Charles Babbage

Charles Babbage Dec 26 1792 - Oct 18 1871 Born Teignmouth, England. Died London, England. Babbage graduated from Cambridge and at the early age of 24 was elected a fellow of the Royal Society. In 1827 he became Lucasian Professor of Mathematics at Cambridge, a position he held for 12 years although Babbage never taught. He originated the modern analytic computer. By 1834 he invented the principle of the analytical engine, the forerunner of the modern electronic computer. In 1830 he published "Reflections on the Decline of Science in England", a controversial work that resulted in the formation, one year later, of the British Association for the Advancement of Science. In 1834 Babbage published his most influential work "On the Economy of Machinery and Manufactures", in which he proposed an early form of operational research. The computation of logarithms had made him aware of the inaccuracy of human calculation, and he became so obsessed with mechanical computation that he spent pounds 6000 in pursuit of it. A government grant of pounds 17000 was given but support withdrawn in 1842. Although Babbage never built an operational, mechanical computer, his design concepts have been proved correct and recently such a computer has been built following Babbage's own design criteria.

Albert Einstein March 14 1879 - April 18 1955 Born Ulm, Germany. Died Princeton, USA 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.

Augustin Louis Cauchy Aug 21 1789 - May 23 1857 Born Paris, France. Died Sceaux, France 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.

Sir Isaac Newton Jan 4 1643 - March 31 1727 Born Woolsthorpe, England. Died London, England. Newton's life can be divided into three quite distinct periods. The first is his boyhood days from 1643 up to his graduation in 1669. The second period from 1669 to 1687 was the highly

productive period in which he was Lucasian professor at Cambridge. The third period (nearly as long as the other two combined) saw Newton as a highly paid government official in London with little further interest in mathematics. Isaac Newton was born in the manor house of Woolsthorpe, near Grantham in Lincolnshire. Although he was born on Christmas Day 1642, the date given on this card is the Gregorian calendar date. (The Gregorian calendar was not adopted in England until 1752.)Newton came from a family of farmers but never knew his father who died before he was born. His mother remarried, moved to a nearby village, and left him in the care of his grandmother. Upon the death of his stepfather in 1656, Newton's mother removed him from grammar school in Grantham where he had shown little promise in academic work. His school reports described him as 'idle' and 'inattentive'. An uncle decided that he should be prepared for the university, and he entered his uncle's old College, Trinity College, Cambridge, in June 1661. Newton's aim at Cambridge was a law degree. Instruction at Cambridge was dominated by the philosophy of Aristotle but some freedom of study was allowed in the third year of study. Newton studied the philosophy of Descartes, Gassendi, and Boyle. The new algebra and analytical geometry of Viète, Descartes, and Wallis; and the mechanics of the Copernican astronomy of Galileo attracted him. Newton talent began to emerge on the arrival of Barrow to the Lucasian chair at Cambridge. His scientific genius emerged suddenly when the plague closed the University in the summer of 1665 and he had to return to Lincolnshire. There, in a period of less than two years while Newton was still under 25 years old, he began revolutionary advances in mathematics, optics, physics, and astronomy. While Newton remained at home he laid the foundation for differential and integral calculus several years before its independent discovery by Leibniz. The 'method of fluxions', as he termed it, was based on his crucial insight that the integration of a function is merely the inverse procedure to differentiating it. Taking differentiation as the basic operation, Newton produced simple analytical methods that unified many separate techniques previously developed to solve apparently unrelated problems such as finding areas, tangents, the lengths of curves, and their maxima and minima. Newton's "De Methodis Serierum et Fluxionum" was written in 1671 but Newton failed to get it published and it did not appear in print until John Colson produced an English translation in 1736. Barrow resigned the Lucasian chair in 1669 recommending that Newton (still only 27 years old) be appointed in his place. Newton's first work as Lucasian Professor was on optics. He had reached the conclusion during the two plague years that white light is not a simple entity. Every scientist since Aristotle had believed this but the chromatic aberration in a telescope lens convinced Newton otherwise. When he passed a thin beam of sunlight through a glass prism Newton noted the spectrum of colours that was formed. Newton argued that white light is really a mixture of many different types of rays which are refracted at slightly different angles, and that each different type of ray produces a given spectral colour. Newton was led by this to the erroneous, conclusion that telescopes using refracting lenses would always suffer chromatic aberration. He therefore proposed and constructed a reflecting telescope. Newton was elected a fellow of the Royal Society in 1672 after donating a reflecting telescope.

Also in 1672 Newton published his first scientific paper on light and colour in the Philosophical Transactions of the Royal Society. Newton's paper was well received but Hooke and Huygens objected to Newton's attempt to prove by experiment alone that light consists in the motion of small particles rather than waves. Perhaps because of Newton's already high reputation his corpuscular theory reigned until the wave theory was revived in the 19th C. Newton's relations with Hooke deteriorated and he turned in on himself and away from the Royal Society. He delayed the publication of a full account of his optical researches until after the death of Hooke in 1703. Newton's "Opticks" appeared in 1704. It dealt with the theory of light and colour and with (i) investigations of the colours of thin sheets (ii) 'Newton's rings' and (iii) diffraction of light. To explain some of his observations he had to use a wave theory of light in conjunction to his corpuscular theory. Newton's greatest achievement was his work in physics and celestial mechanics, which culminated in the theory of universal gravitation. By 1666 Newton had early versions of his three laws of motion. He had also discovered the law giving the centrifugal force on a body moving uniformly in a circular path. However he did not have a correct understanding of the mechanics of circular motion. Newton's novel idea of 1666 was to imagine that the Earth's gravity influenced the Moon, counter- balancing its centrifugal force. From his law of centrifugal force and Kepler's third law of planetary motion, Newton deduced the inverse- square law. In 1679 Newton applied his mathematical skill to proving a conjecture of Hooke's, showing that if a body obeys Kepler's second law then the body is being acted upon by a centripetal force. This discovery showed the physical significance of Kepler's second law. In 1684 Halley, tired of Hooke's boasting, asked Newton whether he could prove Hooke's conjecture and was told that Newton had solved the problem five years before but had now mislaid the paper. At Halley's urging Newton reproduced the proofs and expanded them into a paper on the laws of motion and problems of orbital mechanics. Halley persuaded Newton to write a full treatment of his new physics and its application to astronomy. Over a year later (1687) Newton published the "Philosophiae naturalis principia mathematica" or "Principia" as it is always known. The "Principia" is recognised as the greatest scientific book ever written. Newton analysed the motion of bodies in resisting and non resisting media under the action of centripetal forces. The results were applied to orbiting bodies, projectiles, pendulums, and free-fall near the Earth. He further demonstrated that the planets were attracted toward the Sun by a force varying as the inverse square of the distance and generalised that all heavenly bodies mutually attract one another. Further generalisation led Newton to the law of universal gravitation: all matter attracts all other matter with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. Newton explained a wide range of previously unrelated phenomena:- the eccentric orbits of comets; the tides and their variations; the precession of the Earth's axis; and motion of the Moon as perturbed by the gravity of the Sun.

After suffering a nervous breakdown in 1693, Newton retired from research to take up a government position in London becoming Warden of the Royal Mint (1696) and Master(1699). In 1703 he was elected president of the Royal Society and was re-elected each year until his death. He was knighted in 1708 by Queen Anne, the first scientist to be so honoured for his work.

Blaise Pascal June 19 1623 - Aug 19 1662 Born Clermont-Ferrand, France. Died Paris, France. Pascal's father >(Pascal, Étienne) had unorthodox educational views and decided to teach his son himself. He decided that Pascal was not to study mathematics before the age of 15 and all mathematics texts were removed from their house. Pascal however, his curiosity raised by this, started to work on geometry himself at the age of 12. He discovered that the sum of the angles of a triangle are 2 right angles and, when his father found out he relented and allowed Pascal a copy of Euclid. At the age of 14 Pascal started to attend Mersenne's meetings. Mersenne belonged to the religious order of the Minims, and his cell in Paris was a frequent meeting place for Fermat, Pascal, Gassendi, and others. At the age of 16 Pascal presented a single piece of paper to one of Mersenne's meetings. It contained a number of projective geometry theorems, including Pascal's mystic hexagon. Pascal invented the first digital calculator (1642) to help his father. The device, called the Pascaline, resembled a mechanical calculator of the 1940's. Further studies in geometry, hydrodynamics, and hydrostatic and atmospheric pressure led him to invent the syringe and hydraulic press and to discover Pascal's law of pressure. He worked on conic sections and produced important theorems in projective geometry. In correspondence with Fermat he laid the foundation for the theory of probability. His most famous work in philosophy is "Pensées", a collection of personal thoughts on human suffering and faith in God. 'Pascal's wager' claims to prove that belief in God is rational with the following argument. "If God does not exist, one will lose nothing by believing in him, while if he does exist, one will lose everything by not believing." His last work was on the cycloid, the curve traced by a point on the circumference of a rolling circle. Pascal died at the age of 39 in intense pain after a malignant growth in his stomach spread to the brain.

Karl Gustav Jacob Jacobi Dec 10 1804 - Feb 18 1851 Born Potsdam, Germany. Died Berlin, Germany. Jacobi founded the theory of elliptic functions. Jacobi's father was a banker and his family were prosperous so he received a good education at the University of Berlin. He obtained his Ph.D. in 1825 and taught mathematics at the University of Königsberg from 1826 until his death, being appointed to a chair in 1832. He founded the theory of elliptic functions based on four theta functions. His "Fundamenta nova theoria functionum ellipticarum" in 1829 and its later supplements made basic contributions to the theory of elliptic functions. In 1834 Jacobi proved that if a single-valued function of one variable is doubly periodic then the ratio of the periods is imaginary. This result prompted much further work in this area, in particular by Liouville and Cauchy. Jacobi carried out important research in partial differential equations of the first order and applied them to the differential equations of dynamics. He also worked on determinants and studied the functional determinant now called the Jacobian. Jacobi was not the first to study the functional determinant which now bears his name, it appears first in a 1815 paper of Cauchy. However Jacobi wrote a long memoir "De determinantibus functionalibus" in 1841 devoted to the this determinant. He proves, among many other things, that if a set of n functions in n variables are functionally related then the Jacobian is identically zero, while if the functions are independent the Jacobian cannot be identically zero.

Jacobi's reputation as an excellent teacher attracted many students. He introduced the seminar method to teach students the latest advances in mathematics.

David Hilbert

Jan 23 1862 - Feb 14 1943 Born Königsberg, Germany (now Kaliningrad, Russia). Died Göttingen, Germany. Hilbert received his Ph.D. from the University of Königsberg and was a member of staff there from 1886 to 1895 In 1895 he was appointed to the chair of mathematics at the University of Göttingen, where he continued to teach for the rest of his life. Hilbert's first work was on invariant theory, in 1888 he proved his famous Basis Theorem. First he gave an existence proof but, after Cayley, Gordan, Lindemann and others were baffled, in 1892 Hilbert produced a constructive proof which satisfied everyone. In 1893 while still at Königsberg he began a work "Zahlbericht" on algebraic number theory. The "Zahlbericht" (1897) is a brilliant synthesis of the work of Kummer, Kronecker and Dedekind but contains a wealth of Hilbert's own ideas. The ideas of the present day subject of 'Class field theory' are all contained in this work. Hilbert's work in geometry had the greatest influence in that area after Euclid. A systematic study of the axioms of Euclidean geometry led Hilbert to propose 21 such axioms and he analysed their significance. He published "Grundlagen der Geometrie" in 1899 putting geometry on a formal axiomatic setting. His famous 23 Paris problems challenged (and still today challenges) mathematicians to solve fundamental questions. In 1915 Hilbert discovered the correct field equation for general relativity before Einstein but never claimed priority. In 1934 and 1939 two volumes of "Grundlagen der Mathematik" were published which were intended to lead to a 'proof theory' a direct check for the consistency of mathematics. Göde's paper of 1931 showed that this aim is impossible. Hilbert contributed to many branches of mathematics, including invariants, algebraic number fields, functional analysis, integral equations, mathematical physics, and the calculus of variations

Jean Baptiste Joseph Fourier March 21 1768 - May 16 1830 Born Auxerre, France. Died Paris, France. 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. 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. 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.

George Gabriel Stokes Aug 13 1819 - Feb 1 1903 Born Sligo, Ireland. Died Cambridge, England. Stokes established the science of hydrodynamics with his law of viscosity (1851), describing the velocity of a small sphere through a viscous fluid.

Stokes published papers on the motion of incompressible fluids in 1842-43 and on the friction of fluids in motion and the equilibrium and motion of elastic solids in 1845. In 1849 Stokes was appointed Lucasian Professor of Mathematics at Cambridge. In 1851 Stokes was elected to the Royal Society and was secretary of the Society from 1854 to 1884 when he was elected president. He investigated the wave theory of light, named and explained the phenomenon of fluorescence in 1852, and in 1854 theorised an explanation of the Fraunhofer lines in the solar spectrum. He suggested these were caused by atoms in the outer layers of the Sun absorbing certain wavelengths. However when Kirchhoff later published this explanation Stokes disclaimed any prior discovery. Stokes developed mathematical techniques for application to physical problems, founded the science of geodesy, and greatly advanced the study of mathematical physics in England. His mathematical and physical papers were published in 5 volumes, the first 3 of which Stokes edited himself in 1880, 1883 and 1891. The last 2 were edited by Sir Joseph Larmor in 1887 and 1891.