Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols.
Augustus de Morgan
The 178th day of the year; 178 = 2 x 89. Note that 2 and 89 are the smallest and the largest Mersenne prime exponents under 100. *Prime Curios
178 is a palindrome in base 6,\( [454]_6 \) and in base 8 \([262]_8\)
Strangely enough, 178 and 196 are related... In fact, 178 has a square with the same digits as 196:
1782 = 31,684
1962 = 38,416
178 also has a cube with the same digits as 196:
1783 = 5,639,752
1963 = 7,529,536
*Zoo of Numbers
178 = 13^2 + 3^2
178 is a palindrome in base 6 (454), base 7 (343), and base 8 (262)
178 is a semi-prime, the product of 2 and 89, which are the smallest, and largest Mersenne prime exponents under 100.
More Math Facts for each year day here.
432 B.C. Meton observed the summer solstice and began his cycle. Meton was one of the first Greek astronomers to make accurate astronomical observations. It is widely believed that, working with Euctemon, he observed the summer solstice, which marked the Athenian New Year, in 432 BC.
The Metonic cycle appears in the oldest known astronomical device, the Antikythera Mechanism (2nd century BC) together with its multiple the Callippus cycle of 76 years.
The foundations of Meton's observatory in Athens are still visible just behind the podium of the Pnyx, the ancient parliament. Meton found the dates of equinoxes and solstices by observing sunrise from his observatory. The bisectrice of the observatory lies in an easterly direction, between the Acropolis and the Lycabetus hill.*Wik
1739 "Heavens!, Maupertuis is a flea. Is he ever in one place?" So wrote Francoise de Graffigny to a friend about the French mathematician/man of letters, Pierre-Louis Moreau de Maupertuis. Graffigny affectionately gave the nickname to describe his "frenetic ubiquity." *Mary Terrall, The Man Who Flattened the Earth.
A French mathematician, philosopher and man of letters. He became the Director of the Académie des Sciences, and the first President of the Prussian Academy of Science, at the invitation of Frederick the Great.
In the 1730s, the shape of the Earth became a flashpoint in the battle among rival systems of mechanics. Maupertuis, based on his exposition of Newton (with the help of his mentor Johan Bernoulli) predicted that the Earth should be oblate, while his rival Jacques Cassini measured it astronomically to be prolate. In 1736 Maupertuis acted as chief of the French Geodesic Mission sent by King Louis XV to Lapland to measure the length of a degree of arc of the meridian. His results, which he published in a book detailing his procedures, essentially settled the controversy in his favour.
In 1847, New York and Boston were linked by telegraph wires. This enabled the New York newspapers to receive foreign news brought by Cunard's steamers to the Boston port about 190 miles away. When the Cambria next arrived in Boston, three New York Newspapers on 18 Jul 1846 carried identical brief first-day telegraphic summaries of the Cambia's news*. This telegraph link opened three years after the first U.S. telegraph line was opened on 24 May 1844 with a message sent by Samuel Morse 80 miles from Washington D.C. and Baltimore, Md.*TIS
1908 The academy of sciences of Gottingen announced a prize of one hundred thousand marks, according to the will of Dr. Paul Wolfskehl, of Darmstadt, for the proof of Fermat’s great theorem. A German industrialist and amateur mathematician, Wolfskehl bequeathed 100,000 marks to the Göttingen Academy of Sciences to be offered as a prize for a complete proof of Fermat's Last Theorem. On 27 June 1908, the Academy published nine rules for awarding the prize. Among other things, these rules required that the proof be published in a peer-reviewed journal; the prize would not be awarded for two years after the publication; and that no prize would be given after 13 September 2007, roughly a century after the competition was begun. Wiles collected the Wolfskehl prize money, then worth $50,000, on 27 June 1997.
Prior to Wiles' proof, thousands of incorrect proofs were submitted to the Wolfskehl committee, amounting to roughly 10 feet (3 meters) of correspondence. In the first year alone (1907–1908), 621 attempted proofs were submitted, although by the 1970s, the rate of submission had decreased to roughly 3–4 attempted proofs per month. According to F. Schlichting, a Wolfskehl reviewer, most of the proofs were based on elementary methods taught in schools, and often submitted by "people with a technical education but a failed career". In the words of mathematical historian Howard Eves, "Fermat's Last Theorem has the peculiar distinction of being the mathematical problem for which the greatest number of incorrect proofs have been published."*Wik
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1966 An almost 300 year old conjecture of Leonhard Euler is proven wrong. Euler had conjectured that, in the fashion that \(x^2 + y^2 = z^2 \) it always takes n terms to sum to an n-th power: two squares, three cubes, four fourth powers,etc. In 1966, L. J. Lander and T. R. Parkin found the first counterexample: four fifth powers that sum to a fifth power. They showed that \( 27^5 + 84^5 + 110^5 + 133^5 = 144^5.\) In 1988 Noam Elkies of Harvard University found a counterexample for fourth powers: \(2,682,440^4 + 15,365,639^4 + 187,960^4 = 20,615,673^4. Subsequently, Roger Frye of Thinking Machines Corporation did a computer search to find the smallest example: 95,800^4 + 217,519^4 + 414,560^4 = 422,481^4.*David Darling
1967 The first ATM in England that was put into use was by Barclays Bank in Enfield Town in North London, United Kingdom, on 27 June 1967. This machine was the first in the UK and was used by English comedy actor Reg Varney, at the time so as to ensure maximum publicity for the machines that were to become mainstream in the UK. This instance of the invention has been credited to John Shepherd-Barron of printing firm De La Rue, who was awarded an OBE in the 2005 New Year's Honours List. His design used special cheques that were matched with a personal identification number, as plastic bank cards had not yet been invented. *Wik (The plaque posted at the sight makes the claim to be the first cash machine in the world, but cash dispensing machines had been installed in Tokyo and another shortly after in Upsalla.)
1977 In 1983, Sally Ride became the first American woman in space. She blasted off aboard Challenger, culminating a long journey that started in 1977 when the Ph.D. candidate answered an ad seeking astronauts for NASA missions.
In a lecture she gave at Berkeley, Ride said she saw the ad on Page 3 of the student newspaper. "The moment I saw that ad, I knew that's what I wanted to do," she said.
By the time Ride decided to apply to become an astronaut, she had already received degrees in physics and English and was on her way to a Ph.D. in physics from Stanford University.
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| *HT Lunar Heritage |
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1977 Italy issued a postage stamp honoring Filippo Brunelleschi (1377–1446). [Scott #1266]. *VFR
1980 Creighton Carvello recited 20,013 digits of π from memory in nine hours and one minute. *VFR
He was a British mnemonist, born in Patna, Bihar, India but lived in the UK from 1949 until his death. His Pi record came in 1979, and in 1987 he appeared on the BBC television program Record Breakers, memorising one shuffled deck of cards in 2 minutes 59 seconds. It was this feat of memory which first inspired Dominic O'Brien, who later went on to gain the title of World Memory Champion eight times.
1767 Alexis Bouvard (27 June 1767 – 7 June 1843) French astronomer and director of the Paris Observatory, who is noted for discovering eight comets and writing Tables astronomiques of Jupiter and Saturn (1808) and of Uranus (1821). Bouvard's tables accurately predicted orbital locations of Jupiter and Saturn, but his tables for Uranus failed, leading him to hypothesize that irregularities were caused by an unknown perturbing body. This spurred observations leading to the discovery of Neptune by Adams and Leverrier.*TIS
1806 Augustus de Morgan (27 June 1806 – 18 March 1871) born in Madura (now Madurai), India, son of a colonel in the Indian Army. He is best known for his work in Formal Logic. “De Morgan’s Laws”, are contained in his first book (1847), although they were known to Peter of Spain in the fourteenth century. *VFR
The rules can be expressed in English as:
"The negation of a conjunction is the disjunction of the negations." and
"The negation of a disjunction is the conjunction of the negations."
*Wik
When he defined and introduced the term "mathematical induction" (1838), he gave the process a rigorous basis and clarity that it had previously lacked. He originated the use of the slash to represent fractions, as in 1/5 or 3/7. In Trigonometry and Double Algebra (1849) he gave a geometric interpretation of complex numbers. *TIS A nice blog about De Morgan's life and relationships is at The Renaissance Mathematicus.
1850 Jorgen Pedersen Gram.(June 27, 1850 – April 29, 1916) Danish mathematician. Today he is best known for his criterion of linear independence of functions. The Gram-Schmidt Orthonormal Basis Theorem in Linear Algebra was first published by him in 1883.
1940 Daniel G. Quillen bon in Orange, New Jersey. In 1978 he won a Fields Medal as the “prime architect of the higher algebraic K-theory, a new tool that successfully employed geometric and topological methods and ideas to formulate and solve major problems in algebra, particu¬larly ring theory and module theory.” *VFR French mathematician who is known for her work in number theory and contributions to the applied mathematics of acoustics and elasticity. Germain was self-taught from books, and from lecture notes supplied by male friends attending the Ecole Polytechnique which she, as a woman, was not permitted to attend. Using a male pseudonym, M. LeBlanc, she corresponded with Lagrange who recognised her skill, and subsequently sponsored her work. She accomplished a limited proof of Fermat's last theorem, for any prime under 100 where certain conditions were met. In 1816, she won a prize sponsored by Napoleon for a mathematical explanation of Chladni figures, the vibration of elastic plates. She died at age 55, from breast cancer. TIS
1899 Lois Wilfred Griffiths (June 27, 1899 – November 9, 1981) was an American mathematician and teacher. She served as a researcher, mathematician, and professor for 37 years at Northwestern University before retiring in 1964. She is best known for her work in polygonal numbers. She published multiple papers and wrote a textbook, Introduction to the Theory of Equations, published in 1945.
Griffiths attended public schools in Washington state, then attended the University of Washington. She served as an assistant to the Comptroller of the university during her undergraduate course. In 1921, she graduated with a bachelor's degree. In 1923 she earned a master's degree, also from the University of Washington, after writing Contact Curves of the Rational Cubic. The paper was published in typewritten arrangement by the University. She was elected as a member of the American Mathematical Society in September 1923, following which her master's thesis was published in the Bulletin of the American Mathematical Society.
In October 1925, she enrolled at the University of Chicago to pursue a doctorate in mathematics. She was supervised for the Ph.D course by well-known mathematician Leonard Dickson. Her thesis Certain quaternary quadratic forms and diophantine equations by generalized quaternion algebras earned her a doctorate degree in 1927.
In 1927, after earning her doctorate, she was engaged as an instructor of mathematics at Northwestern University in Evanston, Illinois, where she spent the remainder of her career. In 1930, she was promoted to assistant professor of mathematics, and in 1938 she was named associate professor. She retired from Northwestern University in 1964 and was named professor emeritus.*Wik
1931 Martinus Justinus Godefriedus Veltman (born June 27, 1931 in Waalwijk) is a Dutch theoretical physicist. He shared the 1999 Nobel Prize in physics with his former student Gerardus 't Hooft for their work on particle theory. In 1963/64, during an extended stay at SLAC he designed the computer program Schoonschip for symbolic manipulation of mathematical equations, which is now considered the very first Computer algebra system. He was awarded the Nobel Prize for Physics in 1999 together with 't Hooft, "for elucidating the quantum structure of electroweak interactions in physics". Veltman is now retired and holds a position of Emeritus Professor at the University of Michigan. Asteroid 9492 Veltman is named in his honor. *Wik
1829 James Smithson (ca. 1765 – 27 June 1829) English scientist who provided funds in his will for the founding of the Smithsonian Institution, Washington, D.C. "for the increase and diffusion of knowledge." He had inherited his fortune chiefly through his mother's family. He was a chemist and minerologist who published 27 scientific papers. The mineral smithsonite (carbonate of zinc) was named for him.*TIS
1872 Heber Doust Curtis (June 27, 1872 – January 9, 1942) was an American astronomer. He participated in 11 expeditions for the study of solar eclipses,[2] and, as an advocate and theorist that additional galaxies existed outside of the Milky Way, was involved in the 1920 Shapley–Curtis Debate concerning the size and galactic structure of the universe.
He studied at the University of Michigan and at the University of Virginia, earning a degree in astronomy from the latter.
From 1902 to 1920 Curtis worked at Lick Observatory, continuing the survey of nebulae initiated by Keeler. He headed up the Lick southern station in Chile from 1905 until 1909, when he returned to take charge of the Crossley telescope.[4] In 1912 he was elected president of the Astronomical Society of the Pacific.
In 1918 he observed Messier 87 and was the first to notice the polar jet which he described as a "curious straight ray ... apparently connected with the nucleus by a thin line of matter."*Wik
Concerning one of those nebulae, which he referred to as N.G.C. 4486, and which we generally call M87, he noted that this roundish nebula had a “curious straight ray” that seemed to come right out of the center of the nebula . He obviously saw this on a photograph, since it is impossible to detect with the naked eye, but he did not publish the photograph along with his paper, but here is another ray photo taken by the Hubble Space Telescope. The jet is 1500 parsecs long, which means that even if you were travelling at Warp One, trekkies, it would take you almost 5000 years to navigate its length. Linda Hall Linrary
1880 Carl Borchardt (22 February 1817 – 27 June 1880) was a German mathematician who worked in a variety of areas in analysis. He edited Crelle's Journal for more than 30 years.*SAU
1883 William H. Spottiswoode FRS HFRSE LLD (11 January 1825 – 27 June 1883) was an English mathematician, physicist and partner in the printing and publishing firm Eyre & Spottiswoode. He was president of the Royal Society from 1878 to 1883.
As a mathematician, he occupied himself with many branches of his favorite science, more especially with higher algebra, including the theory of determinants, with the general calculus of symbols, and with the application of analysis to geometry and mechanics.
In 1870 he was elected president of the London Mathematical Society. In 1871 he began to turn his attention to experimental physics, his earlier researches bearing upon the light polarization and his later work upon the electrical discharge in rarefied gases. He wrote a popular treatise on the former subject for the Nature Series in 1874. In 1878 he was elected president of the British Association and in the same year president of the Royal Society, of which he had been a fellow since 1853.
He died in London of typhoid fever on 27 June 1883 and was buried in the south transept of Westminster Abbey. *Wik
1952 Max Dehn died (November 13, 1878 – June 27, 1952). He solved Hilbert’s third problem in 1900 (shortly after receiving his Ph.D. under Hilbert on another topic in the foundations of geometry): a tetrahedron cannot be cut up into finitely many pieces and reassembled into a cube of equal volume. Thus Dehn became the first mathematician to join “the honors class” of mathematicians who had solved one of the twenty-three problems Hilbert posed in Paris in 1900.
Dehn's doctoral students include Ott-Heinrich Keller, Ruth Moufang, and Wilhelm Magnus; he also mentored mathematician Peter Nemenyi and the artists Dorothea Rockburne and Ruth Asawa.*Wik
1975 Sir Geoffrey Ingram Taylor OM (7 March 1886 – 27 June 1975) was a British physicist, mathematician and expert on fluid dynamics and wave theory. His biographer and one-time student, George Batchelor, described him as "one of the most notable scientists of this (the 20th) century". His final research paper was published in 1969, when he was 83. In it he resumed his interest in electrical activity in thunderstorms, as jets of conducting liquid motivated by electrical fields. The cone from which such jets are observed is called the Taylor cone for his namesake. In the same year Taylor was appointed to the Order of Merit. He suffered a stroke in 1972 which effectively put an end to his work; he died in Cambridge in 1975.
His father, Edward Ingram Taylor, was an artist, and his mother, Margaret Boole, came from a family of mathematicians (his aunt was Alicia Boole Stott and his grandfather was George Boole).[3] As a child he was fascinated by science after attending the Royal Institution Christmas Lectures, and performed experiments using paint rollers and sticky-tape.Taylor read mathematics and physics at Trinity College, Cambridge from 1905 to 1908. He won several scholarships and prizes at Cambridge, one of which enabled him to study under J. J. Thomson. More about Those Amazing Boole Girl
*Wik
She moved to California State University at Los Angeles in 1967 as a full professor of mathematics and married Edward V. Granville in 1970. After retiring from California State in 1984 she joined the faculty of the University of Texas at Tyler as professor and chair of mathematics. There she developed elementary school math enrichment programs. One of three African American women honored by the National Academy of Science in 1999, she has been awarded honorary degrees by Smith College and Lincoln University.
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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