Home Research Teaching Outreach Programs

YouTube Videos (100M+ views)

  • Ben Syversen video on An Ode to Trigonometry, Feb 2025.


  • Veritasium video on Non-Euclidean Geometry, Oct 2023. (12M+ views)


  • Veritasium video on p-adic numbers, June 2023. (8M+ views)


  • Quanta magazine video on a Glimpse at the Langlands Program, June 2022. (2M+ views) Accompanying column here)


  • Veritasium video on the "Cardano" cubic, Nov 2021. (18M+ views)


  • Veritasium video on the 3x+1 Problem, July 2021. (42M+ views)


  • Veritasium video on Cantor Diagonalization/Hilbert Hotel, May 2021. (31M+ views)


  • Veritasium Pi Day video on Newton's Binomial Theorem and his series expansion for Pi, March (almost 14th...) 2021. (15M+ views)


  • Quanta magazine video on the Riemann Hypothesis, Jan 2021. (5M+ views. Accompanying column here)


    • Lectures

    LECTURE COURSES:

    GENERAL PUBLIC LECTURES:

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

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



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





    • Bay Area Math Olympiad (03/2024): ``The Problem of Apollonius''



    RESEARCH LECTURES:

    • Number Theory Web Seminar (5/2021): ``Arithmetic Groups and Sphere Packings''



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



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



    Microblog (Twitter)

    Some more mathematically "significant" tweets recorded here:

    • Some thoughts on AI+Math
    • 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:
    • Faulhaber's formulae via "Bernoulli integration":
    • 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 on Ben Syversen's video "How Simple Math Led Einstein to Relativity":


    • Interview with 3blue1brown's Grant Sanderson