**Things that people learn purely out of curiosity**

**can have a revolutionary effect on human affairs**

The 186th day of the year; 186 is the product of the first four primes less the product of the first four positive integers (7 x 5 x 3 x 2 - 4 x 3 x 2 x 1 = 186) . *Prime Curios

and from Jim Wilder @wilderlab

An equation for July 4th: 7⁴ = 2401 = (2 + 4 + 0 + 1)⁴

EVENTS

1045 The Crab Nebula supernova is recorded in China and Japan. *VFR 1826 Thomas Jefferson , principal author of the Declaration of Independence dies on U.S. Independence day. (See Date under Deaths) He was buried at his home, Monticello. He wrote his own epitaph: “Here was buried Thomas Jefferson, author of the Declaration of Independence, of the statute of Virginia for religious freedom, and father of the University of Virginia.” *VFR I find it striking that when he lists his accomplishments, being President of the US did not make his top three.

1662 “By and by comes Mr. Cooper ... of whom I entend to learn Mathematiques; and so begin with him today ... . After an hour’s being with him at Arithmetique, my ﬁrst attempt being to learn the Multiplication table, then we parted till tomorrow.” Samuel Pepys, in his diary....At the time he was something like a modern Secretary of the Navy. *VFR

1744 Euler wrote Christian Goldbach that he has ﬁnished his book Introductio in analysin inﬁnitorum (Lausanne 1748). In this work the trigonometric and logarithmic functions were ﬁrst treated in their modern form. *VFR

1802 The United States Military Academy at West Point established by act of congress earlier in the year opened on July 4. This school was the ﬁrst engineering school in the U.S. Charles Davies, a noted textbook writer, taught there.*VFR Before 1812 it was conducted as an apprentice school for military engineers and, in effect, as the first U.S. school of engineering.

1819 William Herschel writes to his sister, Caroline, "Lina, there is a great comet. I want you to come and assist me. Come to dine and spend the day here.... we shall have time to prepare maps and telescopes. I saw it's situation last night, it has a long tail." He was eighty years old at the time, and he was still at work when he died, two years later. *Timothy Ferris, Coming of Age in the Milky Way

1843 Liouville began an address to the Academy of Sciences with the words: “I hope to interest the Academy in announcing [that in] the papers of Evariste Galois I have found a solution, as precise as it is profound, of this beautiful problem: whether or not it [the general equation of ﬁfth degree] is solvable by radicals.” This work of Galois was published in 1846. *VFR

**1862**Charles Lutwidge Dodgson, mathematics teacher at Oxford, went boating on the Isis, a tributary of the Thames, with the three daughters of Henry George Liddell, dean of Christ Church, Oxford. He was especially fond of Alice Liddell, then ten, and it was mainly for her that he began the story of another Alice’s tumble down a rabbit hole. The work was published exactly three years later as Alice’s Adventures under Ground under the pseudonym Lewis Carroll, with the famous illustrations by John Tenniel (see note). This work is a favorite of mathematicians, so if you haven’t read it recently, you should. See 26 November 1864. [Note: "When Charles Dodgson – more widely known as Lewis Carroll – made drawings in the early 1960s for his book Alice’s Adventures in Wonderland, he was disappointed with the results. He employed cartoonist John Tenniel to create the now-famous illustrations, while his original ideas were consigned to the archive of Christ Church College, Oxford, where he worked as a lecturer in mathematics until his death in 1898. TATE ETC. sent a cultural historian to view Dodgson’s rarely seen drawings which feature in Tate Liverpool’s ‘Alice in Wonderland’ exhibition. " *Tate ETC] From Nov 2011 to Jan 2012 the Tate Liverpool was showing these original works as part of the "Alice in Wonderland" exhibit. You can see some of them at the web page where I found the notes above.)

1963 The San Francisco Chronicle carried a report entitled, “A Milestone in Math—Professor’s New Concept,” by David Perlman. This popular account of Paul J. Cohen’s proof of the independence of the axiom of choice was probably the ﬁrst published. *VFR

2012 U S Independence day occurs on Wednesday. In what year will it next appear on a Wednesday? And the time after that?

BIRTHS

1790 Sir George Everest, (4 July 1790 – 1 December 1866) British military engineer and geodesist, born in Gwernvale, Powys, Wales, UK. He worked on the trigonometrical survey of India (1818-43), providing the accurate mapping of the subcontinent. For more than twenty-five years and despite numerous hardships, he surveyed the longest arc of the meridian ever accomplished at the time. Everest was relentless in his pursuit of accuracy. He made countless adaptations to the surveying equipment, methods, and mathematics in order to minimize problems specific to the Great Survey: immense size and scope, the terrain, weather conditions, and the desired accuracy. Mount Everest, formerly called Peak XV, was renamed in his honour in 1865. *TIS1868 Henrietta Swan Leavitt (July 4, 1868 – December 12, 1921) American astronomer known for her discovery of the relationship between period and luminosity in Cepheid variables, pulsating stars that vary regularly in brightness in periods ranging from a few days to several months. Leavitt's greatest discovery came from her study of 1777 variable stars in the Magellanic Clouds. She determined the periods of 25 Cepheid variables and in 1912 announced what has since become known as the famous Period-Luminosity relation: "since the variables are probably nearly the same distance from the earth, their periods are apparently associated with their actual emission of light, as determined by their mass, density, and surface brightness." Today the Period-Luminosity relation is used to calculate the distances of galaxies.*TIS

1906 Dan Rutherford (4 July 1906 in Stirling, Scotland - 9 Nov 1966 in St Andrews, Fife, Scotland)studied at St Andrews and Amsterdam. He spent most of his career in St Andrews becoming Gregory Professor of Applied Mathematics. In spite of this title most of his research was in pure mathematics and in particular in algebra. He became President of the EMS in 1940 and 1963. *SAU

1911 Frederick Seitz (July 4, 1911 – March 2, 2008) American physicist who made fundamental contributions to the theory of solids, nuclear physics, fluorescence, and crystals. As Eugene Wigner's first doctoral student, late in 1932, Seitz developed the cellular method of deriving solid-state wave functions. The widespread application of this Wigner-Seitz method to the understanding of metals is regarded as the catalyst for the formation of the field of solid-state physics in the U.S. His subsequent research focused on the theory and properties of crystals. He studied dislocations and imperfections in crystal structures, the effect of irradiation on crystals, and the process of diffusion (the movement of atoms or particles caused by random collision) in crystalline materials.*TIS

1936 Birthday of Guy Otttewel, writer of the eclipse book Understanding Eclipses and many other astronomical publications. *NSEC

1945 John Allen Paulos (July 4, 1945 - )born in Denver, Colorado. Currently a professor at Temple University, he is the author of the popular book Innumeracy. *VFR American mathematician and author of books encouraging people to make sense of the statistics and figures that inform their lives. He represents that mathematics as a subject that is easy to learn and understand. Paulos argues that ignorance of basic mathematical concepts discourages critical thinking and results in costly mistakes and misguided decisions by both political leaders and ordinary people in their everyday lives.*TIS

DEATHS

1742 Guido Grandi died. He corresponded with Leibniz on the sum of the series 1−1+1−1+1−•••. *VFR Luigi Guido Grandi (October 1, 1671 – July 4, 1742) was an Italian priest, philosopher, mathematician, and engineer born in Cremona. He was Jesuit-educated and became a member of the Camaldolese order. He became a professor of philosophy at the Camaldolese monastery in Florence in 1700 and a professor of mathematics in 1714. In mathematics Grandi is best known for studying the rose curve, a curve which has the shape of a petalled flower, and for Grandi's series. He named the rose curve rhodonea. He also contributed to Note on the Treatise of Galileo Concerning Natural Motion in the first Florentine edition of Galileo Galilei's works and helped introduce Gottfried Leibniz's ideas on calculus to Italy. He also worked as an engineer, being superintendent of water at Tuscany, and in that capacity he was involved in the drainage of the Chiana Valley. In 1709 he visited England where he was elected a Fellow of the Royal Society.*Wik

1826 Thomas Jeﬀerson 13 Apr 1743, 4 Jul 1826 at age 83) U.S. president who was throughout his lifetime an extraordinarily learned man, including interests in mathematics and natural sciences. He corresponded with such men as Joseph Priestley, and sometimes contributed time and money to progress in these fields. He collected and classified fossils. He was interested in the experiments being made in ballons and submarines. While visiting Europe, he sent home various mechanical and scientific gadgets produced including a polygraph and phosphorus matches. At his Monticello estate, he practiced scientific farming, and was always on the lookout for a significant new plant or seed. Jefferson died shortly before 1pm. His old friend, John Adams, died a few hours later.*TIS

1901 Peter Guthrie Tait (28 April 1831 – 4 July 1901) Scottish physicist and mathematician who helped develop quaternions, an advanced algebra that gave rise to vector analysis and was instrumental in the development of modern mathematical physics.*TIS Tait was a fellow-pupil of Maxwell at Edinburgh Academy and both of them went on to study at Edinburgh University and Cambridge. Tait became Professor of Mathematics at Queen's College Belfast and then moved to the Chair of Natural Philosophy at Edinburgh which he occupied for more than 40 years. With his collaborations with Maxwell, Thomson (Lord Kelvin) and Hamilton he made important contributions in both mathematics and physics. He became one of the first honorary members of the EMS in 1883. *SAU

1910 Giovanni Virginio Schiaparelli, (14 March 1835 - 4 July 1910) Italian astronomer who is remembered for his observations of Mars over seven oppositions and named the "seas" and "continents". In 1877, he saw on the surface of the planet Mars the markings that he called canali (channels), later misinterpreted as "canals." He made extensive studies, both observational and theoretical, of comets, determining from the shapes of their tails that there was a repulsive force from the sun. He showed that meteor swarms travel through space in cometary orbits. He explained the regular meteor showers as the result of the dissolution of comets and proved it for the Perseids. He suggested that Mercury and Venus rotate on their axes, discovered the asteroid Hesperia (1861) and was a major observer of double stars.*TIS

1934 Marie Marja Sklodowska Curie (7 November 1867 – 4 July 1934) was a Polish-born French chemist and physicist. In 1898, her celebrated experiments on uranium minerals led to discovery of two new elements. First she separated polonium, and then radium a few months later. The quantity of radon in radioactive equilibrium with a gram of radium was named a curie (subsequently redefined as the emission of 3.7 x 1010 alpha particles per sec.) With Henri Becquerel and her husband, Pierre Curie, she was awarded the 1903 Nobel Prize for Physics. She was then sole winner of a second Nobel Prize in 1911, this time in Chemistry. Her family won five Nobel awards in two generations. She died of radiation poisoning from her pioneering work before the need for protection was known.*TIS

1962 Thomas Jefferson Jackson See (19 Feb 1866 in Montgomery City, Missouri - 4 July 1962 in Oakland, California, USA) was an U S astronomer who studied in the University of Missouri and in Berlin. He fell out with his astronomical colleagues and was eventually banned from publishing. He spend the last part of his life arguing against Einstein's Theory of Relativity. *SAU

1986 Oscar Zariski's work was on foundations of algebraic geometry using algebraic methods. He worked on the theory of normal varieties, local uniformisation and the reduction of singularities of algebraic varieties.*SAU

1987 Bengt Strömgren (21 Jan 1908; 4 Jul 1987) Bengt (Georg Daniel) Strömgren was a Danish astrophysicist who pioneered the present-day knowledge of the gas clouds in space. Researching for his theory of the ionized gas clouds around hot stars, he found relations between the gas density, the luminosity of the star, and the size of the "Strömgren sphere" of ionized hydrogen around it. He surveyed such H II regions in the Galaxy, and he also did important work on stellar atmospheres and ionization in stars. *TIS

2002 Laurent-Moïse Schwartz (5 March 1915 in Paris – 4 July 2002 in Paris) was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields medal in 1950 for his work (developing the theory of distributions, a new notion of generalized functions motivated by the Dirac delta-function of theoretical physics). He was the first French mathematician to receive the Fields medal. For a long time he taught at the École polytechnique. *Wik

Credits

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts

*NSEC= NASA Solar Eclipse Calendar

*SAU=St Andrews Univ. Math History

*TIS= Today in Science History

*VFR = V Frederick Rickey, USMA

*Wik = Wikipedia

*WM = Women of Mathematics, Grinstein & Campbell