It is nothing short of a miracle that modern methods of instruction have not yet entirely strangled the holy curiosity of inquiry.
~Albert Einstein
The 108th day of the year; 108 can be written as the sum of a cube and a square (a^3 + b^2) in two ways. This is the smallest number with this property. *Prime Curios
AND 108 = 1¹ • 2² • 3³ *jim wilder @wilderlab
The concatenation of 108 with its previous and next number is prime, i.e., 108107 and 108109 are primes.
108 is the smallest possible sum for a set of six distinct primes such that the sum of any five is prime: {5, 7, 11, 19, 29, 37}. (Don't just sit there, there must be another that is larger. Find it.
Today and tomorrow are both examples of ambinumerals, numbers which form a different number when rotated 180o 108 becomes 801. Numerals like 181 which stay the same when rotated are called strobogrammatic numerals
1557 Maurolico completed the first volume of his Arithmetic at three o’clock in the morning on Easter Sunday. [Jean Cassinet, Mathematics from Manuscript to Print, 1300–1600, p. 162; Thanks to Dave Kullman]*VFR Throughout his lifetime, he made contributions to the fields of geometry, optics, conics, mechanics, music, and astronomy. He edited the works of classical authors including Archimedes, Apollonius, Autolycus, Theodosius and Serenus. He also composed his own unique treatises on mathematics and mathematical science.
His Arithmeticorum libri duo (1575) includes the first known proof by mathematical induction. (Yea!)
His De Sphaera Liber Unus (1575) contains a fierce attack against Copernicus' heliocentrism, in which Maurolico writes that Copernicus "deserved a whip or a scourge rather than a refutation". (Boo!)
His unpublished manuscript Compaginationes solidorum regularium (1537) includes a statement of Euler's formula V-E + F = 2 for the Platonic solids, long before Leonhard Euler formulated it more generally for convex polyhedra in 1752.
Maurolico's astronomical observations include a sighting of the supernova that appeared in Cassiopeia in 1572. Tycho Brahe published details of his observations in 1574; the supernova is now known as Tycho's Supernova. *Wik
Star map of the constellation Cassiopeia showing the position (labelled I) of the supernova of 1572; from Tycho Brahe's De nova stella
1694 An ad for William Leybourne's Pleasure with Profit appears in The Proceedings of the Old Bailey:
Pleasure with Profit: Consisting of Recreations of divers kinds, viz. Numerical, Geometrical, Mathematical, Astronomical, Arithmetical, Cryptographical, Magnetical, Authentical, Chymical, and Historical. Published to Recreate Ingenious Spirit, and to induce them to make further scrutiny how these (and the like) Sublime Sciences. And to divert them from following such Vices, to which Youth (in this Age) are so much inclin'd. By William Laybourn, Philomathes.
A nice discussion of the "Uphill Climber", one of the problems in the book, is explained by the excellent mathematical writer, Julian Havel. *http://plus.maths.org
1775 Paul Revere’s Ride. The revolutionary War began the next day. Now you probably think this has nothing to do with mathematics, but how do you suppose he got that lantern up in the church steeple? Easy, he used a key to get in. Since he was a change ringer, a highly mathematical activity, he needed a key to get up to the bells. *VFR
Revere was not in the church himself that night, and two families claim credit for their ancestor being the actual hanger of the lights. A plaque in the Old North Church (by his ancestors) credits Robert Newman, a Sexton of the church who probably had a key himself. (Maybe less math than we thought) And don't be fooled by the SEXton to think it is related to six, it is from the same root as sacred. PB
1796 Professor E. A. W. Zimmerman sends a short notice of Gauss’s work on constructibility of regular polygons (see March 30, 1796) to the Jenenser Intelligenzblatt. He adds, “It is worthy of notice that Herr Gauss is now in his 18th year and has devoted himself here in Brunswick to philosophy and classical literature with just as great success as to higher mathematics.” [Tietze, 204] *VFR (found this on Twitter from Matt Henderson....and loved it..
"Erdős believed God had a book of all perfect mathematical proofs.
God believes Gauss has such a book.")
1810 Gauss elected a member of the Berlin Academy of Sciences. *VFR
1831 Founding of the University of the City of New York. [Muller] *VFR
1881, The Natural History Museum in London @NHM_London was opened for the public. It is one of the largest natural history museum‘s of the world.* @SCIHIBLOG
1905 The first mention of the word genetics seems to occur in a letter from William Bateson to Adam Sedgwick.
1942 GE builds first US Jet Aircraft Engine: In1941, the U.S. Army Air Corps picked GE's Lynn, Massachusetts, plant to build a jet engine based on the design of Britain's Sir Frank Whittle. Six months later, on April 18, 1942, GE engineers successfully ran the I-A engine.
In October 1942, at Muroc Dry Lake, California, (today, Edwards Air Force Base) two I-A engines powered the historic first flight of a Bell XP-59A Airacomet aircraft, launching the United States into the Jet Age. *About GE website
Bell P-59B Airacomet |
1958 On his 100th birthday India issued a stamp commemorating the centenary of the birth of Dr. Dhondo Keshav Karve (1858–1922), pioneer of women’s education. [Scott #299]*VFR
1986 IBM First to Use Megabit Chip:
Newspapers report that IBM had become the first computer manufacturer to use a megabit chip -- a memory chip capable of storing 1 million bits of information -- in a commercial product, its Model 3090. The announcement is heralded as a notable triumph for American computer makers, whose work had been perceived as having fallen behind that of the Japanese electronics industry.*CHM
2011 Scientists demonstrate mathematically that asymmetrical materials should be possible; such material would allow most light or sound waves through in one direction, while preventing them from doing so in the opposite direction; such materials would allow the construction of true one-way mirrors, soundproof rooms, or even quantum computers that use light to perform calculations. *Wik
1838 Paul Émile Lecoq de Boisbaudran (18 April 1838 – 28 May 1912) French chemist who developed improved spectroscopic methods which had recently been developed by Kirchhoff. In 1859, he set out to scan minerals for unknown spectral lines. Fifteen years of persistence paid off when he discovered the elements gallium (1875), samarium (1880), and dysprosium (1886). He ranks with Robert Bunsen, Gustav Kirchhoff and William Crookes as one of the founders of the science of spectroscopy. Guided by the general arrangement of spectral lines for elements in the same family, he believed the element he called gallium (in honour of France) was the eka-aluminium predicted by Mendeleev between aluminium and indium. Since it is liquid between about 30 - 1700 deg C, a gallium in quartz thermometer can measure high temperatures. *TIS
1892 Dmitrii Evgenevich Menshov (18 April 1892 in Moscow, Russia - 25 Nov 1988)
For his work on the representation of functions by trigonometric series, Menshov was awarded a State Prize in 1951. He was then elected a Corresponding Member of the USSR Academy of Sciences in 1953. In 1958 Menshov attended the International Congress of Mathematicians in Edinburgh and he was invited to address the Congress with his paper On the convergence of trigonometric series. *SAU
1907 Lars Valerian Ahlfors (18 Apr 1907; 11 Oct 1996 at age 89) Finnish mathematician who was awarded one of the first two Fields Medals in 1936 for his work with Riemann surfaces. He also won the Wolf Prize in 1981.*TIS
1904 Stefan E Warschawski (18 April 1904 in Lida, Russia (now Belarus)- 5 May 1989 in San Diego, California, USA) With careful scholarship, he made lasting contributions to the theory of complex analysis, particularly to the theory of conformal mappings. With keen judgment, he guided two mathematics departments to eminence. With modest gratitude, he cemented many friendships along the way.*SAU
1911 Maurice Goldhaber (18 Apr 1911; 11 May 2011 at age 100) Austrian-American physicist who devised an experiment to show that neutrinos always rotate in one direction (only counterclockwise). His method was simple, elegant, and used an apparatus small enough to fit on a benchtop, rather than employing a huge accelerator. He also discovered that the nucleus of the deuterium atom consists of a proton and a neutron. In the decade (1961-73) that he headed the Brookhaven National Laboratory in New York, he oversaw the experiments there which led to three Nobel Prizes. He died at age 100.*TIS
1916 Ellis Robert Kolchin (April 18, 1916 – October 30, 1991) was an American mathematician at Columbia University. Kolchin earned a doctorate in mathematics from Columbia University in 1941 under supervision of Joseph Ritt. He was awarded a Guggenheim Fellowship in 1954 and 1961.
Kolchin worked on differential algebra and its relation to differential equations, and founded the modern theory of linear algebraic groups.*Wik
1918 Hsien Chung Wang (18 April 1918 in Peking (now Beijing), China - 25 June 1978 in New York, USA)worked on algebraic topology and discovered the 'Wang sequence', an exact sequence involving homology groups associated with fibre bundles over spheres. These discoveries were made while he worked with Newman in Manchester. Wang also solved, at that time, an important open problem in determining the closed subgroups of maximal rank in a compact Lie group. *SAU
1928 Mikio Sato (April 18, 1928 - 9 January 2023) is a Japanese mathematician, who started the field of algebraic analysis. He studied at the University of Tokyo, and then did graduate study in physics as a student of Shin'ichiro Tomonaga. From 1970 Sato has been professor at the Research Institute for Mathematical Sciences, of Kyoto University.
He is known for his innovative work in a number of fields, such as prehomogeneous vector spaces and Bernstein–Sato polynomials; and particularly for his hyperfunction theory. This initially appeared as an extension of the ideas of distribution theory; it was soon connected to the local cohomology theory of Grothendieck, for which it was an independent origin, and to expression in terms of sheaf theory. It led further to the theory of microfunctions, interest in microlocal aspects of linear partial differential equations and Fourier theory such as wave fronts, and ultimately to the current developments in D-module theory. Part of that is the modern theory of holonomic systems: PDEs over-determined to the point of having finite-dimensional spaces of solutions.
He also contributed basic work to non-linear soliton theory, with the use of Grassmannians of infinite dimension. In number theory he is known for the Sato–Tate conjecture on L-functions.*Wik
1945 Joseph Bernstein (April 18, 1945, ) is an Israeli mathematician working at Tel Aviv University. He works in algebraic geometry, representation theory, and number theory.
Bernstein received his Ph.D. in 1972 under Israel Gelfand at Moscow State University. He was a visiting scholar at the Institute for Advanced Study in 1985-86 and again in 1997-98.
Bernstein was elected to the Israel Academy of Sciences and Humanities in 2002 and was elected to the United States National Academy of Sciences in 2004. In 2004, Bernstein was awarded the Israel Prize for mathematics. In 2012 he became a fellow of the American Mathematical Society. *Wik
1949 Charles Louis Fefferman ( April 18, 1949, )born in Washington, D.C. In 1978 he received a Fields Medal for his work on complex analysis.*VFR As a child prodigy, his accelerated schooling resulted a B.S. degrees in physics and mathematics by age 17 and a Ph.D. in mathematics at age 20 from Princeton University (1969). When in he became a professor (1971) at the University of Chicago at the age of 22, he was the youngest full professor ever in the U.S. Two years later, he returned to Princeton as a professor (1973). His Ph.D. dissertation was on "Inequalities for Strongly Regular Convolution Operators." His field of study includes his interest in physics - applied mathematics in vibrations, heat, turbulence, though he is best known for his theoretical work. *TIS
1674 John Graunt- (24 Apr 1620, 18 Apr 1674 at age 54) English statistician, generally considered to be the founder of the science of demography, the statistical study of human populations. His analysis of the vital statistics of the London populace influenced the pioneer demographic work of his friend Sir William Petty and, even more importantly, that of Edmond Halley, the astronomer royal. *TIS
John Graunt was the first person to compile data that showed an excess of male births over female births. He also noticed spatial and temporal variation in the sex ratio, but the variation in his data is not significant. John Arbuthnott was the first person to demonstrate that the excess of male births is statistically significant. He erroneously concluded that there is less variation in the sex ratio than would occur by chance, and asserted without a basis that the sex ratio would be uniform over all time and space. (pb)
1802 Erasmus Darwin (12 December 1731 – 18 April 1802) Prominent English physician, poet , philosopher, botanist, naturalist and the grandfather of naturalist Charles Darwin and the biologist Francis Galton. Erasmus Darwin was one of the leading intellectuals of 18th century England. As a naturalist, he formulated one of the first formal theories on evolution in Zoonomia, or, The Laws of Organic Life (1794-1796). Although he did not come up with natural selection, he did discuss ideas that his grandson elaborated on sixty years later, such as how life evolved from a single common ancestor, forming "one living filament". Although some of his ideas on how evolution might occur are quite close to those of Lamarck, Erasmus Darwin also talked about how competition and sexual selection could cause changes in species.. *TIS
1883 Édouard Albert Roche (17 Oct 1820, 18 Apr 1883 at age 62) was a French mathematical astronomer who studied the internal structure of celestial bodies and was the first to propose a model of the Earth with a solid core. He determined (1850) the Roche Limit for a satellite to have a stable orbit around a planet of equal density. The smaller body could not lie within 2.44 radii of the larger body without breaking apart from effect of the gravitational force between them. He later made a rigorous mathematical analysis of Pierre Laplace's nebular hypothesis and showed (1873) the instability of a rapidly rotating lens-shaped body.*TIS
1913 Mary Cannell (19 July 1913 in Liverpool, England - 18 April 2000) It was the work which she undertook after she retired which earns her a place as a highly respected historian of mathematics. Her work stemmed from the fact that George Green had worked as a miller near Nottingham. Green was a mathematician who was well known to almost all students of mathematics around the world, yet little was known of his life. Flauvel writes:- ... widespread knowledge of Green himself dates only from the 1970s when Cannell and other Nottingham colleagues worked to restore his windmill and his memory...When I first visited Green's windmill in Nottingham the booklet which I purchased was George Green Miller and Mathematician written in 1988 by Mary Cannell. She produced a major biography of Green, George Green : Mathematician and Physicist 1793-1841 : The Background to His Life and Work in 1993. In addition she wrote research articles on Green's life and work bringing to the world of mathematics an understanding of Green's remarkable life.
Flauvel writes:- She charmed audiences on several continents, promoting interest in Green and early 19th-century mathematical physics, in the clear tones and pure vowels of pre-war English, somewhere between Miss Marple and Dame Peggy Ashcroft. ... Mary Cannell was working on projects of one sort or another - the Green website, the revised edition of the biography, research papers, the catalogue in the university of Nottingham library - right to the end, in days filled with her characteristic energy and enthusiasm. *SAU
1945 Sir John Ambrose Fleming (29 Nov 1849, 18 Apr 1945 at age 95)English engineer who made numerous contributions to electronics, photometry, electric measurements, and wireless telegraphy. In 1904, he discovered the one directional current effect between a positively biassed electrode, which he called the anode, and the heated filament in an evacuated glass tube; the electrons flowed from filament to anode only. Fleming called the device a diode because it contained two electrodes, the anode and the heated filament. He noted that when an alternating current was applied, only the positive halves of the waves were passed - that is, the wave was rectified (from a.c. to d.c.). It would also take a radio frequency wave and produce d.c.corresponding to the on and off of the Morse code transmitted signals. *TIS Fleming called his invention a “thermionic valve.”
1955 Albert Einstein (14 Mar 1879; 18 Apr 1955 at age 76) German-American physicist who developed the special and general theories of relativity and won the Nobel Prize for Physics in 1921 for his explanation of the photoelectric effect. Recognized in his own time as one of the most creative intellects in human history, in the first 15 years of the 20th century Einstein advanced a series of theories that proposed entirely new ways of thinking about space, time, and gravitation. His theories of relativity and gravitation were a profound advance over the old Newtonian physics and revolutionized scientific and philosophic inquiry.*TIS
An NBC News broadcast of his death is here.
1991 Sir Austin Bradford Hill CBE (8 July 1897 – 18 April 1991) was an English epidemiologist who pioneered the modern randomised clinical trial and, together with Richard Doll, demonstrated the connection between cigarette smoking and lung cancer. Hill is widely known for pioneering the "Bradford Hill" criteria for determining a causal association.
2003 Edgar Frank Codd (19 August 1923 – 18 April 2003) -American computer scientist and mathematician who laid the theoretical foundation for relational databases, for storing and retrieving information in computer records. He also contributed knowledge in the area of cellular automata. *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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