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Hethen moved on to more advanced maths books and Talmey reports that soon“the flight of his mathematical genius was so high that I could no longerfollow.”

Although 11 years younger than Talmey, Einstein’s “exceptionalintelligence…enabled him to discuss with a college graduate subjects farabove the comprehension of children of his age”.

Her most famous work was the solution to the ,which has been called a "genuine highlight of 19th-century mathematics."Other than the simplest cases solved by Euler and Lagrange,exact ("integrable") solutions to theequations of motion were unknown, so Kovalevskaya received fameand a rich prize when she solved the .

Kovalevskaya studied Abelian integrals and partial differential equations,producing the important Cauchy-Kovalevsky Theorem;her application of complex analysis to physics inspired Poincaréand others.

Of this Heaviside said,"Should I refuse a good dinner simply because I do notunderstand the process of digestion?"

Sofia Kovalevskaya (aka Sonya Kowalevski;née Korvin-Krukovskaya)was initially self-taught, sought out Weierstrass as her teacher,and was later considered the greatest female mathematician ever(before Emmy Noether).

His output of papers, mostly published posthumously,is much smaller than most of the others on this list, yet it isconsidered among the most awesome works in mathematics.

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Einstein seems to have wrestled with the problems of an emission theory of light for some time, looking for a set of differential equations describing such a theory that could replace the Maxwell-Lorentz equations; and trying to explain a number of optical experiments, notably the Fizeau experiment, based on some version of the emission theory. He could not find any such equations, and his attempt to explain the Fizeau experiment led him to more and more bizarre assumptions to avoid an outright contradiction. So he more-or-less abandoned this approach (you will soon see why I say more-or-less), after perhaps a year or more of effort, and returned to a reconsideration of the Maxwell-Lorentz equations. Perhaps there was a way of making these equations compatible with the relativity principle once one abandoned Lorentz's interpretation via the ether concept.

But here he ran into the most blatant-seeming contradiction, which I mentioned earlier when first discussing the two principles. As noted then, the Maxwell-Lorentz equations imply that there exists (at least) one inertial frame in which the speed of light is a constant regardless of the motion of the light source. Einstein's version of the relativity principle (minus the ether) requires that, if this is true for one inertial frame, it must be true for all inertial frames. But this seems to be nonsense. How can it happen that the speed of light relative to an observer cannot be increased or decreased if that observer moves towards or away from a light beam? Einstein states that he wrestled with this problem over a lengthy period of time, to the point of despair. We have no details of this struggle, unfortunately.

Albert Einstein (March 14, 1879 to April 18, 1955) was a German mathematician and physicist who developed the special and general theories of relativity. In 1921, he won the Nobel Prize for physics for his explanation of the photoelectric effect. In the following decade, he immigrated to the U.S. after being targeted by the Nazis. His work also had a major impact on the development of atomic energy. In his later years, Einstein focused on unified field theory. With his passion for inquiry, Einstein is generally considered the most influential physicist of the 20th century.

As a physicist, Einstein had many discoveries, but he is perhaps best known for his theory of relativity and the equation E=MC2, which foreshadowed the development of atomic power and the atomic bomb.

Einstein first proposed a special theory of relativity in 1905 in his paper, “On the Electrodynamics of Moving Bodies,” taking physics in an electrifying new direction. By November 1915, Einstein completed the . Einstein considered this theory the culmination of his life research. He was convinced of the merits of general relativity because it allowed for a more accurate prediction of planetary orbits around the sun, which fell short in ’s theory, and for a more expansive, nuanced explanation of how gravitational forces worked. Einstein's assertions were affirmed via observations and measurements by British astronomers Sir Frank Dyson and Sir Arthur Eddington during the 1919 solar eclipse, and thus a global science icon was born.

Einstein’s 1905 paper on the matter/energy relationship proposed the equation E=MC2: energy of a body (E) is equal to the mass (M) of that body times the speed of light squared (C2). This equation suggested that tiny particles of matter could be converted into huge amounts of energy, a discovery that heralded atomic power. Famed quantum theorist Max Planck backed up the assertions of Einstein, who thus became a star of the lecture circuit and academia, taking on various positions before becoming director of the Kaiser Wilhelm Institute for Physics from 1913 to 1933.

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