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Bampot

Math and Physics Can't Prove All Truths (www.scientificamerican.com)

submitted 2 weeks ago by Bampot to c/jingszo

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Physicists have described a system that requires an incomputable number to fully understand, another example of the provably unprovable puzzles of mathematics

You will never be able to prove every mathematical truth. For me, this incompleteness theorem, discovered by Kurt Gödel, is one of the most incredible results in mathematics. It may not surprise everyone—there are all sorts of unprovable things in everyday life—but for mathematicians, this idea was a shock. After all, they can construct their own world from a few basic building blocks, the so-called axioms.

Only the rules they have created apply there, and all truths are made up of these basic building blocks and the corresponding rules.

If you find the right framework, experts long believed, you should therefore be able to prove every truth in some way.

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[–] [email protected] 2 points 2 weeks ago* (last edited 2 weeks ago)

If I recall correctly, Gödel's theorem was that no single system can prove everything without being inconsistent. But nothing stops you from having multiple systems and choosing one or another depending on what needs proving. As long as all these systems are consistent with the physical universe, the results will be useful.