Birthday Calendar Dates

 

January     30                          July                 4, 13, 14, 10, 21                                  Wednesday 18th:  1/30      2/3      2/16

February    3, 16, 19               August            5, 23, 30                                              Thursday 19th:      2/19      3/3      3/8

March        2, 3, 8, 23             September      8, 9, 22                                                Friday 20th:           3/23     4/1

April           1, 26                     October           25                                                        Monday 23rd:       4/26      6/5      6/9

May                                        November       13                                                        Tuesday 24th:       6/23      6/25    7/4

June           5, 9, 23, 25           December                                                                   Wednesday 25th:  7/10      7/13    7/14

                                                                                                                                    Thursday 26th:      7/21      8/5      8/23

                                                                                                                                    Friday 27th:           8/30      9/8   

2nd dates already taken:   6/17     8/2                                                                        Tuesday 1st:          9/9        9/22  

                                                                                                                                    Wednesday 2nd:  10/25     11/13

 

 

 

January 30

 

Mary Frances Winston was the first American woman to accomplish this feat. What was it?

 

Mary Frances Winston, the first American woman to receive her Ph.D. at a German university (Gottingen), was elected to membership in the American Mathematical Society.

 

Bio         Sketch

 

 

 

 

February 3

 

How was Newton's manuscript on Optics destroyed on this date?

 

A fire in Isaac Newton's study destroyed the manuscript in 1692. It is said that the event greatly upset the man.

 

Bio                        Resources                  Voltaire on Newton's Optics

 

 

 

 

 

 February 16

 

What mathematical astronomer spent 12 years with people hired to do the computations developing 15 place table of sines for every 10" of arc?

 

Born on February 16, 1514, Georg Joachim Rhaeticus was the leading Teutonic mathematical astronomer of the 16th century and a disciple of Copernicus. It was because of importunities of Rhaeticus that Copernicus. great work was dramatically published just before the author died. Rhaeticus spent 12 years with people hired to do the computations for two remarkable and still useful trigonometric tables. One was a 10-place table of all six of the trigonometric functions for every 10. of arc. The other was a 15-place table of sines for every 10" of arc. Rhaeticus was the first to define the trigonometric functions as ratios of the sides of a right triangle. 

 

Biographical Sketch        A trig table

 

 

 

 

February 19

 

What mathematician's mother probably saved his life by licking his wounded head for days?

 

Twelve-year-old Nicolo Tartaglia was seriously wounded when the French sacked Brescia (Italy) on February 19, 1512. The boy suffered several saber cuts that split his skull in 3 places and cleft his jaws and palate. He was left for dead, but his mother found him and managed to carry him off. Recalling that a dog, when wounded, licks the injured place, she licked the boy's head for days. He ultimately recovered but the injury to his palate left him with an impediment in his speech, and it was from this that he received his nickname of Tartaglia, the stammerer. The "g" in Tartaglia is silent, so his name also appears as Tartalea.

 

Tartaglia        Ferro        Audio history        A bit more history    Even more

 

 

 

 

 

 

March 3

 

When was Georg Cantor born? 

 

            Georg Ferdinand Ludwig Philip Cantor was born of Danish parents in St. Petersburg, Russia, on March 3rd, 1845, and moved with his parents to Frankfurt, Germany, in 1352.  Georg developed a deep interest in medieval theology and its intricate arguments on the continuous and the infinite.  As a consequence, he gave up his father’s suggestion of preparing for a career in engineering.  Rather, Cantor concentrated on philosophy, physics, and mathematics.  He studied at Zurich, Gottingen, and Berlin (where he took his doctorate in 1867).  He then spent a long teaching career at the University of Halle from 1869 until 1905. In 1874 he commenced his revolutionary work on set theory and the theory of the infinite.  With this work he created a whole new field of mathematical research.  Today, Cantor's set theory has penetrated into almost every branch of mathematics, and it has proved to be of particular importance in the foundations of real function theory.  Cantor died in a mental hospital in Halle in 1918.  Well known is his famous aphorism: "The essence of mathematics lies in its freedom."

 

 Cantor Bio        Publications      Theory of Infinite Sets (blurb)

 

Theory of Infinite Sets (detailed)      A History of Set Theory

 

 

 

 

March 8

 

Who was George Chrystal? 

 

            Chrystal taught at the University of Edinburgh.  His famous and very comprehensive Textbook on Algebra (1889) is still useful today.  In 1878, W. A. Whitworth introduced subfactorial n, defined by n! = n!(1-1/1! + 1/2! - ... + (-1)n /n!)  It represents the number of derangements of a sequence of n objects in which no one of the n objects occupies its original position.  Whitworth denoted his subfactorial n by the symbol || n since the symbol | n  had been used for factorial n.  Chrystal, in Part II of his famous algebra text, suggested the more convenient notation n! which, much to the delight of printers, has generally been used ever since.  Chrystal’s university lectures were not easy to follow.  J. M. Barrie, the eminent Scotch play write and novelist, has written amusingly about this feature of Chrystal’s courses.  Chrystal’s lectures were apparently only for the gifted few and soon pulled away from the average student.  He was, Barrie says, "a fine hare for the hounds who could keep up with him." The students "doggedly took notes, their faces lengthening daily.  Their notebooks reproduced exactly the hieroglyphics of the blackboard, and, examined at night, were as suggestive as the photographs of persons one has never seen."  Chrystal’s classes were quiet,  "nothing heard but the patter of pencils, rats scraping for grain, of which there was abundance, but not one digestion in a bunch."  There is a Legend that says one day on Chrystal’s classroom door appeared the notice: "There will be no class today, as the student is unwell." "In the middle of some brilliant reasoning," recalls Barrie, "Chrystal would stop to add 4, 7, and 11.  Addition of this kind was the only thing he could not do, and he looked to the class for help - - ‘20,’ they shouted, ‘24,’  '17,' while he thought it over.  These appeals to their intelligence made them beam." Chrystal died in 1911. 

 

G. Chrystal Bio     Overview     Details     References     Quote    Subfactorial

 

[Note:  Another commonly used notation for subfactorial is !n .]

 

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 March 23

 Which early 20th century female mathematician was known as an outstanding abstract algebraist?

This is the birth date in 1882 of Amalie Emmy Noether who one of the most outstanding mathematicians in the field of abstract algebra.  She was born in Erlangen, Germany.  Her father, Max Noether (1844-1921), was a distinguished mathematician at the University of Erlangen.  Max Noether was an algebraist, as was Paul Gordan (1837-1912), who also was associated with the University, a close friend of the Noether family, and the major professor for Emmy’s doctoral thesis.  Emmy was greatly influenced by Ernst Fischer (1875-1959), another algebraist with whom she worked after Gordon’s retirement in 1910.  After leaving Erlangen, Emmy studied at Gottingen, where she passed her habilitation examination in 1919.  In 1922 she became extraordinary professor at Gottingen, a position she held until 1933, when, under the excesses of the German national revolution, she was prohibited from academic participation.  She therefore left Germany to accept a professorship at Bryn Mawr College in Pennsylvania and to become a member of the Institute for Advanced Study at Princeton.  She died in 1935, at the age of 53 and at the height of her creative powers.  A centenary celebration of Emmy Noether's birth was held at Bryn Mawr College in 1982.

Emmy Noether       Max Noether       Paul Gordan     Ernst Fischer

 Noetherian Rings

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April 1

 

 

            When was President Garfield’s original proof of the Pythagorean theorem first published?

 

            The New England Journal of Education (vol. 3, p. 161, 1876) published, in its weekly mathematics column, an original proof of the Pythagorean theorem by General James Abram Garfield.  A few of our country's presidents have been tenuously connected with mathematics.  George Washington was a surveyor, Thomas Jefferson did much to encourage the teaching of higher mathematics in the United States, and Abraham Lincoln is credited with learning logic by studying Euclid's Elements.  More creative was James Abram Garfield (1831-1881), the country's twentieth president, who in his student days developed a keen interest and fair ability in elementary mathematics.    It was in 1876, while he was a member of the House of Representatives and five years before he became President of the United States, that he independently discovered a very pretty proof of the Pythagorean theorem.  He hit upon the proof in a mathematics discussion with some other members of Congress, and the proof was subsequently printed in the New England Journal of Education.  The proof depends upon calculating the area of the trapezoid in the figure below in two different ways - - first by the formula for the area of a trapezoid (as the product of half the sum of the parallel sides and the perpendicular distance between these sides) and as the sum of the three right triangles into which the trapezoid is dissected.  A student can easily supply the details.  Since a trapezoid, as pictured, exists for any right triangle of legs a and b and hypotenuse c, the Pythagorean theorem is established.

 

James A. Garfield          Pythagorean Theorem        New England Journal of Education

 

 

 

April 26

 

What is the famous story involving British number theorist G. H. Hardy and the spectacular Indian mathematician Srinivasa Aaiyangar Ramanujan?

 

Srinivasa Aaiyangar Ramanujan died on this date in 1920.  Perhaps the most spectacular Indian mathematician of modern times has been the impoverished clerk and untrained genius Ramanujan (1887-1920), who possessed amazing ability to see quickly and deeply into intricate number relations. He was "discovered" in 1913 by the eminent British number theorist G. H. Hardy (1877-1947), whose efforts brought Ramanujan in the following year to England to study at Cambridge University.  There resulted a most remarkable mathematical association between the two men.  The most frequently told story illustrating Ramanujan's uncanny abilities is about a visit once made by Hardy when Ramanujan was ill in a hospital at Putney.  Hardy arrived at the hospital in a taxi bearing the seemingly dull number 1729.  Hardy took down the number and, in curiosity, asked Ramanujan if there is anything interesting about it. Without hesitation Ramanujan said there certainly is, inasmuch as it is the smallest positive integer that can be represented in two different ways as a sum of two cubes.  The publication in the 1920s of Ramanujan's notebooks, and the subsequent work done on them, has disclosed many facets of the man's unusual genius.  Ramanujan had the same preternatural ability with numbers that was possessed by his early predecessors, and his work exhibited the same disorganized character, strong intuition, and slighting of deductive processes also found in the earlier men's work.  Ramanujan might almost be called a twentieth-century Bhaskara.  We see in Ramanujan's work many of the differences between early Hindu and Greek mathematics.  Of course, much of this may be traced to the fact that Ramanujan was largely self-taught.

Ramanujan        G.H. Hardy      Ramanujan’s Notebooks  

 

 

June 5

 

Who showed a penchant for mathematics when only 12 years old?

 

Death of Roger Cotes, on this day in 1716.  Cotes was one of those mathematicians, like Pascal and Galois, who died at an early age and who showed remarkable promise in their field.  Cotes died of a violent fever at the age of 33.  He had shown a penchant for mathematics when he was only twelve years old.  When only twenty-four, he was appointed to the Flumian Professorship of Astronomy, as the first to fill this chair that had been established in 1704 by Dr. Plume, the Archdeacon of Rochester.  In 1713, Cotes published at Cambridge the second edition of Newton's Principia.  His mathematical writings were collected and published shortly after his untimely death.  Newton once said, "If Cotes had lived, we had known something.” The following theorem in geometry is known as Cotes' theorem: The product of the distances of a point P from the vertices of a regular n-gon inscribed in a circle of radius r is equal to |an – rn| if P lies on a radial line through a vertex of the polygon and at distance a from the center of the circle.  Cotes was born on July 10, 1682.

 

Cotes            Cotes’ Circle Property          Cotes’ Spiral                  Cotes’ Number

       

Harmonia Mensuraram         Biography