So there are currently tons of unsolved math problems such as The Collatz Conjecture, The Riemann Hypothesis, Goldbach’s conjecture and so on… I get that they are so hard that being good at mathematics isn’t enough, but why can’t computers solve them? Or at least solve some parts of the problem, getting a chunk of the work done for the mathematicians that work on them?
Will computers be able to eventually solve this problems in the future as we’ll develop better technology?
In: Mathematics
We do that when we can. A computer can go through a bunch of calculations and if you have a complete set, then it can brute force the problem. This actually happened with proving that the minimum number of clues needed to solve a sudoku is 17. They limited the set to a few billion unique possible states, and set the computer running for a couple months, and they proved it.
But let’s say you’re trying to find a counterexample to the Riemann hypothesis. You plug in .1+.00000000000001i then .1+.00000000000002i etc. It’s a literal infinite amount of calculations to be made. That will not do at all. You need a systematic solution that doesn’t go through every possible value. And it’s equally hard to write a program that can make a systematic solution itself, because not only do you have to prove that that solution is true, but also that your program to find that solution validly connects your solution to the rest of mathematics.
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