Julian Henry

Hi, I’m Julian.

Software engineer in Houston. I write about math and build open-source tools.

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Series Chapter lists →

  1. Algorithms 5 volumes 2026

    On Multiplication

    How multiplying big integers got faster: schoolbook n², Karatsuba, the FFT, n log n, and a 2026 preprint claiming to go lower.

    1. ISchoolbook, Karatsuba, Toom-Cook
    2. IIThe Fourier Transform
    3. IIISchönhage-Strassen and Harvey-van der Hoeven
    4. IVSorting and the Mirage of n log n
    5. VBelow n log n

  2. Algebra 6 volumes 2026

    Abel–Ruffini

    Why no formula in radicals solves every quintic: Arnold's short proof by loops and commutators, then the Galois-theory version that names specific unsolvable quintics.

    1. IThe Short Proof
    2. IIRoots Exist
    3. IIISymmetries of the Roots
    4. IVWhere the Roots Live
    5. VTowers and the Galois Correspondence
    6. VIQuintic Symmetry

  3. Topology 6 volumes 2026

    Sphere Eversion

    Why a sphere can be turned inside out without a crease and a circle in the plane cannot, from open sets to Smale's theorem.

    1. IOpen, Closed, Clopen
    2. IIPaths and Homotopy
    3. IIIManifolds and Immersions
    4. IVCurves in the Plane
    5. VFrames and Smale's Theorem
    6. VISeeing the Eversion

  4. Quant finance 6 volumes 2026

    Mean-Reverting VIX

    Models the VIX as a mean-reverting process, prices its futures and options, and shows what one day's option chain can and cannot identify.

    1. IThe Rubber Band
    2. IIFutures, Options and a Flat Smile
    3. IIIJumps, Vol-of-Vol and the Fourier Trick
    4. IVCalibration, and What the Thesis Didn't Say
    5. V2026, viz. VIX
    6. VITrading It, Honestly

  5. Number theory 5 volumes 2025

    Primitive Sets

    Why the primes outweigh every other set of integers where none divides another: the shape of Lichtman's 2022 proof, starting from divisibility.

    1. INo One Divides Another
    2. IIThe Erdős Sum
    3. IIITerritories and the e^γ Bound
    4. IVSlots and the √v Packing
    5. VThe Quarter-Turn

  6. Quant finance 3 volumes 2024

    Black-Scholes-Merton

    What an option is, the Black–Scholes price of a call derived from scratch, and what happens to the formula when each assumption fails.

    1. IOptions, Explained
    2. IIDeriving BSM from Scratch
    3. IIINuance, and Other Approaches

Essays and project notes All of them →