The Notebook · essays in long form
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Notes from the intersection of mathematics, finance & AI.

I write here when a question refuses to leave me alone. Expect proofs beside P&Ls, gradients beside gradients of a different sort, and the occasional argument that the three are one subject viewed from different rooms.

Fundamentals
evergreen · start here · the basics
Mathematics
foundations · philosophy · proofs
Finance
markets · unit economics · capital
AI
neural nets · LLMs · the math underneath
Backend
Django · APIs · boring production
FeaturedFinanceApril 22, 2026 16 min

The Clash of the Titans: How 2026 Becomes the Epic Year of the AI IPO

Three S-1s. Ninety days. $240 billion of fresh equity. Anthropic in October. OpenAI in Q4. SpaceX, carrying xAI inside it like a Trojan horse with a chatbot, in summer. There has never been a quarter like this in modern equity-markets history — and inside it, three radically different theories of what an AI company is will collide. The trial that could detonate it all begins in nine days. The strangest underwriter covenant ever printed is already on the syndicate desks. By 2028, two of the three listings will look obviously correctly valued. One will look catastrophically wrong, and the bear case will be the most-cited finance textbook of the decade. This is the dispatch from the cliff edge.

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AIApril 21, 2026 23 min

Why Algorithmic Trading and Machine Learning Are the Same Problem in Different Clothes

The vocabulary separating algo trading from machine learning is a historical accident. Strip it away and you find one subject: gradient descent on a regularised empirical risk, with the covariance matrix doing the heavy lifting and the Bellman equation governing sequential decisions. This essay writes the equations twice, in each field's dialect, and points at the object in the middle — ridge equals shrinkage, Kalman equals state-space RNN, Merton equals policy gradient, Feynman–Kac equals Anderson's reverse SDE. Where the analogy holds, where it breaks, and why the practitioner who masters the shared math has a larger edge than the one who masters the framework.

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AIApril 20, 2026 17 min

Why LightGBM Is Still the First Model I Train for a Trading Strategy

Three weeks ago a friend killed a transformer after it lost money live against the LightGBM it was supposed to replace. Nobody was surprised. This is an essay about why, on small, noisy, non-stationary data, humble models keep beating fashionable ones — and the specific workflow that makes LightGBM the default first choice on a 2026 trading desk.

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BackendApril 19, 2026 16 min

Why, in the Age of AI, Django Is Still the Best Backend Framework — By Far

FastAPI won the async argument. Next.js won the fullstack argument. Rails won the ergonomics argument. Django just kept shipping. In the age of LLM apps that assemble a dozen vendor APIs into a useful product, the batteries-included framework is not the nostalgic choice — it's the pragmatic one.

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FinanceApril 18, 2026 22 min

The Eloquent Math Behind the Top Five Trading Strategies

Trading strategies are not infinite. Five families account for almost every durable quant return stream of the last half-century. This essay takes each one, writes the math as the original paper wrote it, shows the graph that makes the math obvious, and — because a strategy without its failure modes is a prospectus — names the precise conditions under which each one stops working.

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