Augustin Louis Cauchy

Aug 21 1789 - May 23 1857

Born Paris, France. Died Sceaux, France.

Augustin Louis Cauchy pioneered the study of analysis and the theory of permutation groups. He also researched in convergence and divergence of infinite series, differential equations, determinants, probability and mathematical physics.

Cauchy stated as a military engineer and in 1810 went to Cherbourg to work on Napoleon's English invasion fleet. In 1813 he returned to Paris and, after persuasion from Lagrange and Laplace, devoted himself to mathematics.

He held various posts in Paris at Faculté des Sciences, the Collège de France and École Polytechnique. In 1816 he won the Grand Prix of the French Academy of Science.

He pioneered the study of analysis and the theory of substitution groups (now called permutation groups). Cauchy proved in 1811 that the angles of a convex polyhedron are determined by its faces. In 1814 he published the memoir on definite integrals that became the basis of the theory of complex functions.

His other contributions include researches in convergence and divergence of infinite series, differential equations, determinants, probability and mathematical physics.

Numerous terms in mathematics bear his name:- the Cauchy integral theorem, in the theory of complex functions; the Cauchy-Kovalevskaya existence theorem for the solution of partial differential equations; the Cauchy-Riemann equations and Cauchy sequences.

Cauchy was the first to make a rigorous study of the conditions for convergence of infinite series and he also gave a rigorous definition of an integral. His text "Cours d'analyse" in 1821 was designed for students at École Polytechnique and was concerned with developing the basic theorems of the calculus as rigorously as possible. The 4-volume text "Exercises d'analyse et de physique mathematique" published between 1840 and 1847 proved extremely important.

He produced 789 mathematics papers but was disliked by most of his colleagues. He displayed self-righteous obstinacy and an aggressive religious bigotry. An ardent royalist he spent some time in Italy after refusing to take an oath of allegiance. He left Paris after the revolution of 1830 and after a short time in Switzerland he accepted an offer from the King of Piedmont of a chair in Turin where he taught from 1832. In 1833 Cauchy went from Turin to Prague in order to follow Charles X and to tutor his son.

Cauchy returned to Paris in 1838 and regained his position at the Academy but not his teaching position because he refused to take an oath of allegiance. When Louis Philippe was overthrown in 1848 Cauchy regained his chair at the Sorbonne. He held this post until his death.

Albert Einstein

March 14 1879 - April 18 1955

Born Ulm, Germany. Died Princeton, USA.

Albert Einstein contributed more than any other scientist to the modern vision of physical reality. His theory of relativity is held as human thought of the highest quality.

In 1894 Einstein's family moved to Milan and Einstein decided officially to relinquish his German citizenship in favour of Swiss. In 1895 Einstein failed an examination that would have allowed him to study for a diploma as an electrical engineer at Zurich. After attending secondary school at Aarau, Einstein returned (1896) to the Zurich Polytechnic, graduating (1900) as a secondary school teacher of mathematics and physics.

He worked at the patent office in Bern from 1902 to 1909 and while there he completed an astonishing range of theoretical physics publications, written in his spare time without the benefit of close contact with scientific literature or colleagues. Einstein earned a doctorate from the University of Zurich in 1905. In 1908 he became a lecturer at the University of Bern, the following year becoming professor of physics at the University of Zurich.

By 1909 Einstein was recognised as a leading scientific thinker. After holding chairs in Prague and Zurich he advanced (1914) to a prestigious post at the Kaiser-Wilhelm Gesellschaft in Berlin. From this time he never taught a university courses. Einstein remained on the staff at Berlin until 1933, from which time until his death he held a research position at the Institute for Advanced Study in Princeton.

In the first of three papers (1905) Einstein examined the phenomenon discovered by Max Planck, according to which electromagnetic energy seemed to be emitted from radiating objects in discrete quantities. The energy of these quanta was directly proportional to the frequency of the radiation. This seemed at odds with the classical electromagnetic theory, based on Maxwell's equations and the laws of thermodynamics which assumed that electromagnetic energy consisted of waves which could contain any small amount of energy. Einstein used Planck's quantum hypothesis to describe the electromagnetic radiation of light.

Einstein's second 1905 paper proposed what is today called the special theory of relativity. He based his new theory on a reinterpretation of the classical principle of relativity, namely that the laws of physics had to have the same form in any frame of reference. As a second fundamental hypothesis, Einstein assumed that the speed of light remained constant in all frames of reference, as required by Maxwell's theory.

Later in 1905 Einstein showed how mass and energy were equivalent. Einstein was not the first to propose all the components of special theory of relativity. His contribution is unifying important parts of classical mechanics and Maxwell's electrodynamics.

The third of Einstein's papers of 1905 concerned statistical mechanics, a field of that had been studied by Ludwig Boltzmann and Josiah Gibbs.

After 1905 Einstein continued working in the areas described above. He made important contributions to quantum theory, but he sought to extend the special theory of relativity to phenomena involving acceleration. The key appeared in 1907 with the principle of equivalence, in which gravitational acceleration was held to be indistinguishable from acceleration caused by mechanical forces. Gravitational mass was therefore identical with inertial mass.

By 1911 Einstein was able to make preliminary predictions about how a ray of light from a distant star, passing near the Sun, would appear to be bent slightly, in the direction of the Sun.

About 1912, Einstein began a new phase of his gravitational research, with the help of his mathematician friend Marcel Grossmann, by expressing his work in terms of the tensor calculus of Tullio Levi-Civita and Gregorio Ricci-Curbastro. Einstein called his new work the general theory of relativity. After a number of false starts he published, late in 1915, the definitive version of general theory.

When British eclipse expeditions in 1919 confirmed his predictions, Einstein was idolised by the popular press. Einstein returned to Germany in 1914 but did not reapply for German citizenship. Einstein received the Nobel Prize in 1921 but not for relativity rather for his 1905 work on the photoelectric effect.

He worked at Princeton on work which attempted to unify the laws of physics.

Jean Baptiste Joseph Fourier

March 21 1768 - May 16 1830

Born Auxerre, France. Died Paris, France.

Jean Baptiste Joseph Fourier studied the mathematical theory of heat conduction. He established the partial differential equation governing heat diffusion and solved it by using infinite series of trigonometric functions.

Fourier trained for the priesthood but did not take his vows. Instead took up mathematics studying (1794) and later teaching mathematics at the new Eacute;cole Normale.

In 1798 he joined Napoleon's army in its invasion of Egypt as scientific advisor. He helped establish educational facilities in Egypt and carried out archaeological explorations. He returned to France in 1801 and was appointed prefect of the department of Isere by Napoleon.

He published "Theacuteorie analytique de la chaleur" in 1822 devoted to the mathematical theory of heat conduction. He established the partial differential equation governing heat diffusion and solved it by using infinite series of trigonometric functions. In this he introduced the representation of a function as a series of sines or cosines now known as Fourier series.

Fourier's work provided the impetus for later work on trigonometric series and the theory of functions of a real variable.

Carl Friedrich Gauss

April 30 1777 - Feb 23 1855

Born Brunswick, Germany. Died Göttingen, Germany.

Carl Friedrich Gauss's dissertation gave the first proof of the fundamental theorem of algebra. At the age of 24 he published his theory of numbers, one of the most brilliant achievements in the history of mathematics.

A child prodigy, Gauss taught himself to read and to count by the age of three. Recognising Gauss's talent, the Duke of Brunswick in 1792 provided him with money to allow him to pursue his education. He attended Caroline College from 1792 to 1795 and at this time Gauss formulated the least-squares method and a conjecture on the distribution of primes. This conjecture was proved by Jacques Hadamard in 1896.

In 1795 Gauss went to Göttingen where he discovered the fundamental theorem of quadratic residues.

Gauss developed the concept of complex numbers and in 1799 the University of Helmstedt granted Gauss a Ph.D. for a dissertation that gave the first proof of the fundamental theorem of algebra. In his dissertation Gauss severly criticized Legendre, Laplace and other major mathematicians of the day for their lack of rigour.

At the age of 24 he published "Disquisitiones arithmeticae", his theory of numbers, one of the most brilliant achievements in the history of mathematics. The construction of regular polyhedra occur in this work as do integer congruences and the law of quadratic reciprocity.

He also calculated orbits for the minor planets Ceres and Pallas. The asteroid Ceres had been briefly observed in January 1801 but had then, after it had been tracked for 41 days, was lost in the brightness of the Sun. Gauss computed the orbit using his least squares method and correctly predicted where and when Ceres would reappear. After this he accepted a position as astronomer at the Göttingen Observatory.

In 1820 Gauss invented the heliotrope, an instrument with a movable mirror which reflected the Sun's rays. It is used in geodesy. During the late 1820s, in collaboration with the physicist Wilhelm Weber who he met while the guest of Alexander von Humboldt in Berlin, Gauss explored many areas of physics doing basic research in electricity and magnetism, mechanics, acoustics, and optics. In 1833 he constructed the first telegraph.

When in his 80th year a fellow mathematician met him and described him as follows:

... a venerable, fine old fellow, with a contented manly expression. There is an extraordinary aspect of power about him and his every word. He is about 80 years of age, but not a trace of superannuation is seen about him.

Gauss made a careful study of foreign papers in the reading room at Göttingen and in particular made a systematic study of the financial news. This stood him in very good stead since he was able to gain a considerable personal fortune through his dealings on the stock exchange. He died a very rich man.