อันนี้เป็นวาทะของ number theorist ชื่อดัง
Noam Elkies คนที่พิสูจน์ว่าสมการ Diophantine $a^4+b^4+c^4=d^4$ มีคำตอบ (primitive solution, i.e., $\gcd(a,b,c)=1$) อยู่เป็นอนันต์
"The silliest proof I know of the infinitude of primes is to fix one such integer $s$, and observe that if there were finitely many primes then $$\zeta(s) = \prod_{p\, \rm{prime}} \left( 1-\frac{1}{p^s} \right)^{-1}\quad,$$ and thus also $\pi^s$, would be rational, contradicting Lindemann’s theorem (1882) that $\pi$ is transcendental. It is only a bit less silly to take $s = 2$ and use the irrationality of $\pi^2$, which though unknown to Euler was proved a few generations later by Legendre (1794?)."