it had not acquired the taint of disrepute it now carries, and it included a lot of what we would now call chemistry.*John Baez
1610 Galileo discovers a fourth moon (Callisto) of Jupiter. Galileo initially named his discovery the Cosmica Sidera ("Cosimo's stars"), but names that eventually prevailed were chosen by Simon Marius. Marius discovered the moons independently at the same time as Galileo, and gave them their present names, which were suggested by Johannes Kepler, in his Mundus Jovialis, published in 1614.*Wik
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| Simon Marius |
1659 Hendrik van Heuraet sends van Schooten his rectification of the semi-cubical parabola. This was published—his only publication—in the second Latin edition of Descartes’s Geometrie. This result broke the spell of Aristotle’s dictum that curved lines could not in principle be compared with straight lines. *VFR The semicubical parabola was discovered in 1657 by William Neile who had also computed its arc length. *Wik
He is noted as one of the founders of the integral, and author of Epistola de Transmutatione Curvarum Linearum in Rectus [On the Transformation of Curves into Straight Lines] (1659).[1] From 1653 he studied at Leiden University where he interacted with Frans van Schooten, Johannes Hudde, and Christiaan Huygens. In 1658 he and Hudde left for Saumur in France. He returned to Leiden the next year as a physician. After this his trail is lost.*Wik
1800 The Royal Charter for the Royal Institute is granted. Ever since its founding year the Royal Institution has maintained close links with the Royal Family. On 29 June 1799, George Finch, Earl of Winchilsea (1752-1826), the President of what had until then had been called simply the “Institution” reported to a meeting of its committee of Managers ‘that he had had the Honour of mentioning this Institution to his Majesty [George III], and that his Majesty was graciously pleased to honour it with His Patronage and to allow it to be called the Royal Institution’ *Royal Institute web page
1863 Mind the Gap.... The London underground railway, the oldest subway system in the world opened. The first railway was from Paddington to Farringdon. *Wik Harry Beck, A draftsman who worked for the London Underground, was the person who transformed the old geographically based maps into a topological map (1933). He ignored geography and instead focused on the connections between stations. He magnified the central regions and brought in the far away ones. He laid the lines out to run either vertically, horizontally or at 45 degree angles. He stretched and squeezed London's geographical map to make the Underground network look good. And he also introduced the color-coding and the little circles that mark intersections of lines. *plus.maths.org
1865 On this day in 1865, Henry Perigal debated with John Couch Adams at the Astronomical Club about whether the moon rotates. Perigal wrote in his diary:
1874 The U.S. Patent Office issues a patent for the Spalding Adding Machine. The precursor of calculators and computers, mechanical adding machines could do simple arithmetic and were popular in businesses until supplanted by computers in the 1960s. *CHM
1911 A. V. Vasil’ev gave a lecture entitled, “Non-Euclidean Geometry and the Non-Aristotelian Logic.” This is his claim to the discovery of three-valued logics. He did not work out the system in detail, so credit usually goes to LLukasiewicz. *VFR
1920 The New York Times publishes an editorial dismissing the theories of American rocket scientist Robert Goddard as seeming to lack an understanding of high school physics.
1863 Mind the Gap.... The London underground railway, the oldest subway system in the world opened. The first railway was from Paddington to Farringdon. *Wik Harry Beck, A draftsman who worked for the London Underground, was the person who transformed the old geographically based maps into a topological map (1933). He ignored geography and instead focused on the connections between stations. He magnified the central regions and brought in the far away ones. He laid the lines out to run either vertically, horizontally or at 45 degree angles. He stretched and squeezed London's geographical map to make the Underground network look good. And he also introduced the color-coding and the little circles that mark intersections of lines. *plus.maths.org
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| Beck 193 Tube Map |
1865 On this day in 1865, Henry Perigal debated with John Couch Adams at the Astronomical Club about whether the moon rotates. Perigal wrote in his diary:
Dined with the Astronomical Club; after dinner, the question as to the moon's rotation was put to the vote, when the numbers were: 10 for Adams and rotation, 11 for Perigal and non-rotation.
Henry Perigal was a clerk, stockbroker, amateur mathematician and astronomer. He is known for his mechanical production of geometric curves, for his dissection proof of Pythagoras' theorem and for his unorthodox ideas on astronomy. He was so proud of his dissection proof, he had it put on his tombstone.
1911 A. V. Vasil’ev gave a lecture entitled, “Non-Euclidean Geometry and the Non-Aristotelian Logic.” This is his claim to the discovery of three-valued logics. He did not work out the system in detail, so credit usually goes to LLukasiewicz. *VFR
1920 The New York Times publishes an editorial dismissing the theories of American rocket scientist Robert Goddard as seeming to lack an understanding of high school physics.
"The day after its front-page story about Goddard's rocket, an unsigned New York Times editorial, in a section entitled "Topics of the Times", scoffed at the proposal. The article, which bore the title "A Severe Strain on Credulity", began with apparent approval, but soon went on to cast serious doubt:
As a method of sending a missile to the higher, and even highest, part of the earth's atmospheric envelope, Professor Goddard's multiple-charge rocket is a practicable, and therefore promising device. Such a rocket, too, might carry self-recording instruments, to be released at the limit of its flight, and conceivable parachutes would bring them safely to the ground. It is not obvious, however, that the instruments would return to the point of departure; indeed, it is obvious that they would not, for parachutes drift exactly as balloons do.
The article pressed further on Goddard's proposal to launch rockets beyond the atmosphere:
[A]fter the rocket quits our air and really starts on its longer journey, its flight would be neither accelerated nor maintained by the explosion of the charges it then might have left. To claim that it would be is to deny a fundamental law of dynamics, and only Dr. Einstein and his chosen dozen, so few and fit, are licensed to do that. ... Of course, [Goddard] only seems to lack the knowledge ladled out daily in high schools." *Wikipedia
49 years later, just before Apollo 11 landed on the Moon, the Times published a correction.
The three-paragraph statement summarized its 1920 editorial and concluded:
Further investigation and experimentation have confirmed the findings of Isaac Newton in the 17th Century and it is now definitely established that a rocket can function in a vacuum as well as in an atmosphere. The Times regrets the error. *Chasing The Moon: The Book
In 1958, Linus Pauling (1901-1994) presented the petition of 9,000 scientists to the U.N., asking to halt the testing of nuclear bombs. Pauling, together with his wife, was instrumental in collecting thousands of signatures from scientists all over the world for the petition to end nuclear bomb testing, which was presented to Dag Hammarskjöld, secretary general of the United Nations. A few months later the Soviet Union called for an immediate halt to nuclear testing, and in October, after more tests by both sides that added markedly to world concern about fallout, talks began in Geneva to discuss details of a possible test ban. *TIS
1978 A new group of 35 astronauts, including NASA's first female astronauts, was selected. Females selected included Sally Ride, the first American woman in space; Kathryn Sullivan the first American woman to perform an EVA; and Anna Fisher and Shannon Lucid, the first mothers in the astronaut program. *Wik
1978 A new group of 35 astronauts, including NASA's first female astronauts, was selected. Females selected included Sally Ride, the first American woman in space; Kathryn Sullivan the first American woman to perform an EVA; and Anna Fisher and Shannon Lucid, the first mothers in the astronaut program. *Wik
Sullivan dons her space suit in case an EVA was required to support the Hubble Space Telescope deployment on STS-31.
1994 Contest to rename the Big Bang decides, "Nobody won." At a convention of the American Astronomical Society the culmination of a search for a replacement for the term "Big Bang", created by Fred Hoyle to mock an idea he didn't believe in, and which many astronomers disagree with as it is inaccurate, failed to find a winner. Most popular term was Cosmogenesis,but judges Hugh Downs and Carl Sagan decided none was an adequate replacement. *Washington Post
2013 On the evening of Sunday 13th January 2013, to commemorate the opening in 1863 of first underground railway from Paddington to Farringdon, a steam train made three trips to Moorgate.*Wik
Work on the world’s first underground railway started in 1860 when the Metropolitan Railway began building a tunnel more than three miles long from Paddington to Farringdon Street. It was largely financed by the City of London, which was suffering badly from horse-drawn traffic congestion that was having a damaging effect on business.
Over the next two years the line was extended further east into the City to Moorgate and, in the other direction, to Hammersmith. *History Today
Illustration of a train at Praed Street junction near Paddington, 1863.
2023 The first Friday the 13th of 2023, The Other will be October 13. 2015 had a Friday the 13th in February, March, and November; No year since has had as many.The next year with three is 2026. In Spanish-speaking countries, instead of Friday, Tuesday the 13th (martes trece) is considered a day of bad luck. The 13th day of the month is slightly more likely to be a Friday than any other day of the week. There can be no more than three Friday the 13ths in a single calendar year; either in February, March, and November in a common year starting on Thursday (such as 2009, 2015, or 2026) (D), or January, April, and July in a leap year starting on Sunday (such as 1984, 2012, or 2040)
2024 (which also has two Friday the 13ths), the first of the two comes on September 13, 2024, exactly 13 weeks before the second Friday the 13th in December 2024.
1845 François-Félix Tisserand (13 Jan 1845; 20 Oct 1896) was a French astronomer whose 4-volume textbook Traité de mécanique céleste (1889-96; "Treatise on Celestial Mechanics") updated Pierre-Simon Laplace's work. At age 28, he was named Director at Toulouse Observatory (1873-78). He went to Japan to observe the 1874 transit of Venus. The 83-cm telescope he installed at the Toulouse Observatory in 1875 had a wooden base insufficiently stable for photographic work, but he was able to use it for observation of the satellites of Jupiter and of Saturn. From 1892 until his death he was director of the Paris Observatory, where he completed the major work, Catalogue photographique de la carte du ciel, and arranged for its publication. *TIS
1864 Wilhelm Wien (13 Jan 1864; 30 Aug 1928) German physicist who received the Nobel Prize for Physics in 1911 for his displacement law concerning the radiation emitted by the perfectly efficient blackbody (a surface that absorbs all radiant energy falling on it). While studying streams of ionized gas Wien, in 1898, identified a positive particle equal in mass to the hydrogen atom. Wien, with this work, laid the foundation of mass spectroscopy. J. J. Thomson refined Wien's apparatus and conducted further experiments in 1913 then, after work by Ernest Rutherford in 1919, Wien's particle was accepted and named the proton. Wien also made important contributions to the study of cathode rays, X-rays and canal rays.*TIS
1876 Erhard Schmidt (13 January 1876 – 6 December 1959) was a German mathematician whose work significantly influenced the direction of mathematics in the twentieth century. He was born in Tartu, Governorate of Livonia (now Estonia). His advisor was David Hilbert and he was awarded his doctorate from Georg-August University of Göttingen in 1905. His doctoral dissertation was entitled Entwickelung willkürlicher Funktionen nach Systemen vorgeschriebener and was a work on integral equations.
Together with David Hilbert he made important contributions to functional analysis. He is best known for the Gram-Schmidt orthogonalisation process, which constructs an orthogonal base from any vector space.
The method is named after Jørgen Pedersen Gram and Erhard Schmidt, but Pierre-Simon Laplace had been familiar with it before Gram and Schmidt.
*Wik
1876 Luther Pfahler Eisenhart (13 January 1876 – 28 October 1965) was an American mathematician, best known today for his contributions to semi-Riemannian geometry.
Eisenhart played a central role in American mathematics in the early twentieth century. He served as chairman of the mathematics department at Princeton University and later as Dean of the Graduate School there. He is widely credited with guiding the development in America of the mathematical background needed for the further development of general relativity, through his influential textbooks and his personal interaction with Albert Einstein, Oswald Veblen, and John von Neumann at the nearby Institute for Advanced Study, as well as with gifted students such as Abraham Haskel Taub. *Wik
1900 Gertrude Mary Cox (January 13, 1900 – October 17, 1978) was an influential American statistician and founder of the department of Experimental Statistics at North Carolina State University. She was later appointed director of both the Institute of Statistics of the Consolidated University of North Carolina and the Statistics Research Division of North Carolina State University. Her most important and influential research dealt with experimental design; she wrote an important book on the subject with W. G. Cochran. In 1949 Cox became the first female elected into the International Statistical Institute and in 1956 she was president of the American Statistical Association.*Wik The choice of a woman to hold such a post was unusual at that time and came about in a curious way. G W Forster of North Carolina State College contacted Professor Snedecor for names of individuals who would be viable candidates for the position. Professor Snedecor prepared a list of persons (all males) and before mailing it to Dr Forster showed the list to Miss Cox. Her immediate reaction was, "Why didn't you put my name on the list?" Her name was then added in a footnote to the letter, "Of course if you would consider a woman for this position I would recommend Gertrude Cox of my staff." The choice of a woman on the basis of a footnote was an administrative decision which had far-reaching effects. *SAU
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| *Wik |
1902 Karl Menger (Vienna, Austria, January 13, 1902 – Highland Park, Illinois, U.S.A., October 5, 1985) was a mathematician. He was the son of the famous economist Carl Menger. He is credited with Menger's theorem. He worked on mathematics of algebras, algebra of geometries, curve and dimension theory, etc. Moreover, he contributed to game theory and social sciences. He is remembered for the creation of the Menger Sponge*Wik
1907 Harold Maile Bacon (Jan. 13, 1907- August 22, 1992) was an elder statesmen of the Stanford faculty who taught calculus to generations of Stanford undergraduates during a career that spanned more than four decades.
Bacon was widely recognized on campus as the owner of the white colonial-style Row house with the rose-lined driveway. He had ties to the house, and the University, almost since his birth.
He was an ill 6-month-old child when he first visited the campus house he would occupy for more than 60 years. Harriet Dunn, a cousin of Harold Bacon's father, Robert, and owner of the distinctive house, suggested that the child be brought to Stanford from Southern California for examination by Dr. Ray Lyman Wilbur, who lived nearby on the site now occupied by Dinkelspiel Auditorium. (Wilbur, who prescribed medicine and a better diet for young Bacon, later became the university's third president.)
In the 1920s, Harold Bacon enrolled at Stanford, following in the footsteps of his father, who graduated in 1902. Bacon lived in the two-story, six-bedroom house during part of his undergraduate years, then moved in permanently , at the invitation of Harriet Dunn, when he returned in 1930 to teach.
For many years, Bacon directed the undergraduate program in mathematics, according to Halsey Royden, who took classes from Bacon during his student days and later became a faculty colleague.
To students and fellow faculty members, Bacon was "the embodiment of Stanford ways and history," Royden said. At the time he retired, Bacon, through his calculus classes, probably had taught "more engineering and science undergraduates than anyone else in the history of the university," Royden said.
*Stanford Obituary
For a wonderful story describing the nature of Harold Bacon as a man and a teacher, see this cover story, The Prisoner and the Professor, from the Stanford Alumni magazine of Mar/Apr 1997
1931 Elias Menachem Stein (January 13, 1931 – December 23, 2018) was an American mathematician who was a leading figure in the field of harmonic analysis. He was the Albert Baldwin Dod Professor of Mathematics, Emeritus, at Princeton University, where he was a faculty member from 1963 until his death in 2018.
Stein was born in Antwerp Belgium, to Elkan Stein and Chana Goldman, Ashkenazi Jews from Belgium. After the German invasion in 1940, the Stein family fled to the United States, first arriving in New York City. He graduated from Stuyvesant High School in 1949, where he was classmates with future Fields Medalist Paul Cohen, before moving on to the University of Chicago for college. In 1955, Stein earned a Ph.D. from the University of Chicago under the direction of Antoni Zygmund. He began teaching at MIT in 1955, moved to the University of Chicago in 1958 as an assistant professor, and in 1963 became a full professor at Princeton.
Stein worked primarily in the field of harmonic analysis, and made contributions in both extending and clarifying Calderón–Zygmund theory. These include Stein interpolation (a variable-parameter version of complex interpolation), the Stein maximal principle (showing that under many circumstances, almost everywhere convergence is equivalent to the boundedness of a maximal function), Stein complementary series representations, Nikishin–Pisier–Stein factorization in operator theory, the Tomas–Stein restriction theorem in Fourier analysis, the Kunze–Stein phenomenon in convolution on semisimple groups, the Cotlar–Stein lemma concerning the sum of almost orthogonal operators, and the Fefferman–Stein theory of the Hardy space.
He wrote numerous books on harmonic analysis , which are often cited as the standard references on the subject. His Princeton Lectures in Analysis series were penned for his sequence of undergraduate courses on analysis at Princeton. Stein was also noted as having trained a high number of graduate students. According to the Mathematics Genealogy Project, Stein had at least 52 graduate students—including the Fields medalists Charles Fefferman and Terence Tao—some of whom went on to shape modern Fourier analysis.
His honors included the Steele Prize (1984 and 2002), the Schock Prize in Mathematics (1993), the Wolf Prize in Mathematics (1999), and the National Medal of Science (2001). In addition, he had fellowships to National Science Foundation, Sloan Foundation, Guggenheim Foundation, and National Academy of Sciences. Stein was elected as a member of the American Academy of Arts and Sciences in 1982. In 2005, Stein was awarded the Stefan Bergman prize in recognition of his contributions in real, complex, and harmonic analysis. In 2012 he became a fellow of the American Mathematical Society.*Wik
1614 Jeremiah Horrocks (1618, 13 Jan 1641) (some sources give 3 Jan as date of death, England had not converted to Gregorian Calendar) English astronomer and clergyman who applied Johannes Kepler's laws of planetary motion to observations of the Moon and Venus. Once Horrocks managed to obtain a small telescope, his observations convinced him that Lansberg's tables were incorrect. He accepted Kepler's elliptical orbits, and in working on the moon he applied an elliptical orbit to it and established that the line of apsides precessed, an effect which he ascribed to the influence of the sun. Horrocks predicted and observed a transit of Venus on 24 Nov 1639, the first one ever observed, and from the observation he corrected the solar parallax, indicating a much greater distance of the sun than anyone before him had admitted. He died at age only 22.*TIS The only person to predict, and one of only two people to observe and record, the transit of Venus of 1639, which was the first transit of Venus to be convincingly predicted and observed. *Wik
Thony Christie has stated that the "clergyman" notation is incorrect. *@rmathematicus, Wikipedia now (Jan 2013) states, " there is little evidence for this and it is more likely he was a tutor to the Stones' children."
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| Stained Glass of Horrocks at Church in Much Hoole |
1934 Paul Urich Villard (28 Sep 1860, 13 Jan 1934) was a French physicist and chemist who in 1900 identified a third kind of natural radiation, later called gamma rays. He was studying the radiations from uranium salts discovered by Henri Becquerel four years before. Charged particles whose paths were bent in a magnetic field were known, but Villard found a form of penetrating radiation that was not deviated, but it drew little attention from contemporary scientists. A year before, in 1899, Ernest Rutherford named the first two kinds of natural radiation—positive alpha particles and negative beta rays. The third kind became known as gamma rays—with energy higher than X-rays, weak power of ionization, and which Rutherd characterized (1914) as a form of electromagnetic radiation, like light. Villard invented several radiological instruments, including the osmoregulator and Villard's valve. He researched hydrates, and discovered silver hydrate. He wrote Les Rayons Cathodiques (1900). *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
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