Conjecture: All odd numbers are prime.
Mathematician's Proof:
3 is prime. 5 is prime. 7 is prime. By induction, all odd numbers are prime.

Physicist's Proof:
3 is prime. 5 is prime. 7 is prime. 9 is experimental error. 11 is prime. 13 is prime ...

Engineer's Proof:
3 is prime. 5 is prime. 7 is prime. 9 is prime. 11 is prime. 13 is prime ...

Programmer' Proof:
3 is prime, 5 is prime, 7 is prime ... Yep! It's true!

Computer Scientist:
3 is prime, 5 is prime, 7 is prime, 7 is prime, 7 is prime, ...

Artificial Intelligence Expert:
7 is prime, 5 is prime, 3 is prime, 2 is prime, 1 is prime, 1 is prime, ....

Engineering Technician:
3 is prime.

Probablist:
3 is prime (p = 1), 5 is prime (p = 1) 7 is prime (p = 1), 9 is prime (p = 1/2), ...

Statistician:
3 is prime, 5 is prime, 8 is prime, ... [the density of primes within the positive integers is asymptotic to 1/(n*ln(n))]