Julian Henry

Julian Henry: Mathematics and Human Languages

I am a software engineer in Houston. I write long-form explanations of mathematics, derivations included, and build open-source tools for human languages. Recent work includes six-volume series on why no formula in radicals solves the quintic and on how a sphere turns inside out, and glottosphere.com, a dictionary in which every word of a definition is a link.

I studied computer science at the University of Pennsylvania, graduating in 2020 with a thesis on obfuscation as a privacy mechanism. Many of the volumes carry interactive figures you can drag and step through.

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Interests

Series

  1. On Multiplication

    5 volumes 87 min

    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

    Start with Vol. I

  2. Abel–Ruffini

    6 volumes 60 min

    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

    Start with Vol. I

  3. Sphere Eversion

    6 volumes 55 min

    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

    Start with Vol. I

  4. Mean-Reverting VIX

    6 volumes 51 min

    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

    Start with Vol. I

  5. Primitive Sets

    5 volumes 56 min

    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-Circle

    Start with Vol. I

  6. Black-Scholes-Merton

    3 volumes 42 min

    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

    Start with Vol. I

Notes and essays

  • ghee: Terminal Shortcuts Library

    project

    A set of 617 shell aliases and functions for Git, Docker, Kubernetes and more, with a fuzzy-search command, G, to find them.

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  • README Rosetta: Docs in Every Language

    project

    A CLI that translates READMEs and Sphinx docs with a local Ollama model, and the checks that stop the model from mangling code and links.

    Read Cite

  • Mr. Worldwide: Multilingual GIFs

    project

    A Python script that turns one word into a looping GIF of its translations in 80+ languages, and how it handles fonts and contrast.

    Read Cite

  • SuperWand: Image Retheming

    project

    A Python tool that clusters an image's colors with k-means and swaps them for one of 18 themes or another photo's palette, with examples.

    Read Cite

  • ZIT: Zooplankton Image Tool

    project

    A Python tool that composites video frames into one image of where the animals went, using background subtraction, then links detections into tracks.

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  • Quantum Plankton Under Compression

    study

    A quantum neural network beats a classical one at classifying plankton only while the baseline is undertrained. Tuned fairly, logistic regression wins, and the circuit is classically simulable anyway.

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  • The Fast Fourier Transform in WebAssembly

    study

    Why no WebAssembly Karatsuba can beat V8's BigInt multiply, and how a SIMD floating-point FFT does, by up to 4.5× in kernel time.

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  • Tatuagem: The Boastful Code Signer

    project

    A Python CLI that stamps an ASCII-art banner into every source file as a comment, and how it avoids breaking files across hundreds of languages.

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  • Vakyume: PDF-to-C++ Pipeline

    project

    A pipeline that turns a vacuum-engineering textbook's equations into Python and C++ solvers, and where a language model does and does not belong in it.

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  • Grover's Search

    explainer

    Grover's algorithm as two mirrors rotating a vector: why it needs about √N queries, and why running it longer makes it worse.

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  • Undergraduate Thesis: Queries in the Mist

    thesis

    My 2020 undergraduate thesis at Penn: can fake traffic hide real web activity? A classifier attack on the ISP Pollution tool, with the PDF.

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  • An Analytical Essay on Rafael Troyo's 'El Rubí'

    essay

    An undergraduate essay, in Spanish, on how Rafael Ángel Troyo's story 'El rubí' uses the fantastic to approach a taboo subject.

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Education

  • University of Pennsylvania, Bachelor of Applied Science in Computer Science, 2020. Thesis: Queries in the Mist.