Unknown German Retiree Proved The “Gaussian Correlation Inequality” Conjecture

https://www.wired.com/2017/04/elusive-math-proof-found-almost-lost

\boxed {P (a + b) \geq P (a) \times P (b)}

Case “=” : if (a, b) independent 
Case “>” : if (a, b) dependent

Thomas Royen used only high-school math (function, derivative) in his proof in 2014. He then published it in arxiv.org website – like Perelman did with the “Poincaré Conjecture”.