Physicist: Yes. Here’s a proof (there are many):
1) Assume there are a finite number of primes.
2) Multiply them all together and add 1.
3) This new number is not divisible by any of the original primes so it must be a new prime (or be divisible by at least one new prime).
This means that no matter how many primes exist, there must be at least one more. But that’s a one way trip to infinity.
This is a contradiction, so the assumption that there are a finite number of primes is hereby debunked.
There are actually dozens of different proofs of “the infinitude of primes” but this one is probably the simplest.