Will computers make mathematicians obsolete?

Mr.Watson

I mean if we someday has quantum computers etc. wouldn't it be able to solve all math problems just by heave number crunching and doing so, wouldn't that meant that every mathematician would be out of job? So is math really bad career for future?

rudolfstr

not really, it you can't crunch most of problems in math just by checking a finite amount of solutions. Most problems have infinite ammount of posible solutions, so checking them all is imposible.

Mentallic

Quantum computers will supposedly only be able to do whatever our current computers can do, just faster.

micromass

Most mathematics problems there is an infinite cases that need to be checked. No matter how fast your computer is, you can never check infinite cases.
What a computer might possibly do is to randomly come up with theorems. So you start with axioms, and you apply the logical rules on that to come up with new true statements. Given enough time, the compute might (or not) come up with a proof for mathematical statements. But the numbers involved are extremely large here and I don't see this happening any time soon.

Mr.Watson

Well then, will that kind of theorem finding make mathematicians obsolete? Because although you say that not anytime soon, but if somebody would make quantum computer the computing capacity would be unimaginable.

Number Nine

It would be perfectly imaginable; it's being imagined right now in any number of academic journals. It can be quantified precisely. Quantum computers are not miracle devices, they're just very useful.

Part of the problem seems to be that you imagine mathematics to be a collection of calculations or equations, which is not true. Many branches of mathematics don't concern numbers at all, and proofs in these areas involve an extremely long process of logical deduction that often involves techniques from many different fields. It's not as simple as telling a computer (quantum or not) to "Prove the Hodge Conjecture" and then coming back in a week when it's done.

micromass

Unimaginable?? I think you greatly overestimate the power of quantum computing.

Jimmy Snyder

Quantum computing is probabilistic so they are useful for executing probabilistic algorithms. An example is Shor's algorithm for factoring certain composite numbers. I believe the number 15 has been factored this way. Maybe not, but anyway, I changed my public key to 77 just in case. I don't know if such a computer can be used to execute deterministic algorithms.

Borek

micromass

According to wiki, they factored 21 already!

AlephZero

IMO computers will be start to be able to prove math theorems when they can add to this list of jokes: http://www.gdargaud.net/Humor/OddPrime.html

Patrick Kale

I was also worried by an idea similar to this, given my knowledge of mathematics and things like that.

Jimmy Snyder

I must be a quantum computer. They left out priest: All the odd numbers are prime.

FreeMitya

I think pop science has distorted people's views on QC.

micromass

Not only on Quantum Computing, sadly enough.

kaos

An interesting perspective on this issue is the notion of NP completeness in computational complexity. Theorem proving is a NP complete problem (a problem that requires an exponential amount of steps to solve((exponential to the size of the inputs )) but can be verified in a polynomial amount of steps).

Quantum computers are not believed to be able to solve NP complete problems efficiently (quantum computers are able to solve BQP complete problems and NP complete is a harder class). The reason is while a QC can represent an exponential number of states in a superposition, it is not clear how to determine which particular state represents the correct answer. There is paper on it by Bernstein and Vazirani (BBBV theorem) but i cant find a source.

There is a good blog for the computer science aspects of QCs here
http://www.scottaaronson.com/blog/?cat=17

But i am not a computer scientist and my view might be mistaken.

Dembadon

No, computers will not replace mathematicians. Computers need humans to tell them what to do.