New York University mathematical physicist Alan Sokal published in the postmodern humanities journal Social Text a parody entitled “Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity” [1]. His point in doing so was to test whether the field of “cultural studies of science” was seriously lacking in “intellectual standards”. His article is nonsense from start to...

A family of permutations A ⊂ Sn is said to be t-set-intersecting if for any two permutations σ, π ∈ A, there exists a t-set x whose image is the same under both permutations, i.e. σ(x) = π(x). We prove that if n is sufficiently large depending on t, the largest t-set-intersecting families of permutations in Sn are cosets of stabilizers of t-sets. The t = 2 case of this was conjectured by János ...

Abstract Over the recent years deep learning has found successful applications in mathematical reasoning. Today, we can predict fine-grained proof steps, relevant premises, and even useful conjectures using neural networks. This extended abstract summarizes developments of machine reasoning vision N2Formal group at Google Research to create an automatic mathematician. The second part discusses ...

It is said in the New Testament that the apostle Paul, when addressing the Athenians, complimented them for having inscribed “To an unknown god” onto one of their altars. Reading the Babylonian tablet YBC 7289 (Yale Babylonian Collection), one might well be tempted to erect another altar to this unknown mathematician who, nearly four thousand years ago, engraved into clay what is for us one of ...