π is irrational

Proof. If π=a/b with a,b∈ℕ then for any n∈ℕ the integral
aⁿπⁿ⁺¹ ∫₀¹ sin(πx) {xⁿ(1–x)ⁿ/n!} dx
is an integer (apply integration by parts 2n-times & use a/π=b).
But
0 < aⁿπⁿ⁺¹ ∫₀¹ sin(πx) xⁿ(1–x)ⁿ/n! dx < aⁿπⁿ⁺¹/n! < 1
for n large enough.
QED pic.twitter.com/MjD1if1cAz

— Tamás Görbe (@TamasGorbe) April 6, 2019