Physical Sciences

PDF Article on Biography of Soviet Mathematicians

The Digital Mathematics Archive is a digital collection of mathematical sources, with a primary focus on documents from the late 19th century through today. Papers, letters, manuscripts, e-mail messages, Usenet-news postings, computer rendered images and computations, program source code... many of today's source documents are much more ephemeral than the documents of the previous century. This archive will allow some of this material to be preserved and will give it as wide a distribution as possible.

On the 25th of November 1993, Professor Dr. Hans-Egon Richert died in Blaustein near Ulm, Germany, after a long and severe illness. Richert held a chair of Mathematics at the University of Ulm from 1972 until his retirement as an emeritus professor in 1991.
Richert was born 1924 in Hamburg and was raised there. He had to complete high school at a private institution after being expelled from the public school in the period of the Third Reich for "anglophile leanings".
In 1946, at last back in Hamburg after the war and military service, he could begin his studies of mathematics. He obtained his diploma after eight terms and his PhD only one year later. When his mentor, Professor Max Deuring, accepted a position in Göttingen, the young Richert joined him as an assistant and obtained the venia legendi there in 1954. Soon after he was put in charge of one of the best mathematical libraries in Germany.

Leonhard Euler is considered by many to be the most prolific mathematician in history. He published 866 books and papers and won the Paris Academy Prize 12 times. He was born in Basel, Switzerland on April 15, 1707 and died on September 18, 1783. Euler was the son of a Lutheran minister and entered the University of Basel to study theology like his father but opted to change his major to mathematics under the advice of Johann Bernoulli. He worked at the St. Petersburg Academy of Science and later at the Berlin Academy of Science. In 1735, Euler lost sight in one eye, and in the late 1760's, he became completely blind. Although blind, Euler had such an incredible memory and mathematical mind, he was able to dictate treatises on algebra, optics, and lunar motion until his death. Francois Arago said of his mathematical talents, "He calculated just as men breathe, as eagles sustain themselves in the air." Once, Euler settled an argument between students whose calculation differed by a digit at the fifteenth decimal place by calculating the answer in his head. Euler's contributions to mathematics include the introduction of the symbols e, i, f(x), , and sigma for summations. He also made significant contributions to differential calculus, mathematical analysis, and number theory, as well as optics, mechanics, electricity, and magnetism.

Euler developed the function, which is defined as the number of positive integers not exceeding m that are relatively prime to m. For example, would equal:

> with(numtheory);

> phi(7);

Paul Erdös
1913-1996
"My mother said, `Even you, Paul, can be in only one place at one time.'
Maybe soon I will be relieved of this disadvantage.
Maybe, once I've left, I'll be able to be in many places at the same time.
Maybe then I'll be able to collaborate with Archimedes and Euclid."

MAIN PUBLICATIONS
(i) Monographs
Pell's equation. (Russian) Tbilisi, 1952, pp. 90.
Gitterpunkte in mehrdimensionalen Kugeln. Panstwowe Wydawnictwo Naukowe, Warszawa, 1957, pp. 471.
Lattice points in many-dimensional spheres. (Russian) Publ. Academy of Sci., Tbilisi, 1960, pp. 460.
Weylsche Exponentialsummen in der neueren Zahlentheorie. VEB Deutscher Verlag der Wissenschaften, Berlin, 1963, pp. 231. vskip+0.3cm

PDF Biography of Andrei Weil

For the mathematical community, Kustaa Inkeri is the author of significant papers on number theory, especially on topics related to Fermat's Last Theorem. Finnish mathematicians know Inkeri as the founder of the school of number theory in Finland. At the University of Turku, many of us still think of Inkeri as the Head of the Mathematics Department, a position he held for about 20 years.
The present contribution is intended to give a picture of the man behind these achievements. So this is an essay expressly about the person of a mathematician and no attempt will be made to describe or sum up Inkeri's mathematical work. For an appreciation of the latter the reader is asked to take advantage of the rich material in the rest of this volume.

An unusual and attractive edition of Euclid was published in 1847 in England, edited by an otherwise unknown mathematician named Oliver Byrne. It covers the first 6 books of Euclid, which range through most of elementary plane geometry and the theory of proportions. What distinguishes Byrne's edition is that he attempts to present Euclid's proofs in terms of pictures, using as little text - and in particular as few labels - as possible. What makes the book especially striking is his use of colour.

Kurt Mahler was born on 26 July 1903 at Krefeld am Rhein in Germany; he died in his 85th year on 26 February 1988 in Canberra, Australia. From 1933 onwards most of his life was spent outside of Germany, but his mathematical roots remained in the great school of mathematics that existed in Germany between the two world wars. Above all Mahler lived for mathematics; he took great pleasure in lecturing, researching and writing. It was no surprise that he remained active in research until the last days of his life. He was never a narrow specialist and had a remarkably broad and thorough knowledge of large parts of current and past mathematical research. At the same time he was oblivious to mathematical fashion, and very much followed his own path through the world of mathematics, uncovering new and simple ideas in many directions. In this way he made major contributions to transcendental number theory, diophantine approximation, p-adic analysis, and the geometry of numbers. Towards the end of his life, Kurt Mahler wrote a considerable amount about his own experiences; see 'Fifty years as a mathematician', 'How I became a mathematician', 'Warum ich eine besondere Vorliebe fur die Mathematik habe', 'Fifty years as a mathematician II'. There is also a recent excellent account of his life and work by Cassels (J.W.S. Cassels, 1991, 'Obituary of Kurt Mahler', Acta Arith. (3), 58, 215-228). In preparing this memoir we have freely used these sources. We have also drawn on our knowledge of and conversations with Mahler, whom we first met when we were undergraduates in Australia in the early 1960s.