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
Imagine you ask computer “Do purple swans exist?”
It can find the local park and check swans there – nope, they’re all white. But that’s not ALL swans.
It can check the local zoo, and find some white and black swans. But that’s still not all swans.
It can check every zoo on the planet, and every lake on the planet, but even if it doesnt find purple swans that doesnt mean purple swans dont exist. Just means it hasnt found one yet.
A computer can check zoos a lot faster than a human would – but it still faces same problem. Just because you check a billion lakes, doesnt mean you have checked ALL locations where a purple swan can be found. Maybe there’s a purple swan hiding on mars?
A computer is powerful because its fast. It can do number operations really fast – imagine a human who can run between lakes much faster, or a human who can see further distance away to check swans from further away. But that doesnt solve the problem of figuring out if Purple swans exist.
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