Why is there still a lot of unsolved math problems, despite having really advanced computers?
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Computers are good at going through possible solutions and veryifying if they are true. Many math problems involve an infinite number of possible solutions and it doesn’t help if you can go through them quickly — you need a more abstract approach.
There are many problems that exist in life because we don’t know if there’s an easier way to solve it. It could be that it is not a solvable problem. It could be that we haven’t found the answer yet.
Let’s say you wake up one day and you want a unicorn. You look around and – no unicorns. It could be that unicorns actually exist in a remote jungle somewhere – but that means crossings off jungles one at a time and making sure theres no unicorns in there (It could be that unicorns exist, and we’ve just never looked in the right spot (After we found unicorn island, it’s super easy)), It could be that you could make a unicorn via genetic engineering, It could be that unicorns don’t actually exist and you can’t figure out a way to make one either, but maybe we could get a good enough approximation of a unicorn by getting a horse and dressing it up in fancy clothes and a horn. We don’t know until we try and even then there could be a long round of nothing before we give up or have some intuition about some thing.
Math is the same way. Computers are still pretty bad at intuition. They can sometimes figure a solution out by trying a trillion things and seeing if any of them fit. We don’t know if a solution is out there, or there is no solution, or if some mathematician in 50 years will figure something brilliant out that everybody has missed up to this point. Sometimes we don’t need exact solutions and we can sort of make do by getting close enough and a lot of the super computers are really useful in this area also.
Because some things are very very complicated.
It’s a similar idea to chess computers. They’re very powerful and very good but, despite the fact that it’s purely a game of strategy and every piece has predefined moves, therefore there’s only a finite number of moves in each position, nobody and no computer have developed a surefire winning strategy. It’s just too complicated.
Maths is not about answering a question or doing arithmetic.
Maths is about discovering patterns, holes, connections, and analogies between entire areas of mathematics – using geometry to solve a calculus problem that provides a solution to a probabilistic conundrum and then translate that answer back through multi-dimensional matrices to arrive at a seeming paradox which thus proves that you can never have variable X that has a property Y.
The age-old ignorant misconception that maths is just “complicated numbers stuff” is a real disservice and shows people up, and their teachers up. It means you never learned maths, nor what maths actually is.
Computers – incidentally – were invented by mathematicians. They were given life as machines to do what you imply… lots of fast, very simple calculations, and that’s used to do an infinite variety of extremely clever things. But then mathematicians got bored with that, called it computer science, and then carried on doing what they do but with a machine to do all the boring bits that no mathematician cares about.
And the things that computers absolutely suck at? Pattern-finding. Inference. Finding connections and holes. Formulating logical arguments that lead to paradoxes deliberately in order to “prove a negative” to provide more information about another seemingly-unrelated problem that you’re working on.
All the stuff that “advanced computers do well and mathematicians suck at”, that’s never going to solve anything of interest in mathematics. But it plays your games and runs the entire world.
All the stuff that “advanced computers suck at and mathematicians do well”…. that’s actually advanced maths. It’s why AI is rubbish, and why there are things we know that computers literally cannot do. Ever. No matter how powerful or fast or large.
Computers are a tool. They don’t think for themselves, they can’t. But they can be used by something that does think for itself to automate the boring bits so we have more time to spend on the interesting bits.
P.S. Go find a good maths teacher. You can tell a good maths teacher. They will be able to ENTHRALL you about the most ridiculous mathematical things. If you’re weren’t enthralled, likely you had a bad maths teacher. Unfortunately, it’s a real uphill struggle to counteract that as an adult.
Quantum Maths would give us a better understanding, may invoke understanding other dimensions more
This is actually a major unsolved problem in computer science called the P vs NP problem.
https://en.wikipedia.org/wiki/P_versus_NP_problem
Just because you can use a computer to quickly verify a solution to a problem, doesn’t mean you can solve it quickly.
It’s one of the millennium problems, so if you have an answer for it you can win a million bucks. :
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