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}.

EVENTS

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. *Wik **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

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

**1905**The first mention of the word genetics seems to occur in a letter from William Bateson to Adam Sedgwick. A photo of the letter is here

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

1958 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

BIRTHS

1772 David Ricardo (18 April 1772 – 11 September 1823) was an English political economist, often credited with systematizing economics, and was one of the most influential of the classical economists, along with Thomas Malthus, Adam Smith, and John Stuart Mill. He was also a member of Parliament, businessman, financier and speculator, who amassed a considerable personal fortune. Perhaps his most important contribution was the law of comparative advantage, a fundamental argument in favor of free trade among countries and of specialization among individuals. Ricardo argued that there is mutual benefit from trade (or exchange) even if one party (e.g. resource-rich country, highly skilled artisan) is more productive in every possible area than its trading counterpart (e.g. resource-poor country, unskilled laborer), as long as each concentrates on the activities where it has a relative productivity advantage. *Wik 1863 H(ugh) L(ongbourne) Callendar (18 Apr 1863, 21 Jan 1930) was an English physicist famous for work in calorimetry, thermometry and especially, the thermodynamic properties of steam. He published the first steam tables (1915). In 1886, he invented the platinum resistance thermometer using the electrical resistivity of platinum, enabling the precise measurement of temperatures. He also invented the electrical continuous-flow calorimeter, the compensated air thermometer (1891), a radio balance (1910) and a rolling-chart thermometer (1897) that enabled long-duration collection of climatic temperature data. His son, Guy S. Callendar linked climatic change with increases in carbon dioxide (CO2) resulting from mankind's burning of carbon fuels (1938), known as the Callendar effect, part of the greenhouse effect.*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 - ) 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 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

DEATHS

1756 Jacques Cassini (18 Feb 1677; 18 Apr, (*or Sometimes given 16 Apr*) 1756 at age 79) French astronomer whose direct measurement of the proper motions of the stars (1738) disproved the ancient belief in the unchanging sphere of the stars. He also studied the moons of Jupiter and Saturn and the structure of Saturn's rings. His two major treatises on these subject appeared in 1740: Elements of Astronomy and Astronomical Tables of the Sun, Moon, Planets, Fixed Stars, and Satellites of Jupiter and Saturn. He also wrote about electricity, barometers, the recoil of firearms, and mirrors. He was the son of astronomer, mathematician and engineer Giovanni Cassini (1625-1712) with whom he made numerous geodesic observations. Eventually, he took over his father's duties as head of the Paris Observatory.*TIS Cassini was born at the Paris Observatory and died at Thury, near Clermont. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and became maître des comptes in 1706. *Wik

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)

1803 Louis François Antoine Arbogast (October 4, 1759 – April 8, or April 18, 1803) His contributions to mathematics show him as a philosophical thinker somewhat ahead of his time. As well as introducing discontinuous functions, he conceived the calculus as operational symbols. The formal algebraic manipulation of series investigated by Lagrange and Laplace in the 1770s was put in the form of operator equalities by Arbogast in 1800 in Calcul des dérivations.*SAU

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

1923 Pieter Hendrik Schoute (January 21, 1846, Wormerveer–April 18, 1923, Groningen) was a Dutch mathematician known for his work on regular polytopes and Euclidean geometry. *Wik Schoute was a typical geometer. In his early work he investigated quadrics, algebraic curves, complexes, and congruences in the spirit of nineteenth-century projective, metrical, and enumerative geometry. Schläfli's work of the 1850's was brought to the Netherlands by Schoute who, in three papers beginning in 1893 and in his elegant two-volume textbook on many-dimensional geometry 'Mehrdimensionale Geometrie' (2 volumes 1902, 1905), studied the sections and projections of regular polytopes and compound polyhedra. ... Alicia Boole Stott (1870-1940), George Boole's third daughter (of five), ... studied sections of four- and higher-dimensional polytopes after her husband showed her Schoute's 1893 paper, and Schoute later (in his last papers) gave an analytic treatment of her constructions. *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

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.

1999 Gian-Carlo Rota Rota worked on functional analysis for his doctorate and, up to about 1960, he wrote a series of papers on operator theory. Two papers in 1959-60, although still in the area of operator theory, looked at ergodic theory which is an area which requires considerable combinatorial skills. These papers seem to have led Rota away from operator theory and into the area of combinatorics. His first major work on combinatorics, which was to change the direction of the whole subject, was On the Foundations of Combinatorial Theory which Rota published in 1964.

Rota received the Steele Prize from the American Mathematical Society in 1988. The Prize citation singles out the 1964 paper On the Foundations of Combinatorial Theory as:-... the single paper most responsible for the revolution that incorporated combinatorics into the mainstream of modern mathematics. *SAU

2003 Edgar Frank Codd British-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