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
Answer: computers are really good at doing one thing over and over, with minor variations, like adding actual numbers. Some math problems are more about the structure of math, rather than just adding up numbers. And finally, “just adding up numbers” isn’t a guarantee that a math problem is true for all numbers, everywhere, including infinity. So for some things like, say, calculating prime numbers, you can just set a computer to dividing every number with all the numbers that came before it, and eventually get an answer, but it might take longer than the lifetime of the universe to calculate, which isn’t helpful. Figuring out how to predict whether a number will be prime is a much more useful thing, but it only takes one number that you predict to be prime to turn out not to be, and you’re back to square one. And what if there’s a prime you didn’t predict? So theoretical math spends a lot of time in places where computing isn’t as helpful as it could be.
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