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
Depends on the problem.
> The Collatz Conjecture, The Riemann Hypothesis, Goldbach’s conjecture
None of these can be solved by just crunching numbers. For example lets simply state the Collatz Conjecture (also referred to as the 3n+1 problem):
Start by picking a positive integer *n*. If *n* is even, divide it by 2, otherwise triple it and add 1. Does *n* **always** go to 1?
In this case, we *could* in theory use a computer to prove the Collatz Conjecture (that every number will eventually collapse to 1) false by finding a number that breaks the pattern. The problem is you can’t prove the Collatz conjecture true by just sheer computation because you’d have to check an infinite amount of numbers. Even though using computer’s we’ve verified every number up to 2^68 does fall to 1, it’s a possibility that 2^68 + 1 could break the pattern.
Goldbach and Riemann are similar types of problems, we could prove them false with a computer finding a single number that breaks the pattern, but we could never prove it true.
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