Einstein wrote E=mc2 formula, which shows that "matter can be turned to energy and energy into matter." He wrote a paper at age twenty-six showing that, mathematically, the speed of light is always the same.
Plato
Plato firmly believed that mathematics were essential to life. He predicted that future astronomers would need to use geometry to work with the stars. Plato defined many terms including even and odd numbers. He also developed two intellectual methods that would increase geometrical and mathematical thought; he believed that with geometry we "could construct a new foundation of the mind that would bring to light ideas and observations that would have otherwise gone unnoticed." Above Plato's porch read the words, "Let no one unversed in geometry enter my doors."
Galileo Galilei
Galileo wrote Galileo's Paradox, there are "as many perfect squares as there are whole numbers, even though most numbers are not perfect squares." He observes the fact that for every square there is exactly one square root and for every number there is one square, so he supposed that there must be the same amount of each. So that means that there must be finite sets, as opposed to infinite sets. People thought this was an absurd and completely forgot about it, or perhaps only ignored it, for the next two hundred fifty years. But Greg Cantor brought it up again and showed that some infinite sets are larger than others.
Rene Descartes and the Merging of Algebra with Geometry
Rene Descartes was the first mathematician to connect algebra with geometry, as seen in his book La Geometrie. When Descartes heard that Galileo was arrested for claiming that the Earth revolved around the sun, he was a little scared to publish his ideas. But in 1637 his friends persuaded him to publish the Discourse, which discussed science and mathematics. He also came up with the idea of using letters of the alphabet for variables. He found formulas and equations that were general enough to cover geometry and algebra. He often studied curves using algebra. He used algebraic equations to solve a geometric problem. His work took a while to become known, mostly because it was in French, but many other mathematicians came to agree with him.
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