Home Research Teaching Outreach Programs




  • ICERM (11/2022): ``Mirror Mirror on the Wall''

  • MoMath (07/2015): ``Fractal Beauty''

  • Yale (12/2012): ``The Riemann Hypothesis and Music''


  • IAS Princeton (10/2017): ``Geometry and Arithmetic of Sphere Packings''

  • IMPA Brazil (08/2015): ``The Unreasonable Effectiveness of Thin Orbits''

Outreach / Microblog

Some more mathematically "significant" tweets recorded here:

  • Why aren't we introducing the main ideas of Calculus *much* earlier, in grade school, so students aren't bombarded with a million new ideas at once?
  • Thread on Triple-Product L-functions:
  • Thread on Multiplication Algorithms ("New Math"):
  • Followup: A simple algorithm for division:
  • Thread on Siegel Zeros, Prime Polynomials, and the Class Number One problem:
  • Thread on the Arithmeticity Conjecture for Polyhedra:
  • Thread on why the "evidence" for the Collatz Conjecture may not be so strong:
  • An attempt to search for more such evidence:
  • How could one easily discover Euler characteristic?
  • Thread on the origins of Fourier analysis:
  • Thread on the Prime Number Theorem, Part 1:
    and Part 2:
  • Thread on the origins of trigonometry (the Sun and Half-Moon):
    and Part 2: an explainer on the seasons:
  • Thread on new conjectures about Fibonacci numbers (based on joint work above with Jeff Lagarias):
  • Thread on decidability of Goldbach and Riemann hypothesis (see sub threads for more discussion...)
  • The Langlands program in a tweet:
  • Why is the Riemann hypothesis hard? (Spoiler: if we actually knew the answer, we might have a better chance of proving it...):
  • "Factor City" where the building blocks are... primes!
  • Be careful with convergence and tetration...
  • The local-global conjecture for Apollonian packings: "grade" the packing by height=curvature; every large enough, admissible height has some circles in it:
  • People seem to be surprised by how simple the notion of a "radian" is:
  • A fun use of the Green-Tao theorem:
  • People seem to be surprised by how simple the notion of Pi is:
  • RIP John Conway, Part 1:
    and Part 2:
  • Cardano, Tartaglia, and the Cubic Equation (also, why imaginary numbers were accepted *before* negative numbers!...):
  • Some weird decimal expansions:
  • And a fun game on digits:
  • How do you take a p-adic square root?
  • Chebotarev Density Theorem, "low tech version":
  • Moduli space of triangles up to homothety:
  • Taming the gods with your bare hands (aka the birth of trigonometry):
  • Some non-standard divisibility rules:
  • How you can teach calculus to very little kids:
  • The ancients were right, the planets *do* move on epicycles! (relative to us, of course...):
  • The "Music of the Primes" (from a MoMath lecture):
  • What is conditional expectation?:
  • How could you discover, all on your own, that the angles in a triangle add up to 180?
  • Subtlety in some elementary geometry constructions and the parallel postulate:
  • Linear algebra in a tweet:
  • Where did set theory come from? Analysis!
  • Cardinality for kids:
  • What might math and math publishing look like in 20-50 years?
  • On the evolution of Proof and Rigor in Mathematics. And on PhD education.
  • Perspective art and projective geometry (for kids). How easy it is to miss a beautiful and simple idea for millennia!
  • On the discovery of the einstein (aperiodic monotile):
  • Interview on The Cartesian Cafe with Tim Nguyen

  • Interview on Steve Strogatz's "Joy of X" podcast (by Quanta Magazine).

  • Interview with 3blue1brown's Grant Sanderson