Foundations of Mathematics

Axiomatic System

Have any recent proofs been discovered?

It seems that as long as there are mathematicians, there will always be someone who tries to solve mathematical questions using proofs. For example, a researcher at the Georgia Institute of Technology recently came up with a new proof, using a game-type scenario, that real numbers are not countable. Another researcher (Grigori Yakovlevich Perelman; for more about him, see “History of Mathematics”) uncovered the proof of the Poincaré conjecture, or that the three-sphere is the only type of bounded three-dimensional space possible that contains no holes, a conjecture first proposed by H. Poincaré in 1953. And what is the dream of some mathematicians? To eventually have formal proofs of all the central theorems in mathematics right at their fingertips, something some have compared to DNA sequencing—as in the “sequencing of the mathematical genome.”


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