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 ...
 Chemist'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, 743 is prime, 100000000003 is prime ... Yep! It's true!
 Computer Scientist:

3 is prime, 5 is prime, 7 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))]