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
You’re thinking of “Math problem” in similar terms as the problems you’d find in a high-school textbook: neat equations with a definite answer that can be found if you just rearrange and calculate them. Academic mathematics seldom actually works that way.
Mathmatics ask abstract questions that often involve little to no actual calculation to do in the first place. Questions where brute force simply doesn’t work. If I ask you “Is there a largest prime number, and if so what is it?” then you can’t just go try and calculate the largest prime via brute force because for all you know the answer could be “no” and you’d never stop finding prime numbers. However if you go calculate as many as you can be bothered to find and then go “Ok, I’ve found a lot, there are an infinite number of them” you could just as easily have stopped three primes short of the final one. We have examples of patterns that go on for millions of members before just abruptly stopping.
Computers are good at one thing: following instructions really quickly. That’s great if you know what instructions to have it follow, but for things like the Collatz Conjecture we don’t even know that. We can’t write a program for a computer to find the answer because we don’t know what that program would look like or if it even exists.
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