Choose a polynomial's coefficients randomly and independently from your favorite nontrivial distribution. Then it should be irreducible with high probability for polynomials of high enough degree. This was previously conjectured for the uniform distribution on \(\{0,1\}\) by Odlyzko and Poonen; now Breuillard and Varjú have proven that it follows from a form of the Riemann hypothesis. See:

https://www.quantamagazine.org/in-the-universe-of-equations-virtually-all-are-prime-20181210/ (preprint at https://arxiv.org/abs/1810.13360)

JordiGH@JordiGH@mathstodon.xyz@11011110 Thanks so much for the preprint. I find the popularisations of Quanta magazine hard to read. In their attempt to appeal to a broader audience, they speak in broad generalities and metaphors that really mask the nature of what they're describing.