JULY
1 July, 1646.
What mathematician taught himself to read Greek and Latin while he was a child?
OR
What famous mathematician’s funeral was attended only by his secretary?
Leibniz, the great universal genius of the 17th century and Newton's rival in the invention of the calculus, was born in Leipzig. Having taught himself to read Latin and Greek when he was a mere child, he had, before he was 20, mastered the ordinary textbook knowledge of mathematics, philosophy, theology, and law. At this young age, he began to develop the first ideas of his characteristica generalis, that later blossomed into the symbolic logic of George Boole (1815-1864) and, still later, in 1910, into the great Principia mathematics of Whitehead and Russell. When, ostensibly because of his youth, he was refused the degree of doctor of laws at the University of Leipzig, he moved to Nuremberg. There he wrote a brilliant essay on teaching law by the historical method and dedicated it to the Elector of Mainz. This led to his appointment by the Elector to a commission for the recodification of some statutes. The rest of Leibniz’s life from this point on was spent in diplomatic service, first for the Elector of Mainz and then, from about 1676 until his death, for the estate of the Duke of Brunswick at Hanover.
In 1672, while in Paris on a diplomatic mission, Leibniz met Huygens, who was then residing there, and he prevailed upon the scientist to give him lessons in mathematics. The following year, Leibniz was sent on a political mission to London, where he exhibited a calculating machine to the Royal Society. Before he left Paris to take up his lucrative post as librarian for the Duke of Brunswick, Leibniz had already discovered the fundamental theorem of calculus, developed much of his notation in this subject, and worked out a number of the elementary formulas of differentiation.
Leibniz’ appointment in the Hanoverian service gave him leisure time to pursue his favorite studies, with the result that he left behind him a mountain of papers on all sorts of subjects. He was a particularly gifted linguist, winning some fame as a Sanskrit scholar, and his writings on philosophy have ranked him high in this field. He entertained various grand projects that came to naught, such as reuniting the Protestant and Catholic churches.
In 1682, he and Otto Mencke founded the journal Acta eruditorum, of which he became editor-in-chief. Most of his mathematical papers, which were largely written in the ten-year period from 1682 to 1692, appeared in this journal. In 1700, Leibniz founded the Berlin Academy of Science.
The closing years of Leibniz’ life were embittered by the controversy that others brought upon him and Newton concerning whether he had discovered the calculus independently of Newton. In 1714, his employer became the first German King of England, and Leibniz was left, neglected at Hanover. It is said that when he died two years later, in 1716, his funeral was attended only by his faithful secretary.
Leibniz’ search for his characteristica generalis led to plans for a theory of mathematical logic and a symbolic method with formal rules that would obviate the necessity of thinking. Leibniz invented his calculus sometime between 1673 and 1676. It was on October 29, 1675, that he first used the modern integral sign, as a long letter S derived from the first letter of the Latin word summa (sum). Leibniz had a remarkable feeling for mathematical form and was very sensitive to the potentialities of a well-devised symbolism. His notation in the calculus proved to be very fortunate and is unquestionably more convenient and flexible than the fluxional notation of Newton. We conclude with a closing homage to Leibniz' unique talent. There are two broad and antithetical domains of mathematical thought, the continuous and the discrete; Leibniz is the one man in the history of mathematics who possessed both of these qualities of thought to a superlative degree.
2 July, 1852.
Whose second edition book on group theory is considered a classic?
Birthdate of William Burnside, whose research was in such diverse fields as mathematical physics, complex function theory, geometry, group theory, and the theory of probability. On the basis of the first two fields he was elected a fellow of the Royal Society of London in 1893. It was in the theory of groups, however, that he made his most significant contributions, and he is best known today for his outstanding and comprehensive book: Theory of Groups. The first edition of this work came out in1897, and an improved and augmented second edition in 1911. This second edition is regarded as a classic in its field. Burnside died on August 21, 1927.
3 July, 1822.
What mathematician invented our modern computer/calculator 75 years before it could be produced because of the lack of precision tools used today?
Charles Babbage described his ideas for a “difference engine" to the Royal Society of London. It was about 1812 that the English mathematician Charles Babbage (1792-1871) began to consider the construction of a machine to aid in the calculation of mathematical tables. He resigned the Lucasian professorship at Cambridge in order to devote all his energies to the construction of his machine. In 1623, after investing and losing his own personal fortune in the venture, he presented his ideas to the Royal Society. As a result he secured financial aid from the British government and set to work to make a difference engine capable of employing 26 significant figures and of computing and printing successive differences out to the sixth order.
But Babbage's work did not progress satisfactorily, and 10 years later the governmental aid was withdrawn. Babbage thereupon abandoned his difference engine and commenced work on a more ambitious machine, which he called his analytic engine, which was intended to execute completely automatically a whole series of arithmetic operations assigned to it at the start by the operator. This machine. also, was never completed, largely because the necessary precision tools were not yet made. It wasn't until 73 years after his death the Babbage's dream came true - in the great IBM Automatic Sequence Controlled Calculator (the ASCC), completed at Harvard University in 1944 as a Joint enterprise by the University and the International Business Machines Corporation under contract for the Navy Department. The machine is 51 feet long, 8 feet high, with 2 panels 6 feet long, and weighs about 5 tons.
4 July, 1862.
What author of several children’s books published a number of texts in mathematics?
Charles Lutwidge Dodgson went boating on the Isis River, a tributary of the Thames, with the three daughters of Henry George Liddell, dean of Christ Church, Oxford. It was for the daughter Alice, who at the time was 10, that he later wrote his Alice books, under the pseudonym of Lewis Carroll. Dodgson was an English mathematician and logician holding a mathematical lectureship at Christ Church. Many people, literarily acquainted with him as Lewis Carroll, do not know of Dodgson the mathematician and of the fact that he published a number of texts in the field of mathematics. There is a story that Queen Victoria was so struck with Lewis Carroll's Alice books that she sent out a courtier to bring back a copy of every book that man had written, and the courtier returned with a bundle of mathematics books that the poor Queen could not read. Dodgson carried the art of nonsense-writing to a peak, and there are numerous instances in his literary works of remarkably involved syllogisms of logic. There is some evidence that the changes in Alice's size and proportions in the wonderland adventure form a closed set of projective transformations, and there is no doubt that, Through the Looking Glass is based upon an end-game of chess.
Dodgson was shy and was afflicted with a stammer. It was perhaps at least partly because of his stammer that he was drawn to the society of children, especially little girls, in whose company he felt at ease.
He became an outstanding photographer of young children. He enjoyed children's parties. There once was a children's party held in a house in London, and next door there happened to be at the same time an adults' party. To amuse the children, Dodgson decided on his arrival to walk in on all fours. Unfortunately he crawled into the parlor of the wrong house. Teachers of mathematics will recall the Mock Turtle of Alice in Wonderland, whose "regular course" in school contained, among other things, "the different branches of Arithmetic - Ambition, Distraction, Uglification, and Derision." All problemists have, in their collection, Lewis Carron's Pillow Problems and A Tangled Tale.
5 July, 1687.
Who translated works from Arabic even though he did not know a single word of that language?
Edmund Halley wrote to Isaac Newton that Newton's Principia was finally printed. Halley succeeded John Wallis as Savilian professor of geometry and later became astronomer royal. He restored the lost Book VIII of Apollonius' Conic Sections by inference, and edited various works of the ancient Greeks, translating some of them from the Arabic even though he did not know a single word of that language. He also compiled a set of mortality tables of the sort now basic in the life insurance business. His major original Contributions, however, were chiefly in astronomy and of excellent quality. He was very kind to follow scholars. It was at Halley's urging that Newton completed his great Philosophiae naturalis principle mathematical usually referred to by the briefer title Principia, which was then published in 1687 at Halley's expense.
6 July, 1785.
When did the Continental Congress adopt the decimal system of currency with the dollar as unit?
7 July, 1906.
Who wrote An Introduction to Probability Theory and Its Applications, of which it has been said, “No other work in the subject matches these two volumes, with their combination of purest abstract mathematics and interesting application”?
Birthdate of William Feller in Zagreb, Yugoslavia, where he was educated by a private tutor until he entered the University of Zagreb in 1923, there earning the equivalent of an M.S. degree in 1925. A year later he received a Ph.D. from the University of Gottingen, where he remained until 1928. In 1928 he moved to the University of Liel, to head the applied mathematics laboratory. In 1933, after Hitler came to power, he moved to Copenhagen. The following year he moved to the University of Stockholm, as a research associate in probability. In 1939 he came to the United States as a professor of mathematics and served as the first executive editor of Mathematical Reviews. This international review was founded in 1939 (because the German review had come under Nazi control) and has been of inestimable value to mathematicians. Much of its success is due to Feller's policies. In 1945 Feller accepted a professorship at Cornell University, where he remained until he made his final move - to Princeton University as the Eugene Higgins professor of mathematics.
Feller wrote several papers applying probability theory to genetics, and, with Kolmorgorov (Soviet Union) and Levy (France), transformed mathematical probability into one of the most vigorous branches of present-day mathematics. One of Feller's greatest mathematical bequests is his unique two-volume work: An Introduction to Probability Theory and Its Applications. No other work in the subject matches these two volumes, with their combination of purest abstract mathematics and interesting application -- written in a style reflecting the ebullient enthusiasm of the author.
To listen to Feller lecture was a unique experience.
Shortly before his death Feller was named to receive the 1969 prestigious National Medal of Science, but he died before the awards ceremony took place, and his wife accepted the medal on his behalf. Feller died in Now York City on January 14, 1970.
8 July 1661.
What 18-year-old found Euclid’s Elements obvious?
Isaac Newton matriculated at Trinity College, Cambridge. He was 18 years old. It was not until this stage in his schooling that his attention came to be directed to mathematics, by a book on astrology picked up at the Stourbridge Fair. As a consequence, he first read Euclid's Elements, which he found too obvious, then Descartes’ La geometrie, which he found somewhat difficult. He also read Oughtred's Clavis, works of Kepler and Viete, and the Arithmatica infinitorum by Wallis. From reading mathematics, he turned to creating it.
9 July, 1814.
When did Gauss make his 146th, and final entry in his mathematical diary?
It was in this famous diary that he confided in cryptic fashion many of his greatest mathematical achievements. Because Gauss was both slow and reluctant to publish, this diary, which was not found until 1898, has settled a number of disputes on priority. As an illustration of the cryptic nature of the entries in the diary consider that for July 10, l796, which reads
ERPHKA! D + D + D,
and records Gauss' discovery of a proof of the fact that every positive integer is the sum of 3 triangular numbers. (The nth triangular number is Tn = ). All the entries of the diary except 2 have, for the most part, been deciphered. The entry for March 19, 1797, shows that Gauss had already at that time discovered the double periodicity of certain ellipfunctions (he was not yet 20 years old), and a later entry shows that he had recognized the double periodicity for the general case. This discovery alone, had Gauss published it, would have earned him mathematical fame. But Gauss never published it. (See April 30.)
10 July, 1682.
Roger Cotes was born. (See June 5,)
11 July, 1731.
What 11-year-old composed a paper on curves of the third order?