Why is there still a lot of unsolved math problems, despite having really advanced computers?
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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.
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