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
Computers are amazing machines. They can perform calculations many millions of times faster than any human could. If we want to prove that some mathematical statement is true for numbers from 0 to *n*, then a computer can certainly calculate up to *n* much more quickly. But if you want to check all the numbers to infinity – maybe even including numbers with an infinite number of decimals – it doesn’t matter how fast you compute that, it will still take an infinite amount of time. The brute force way doesn’t work.
Instead, “solving” for many maths problems means finding some way to prove it will be true no matter what number is fed into it. Doing this requires creative problem solving ability. Computers…compute, they follow instructions, they aren’t capable of being creative.
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