Physics
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Lorenze Invariance
-essentially says that the laws of physics don’t change when we switch between different reference frames.
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Gravity vs. Quantum Theory
For the past century there have been two incompatible theories on how the universe works: Gravity (courtesy of Einstein’s general theory of relativity) and Quantum Theory (used for the other three fundamental forces of nature: electromagnetism and the strong and weak nuclear forces ). Both work ok, except in extreme environments (like inside a black hole). So, scientists are looking for a good theory of Quantum Gravity. The problem is that relativity wants gravity to be continuous, while quantum theory wants it grainy.
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Fermat’s Last Theorem
The French mathematician Pierre de Fermat died in 1665. A note found in the margin of his textbook Arithmetica declared he had found a proof for his theorem that xn + yn = zn has no solutions where n is a whole number greater than 2, but did not have room to write it down. The proof was finally found by the Cambridge mathematician Andrew Wiles in 1993.