My name is Greg Langmead. From 2011–2025 I was a machine learning manager at Apple, where I worked on Apple News and Stocks.

I have a Ph.D. in mathematics from Columbia University (2001) where I studied gauge theory, supersymmetry, and four-dimensional topology. My dissertation was titled “A Supersymmetric Gauge Theory Formulation of the Donaldson Polynomial Invariants.”

I also have an M.S. in Logic from the Philosophy department at Carnegie Mellon University (2025). My masters thesis was about bringing differential geometry into homotopy type theory. I sometimes use theorem proving software such as Agda and Lean.

Previously I worked at Design Science and SDL Language Weaver.

I’m interested in music and try to find time to practice piano, guitar and sometimes the ukulele. I love learning about the chord progressions used in music and am a frequent visitor to Theorytab.

My interests include mathematics, physics, software, board games (including their iPad versions), and I pile up video games for iOS, Xbox, PC and Mac and never quite get around to playing them. I do the same with books and movies.