![]() ![]() ![]() The only important feature of a route is the sequence of bridges crossed. The difficulty he faced was the development of a suitable technique of analysis, and of subsequent tests that established this assertion with mathematical rigor.Įuler first pointed out that the choice of route inside each land mass is irrelevant. accessing any bridge without crossing to its other endĮuler proved that the problem has no solution.reaching an island or mainland bank other than via one of the bridges, or.The problem was to devise a walk through the city that would cross each of those bridges once and only once.īy way of specifying the logical task unambiguously, solutions involving either The city of Königsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel River, and included two large islands- Kneiphof and Lomse-which were connected to each other, and to the two mainland portions of the city, by seven bridges. Its negative resolution by Leonhard Euler in 1736 laid the foundations of graph theory and prefigured the idea of topology. The Seven Bridges of Königsberg is a historically notable problem in mathematics. Laplace told his students, "Liesez Euler, Liesez Euler, c'est notre maître à tous" ("Read Euler, readĮuler, he is our master in everything" (Beckmann 1971, p. 153).Īdditional biographies: MacTutor (St.Map of Königsberg in Euler's time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges Testament to Euler's proficiency in all branches of mathematics, the great French mathematician and celestial mechanic Finally, he proved theīinomial theorem was valid for any rational exponent. Had Euler pursued the matter, he would have discovered the constant of motion later found in aĭifferent form by Jacobi and known as the Jacobi integral.Įuler also found the solution to the two fixed center of force problem for a third body. In 1772, he introducedĪ synodic coordinates (rotating) coordinate system to the study of the three-body problem (especially the Harmonic series implied an infinite number of Primes, factoring the fifthįermat number (thus disproving Fermat's conjecture), proving Fermat's lesser theorem, and He also did important work in number theory, proving that that the divergence of the He computed the Riemann zeta function to for even numbers. ![]() To a complex power can be written as a complex number, and investigated the beta and gamma functions. Infinitorum (1748) provided the foundations of analysis. He made significant contributions to the study of differential equations. He also made major contributions in optics, mechanics, electricity, and Such huge quantities, Euler is reported to have replied that his pencil seemed to surpass him in intelligence.įrançois Arago said of him "He calculated just as men breathe, as eagles sustain themselves in theĪir" (Beckmann 1971, p. 143 Boyer 1968, p. 482).Įuler systematized mathematics by introducing the symbols e, i, andį( x) for f a function of x. When asked for an explanation why his memoirs flowed so easily in Prolific mathematical writer of all times finding time (even with his 13 children) to publish over 800 papers in his Large slate when his sight was failing him), he continued to publish his results by dictating them. Nevertheless, aided by his phenomenal memory (and having practiced writing on a He had a phenomenal memory, and once did a calculation in his head to settle anĪrgument between students whose computations differed in the fiftieth decimal place. He worked at the PetersburgĪcademy and Berlin Academy of Science. Swiss mathematician who was tutored by Johann Bernoulli. Euler, Leonhard (1707-1783) - from Eric Weisstein's World of Scientific Biography ![]()
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