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
The wildest math problems that we would like to solve today involve irrational numbers – a number that cannot be accurately described with a finite number of digits but instead must be represented through non-numerical means. Pi is a good example of this – “pi” is not so much a “number” as it is a representative of the relationship between a circle’s diameter and circumference. A number rounded to any number of digits can, for almost all intents and purposes, be substituted in for “pi” to solve any number of problems. However, it’s not “pi”, it’s just “close enough to pi to not mess up the intended application of this math problem”. Pi is not the only irrational number, it is merely a common and practical example that we all use multiple times every day, from the spinning parts of your car to the propagation of light and sound waves.
The problems we are talking about however are not looking for an exact answer rounded to so many digits. What we are looking for are *relationships* between different things that can be defined with an equation that will inevitably use irrational numbers. Often the questions we are asking are not so much “how many pi are in this thing”, we are asking “why is pi in this thing” or “why does this part of a phenomena act so much like a circle, wave, etc.”, and just like a dictionary the definition shouldn’t include the word you’re trying to define.
Computers are great at crunching numbers. However, even the best computers only have a finite number of transistors, great as that number may be. However a computer will never have logic, which is a very animal concept that humans have the best grasp on. However, even humans have a finite number of neurons, so we must find ways to describe our world in ways beyond finite things but in ways that finite beings can understand/use – to outsource our unanswered questions to representations and proofs and reasoning. In this way the hardest math problems could be described as philosophy in a way just as much as they could be described as math. And computers don’t do philosophy.
Latest Answers