Quant trader gemchange_ltd has published a long post on X laying out how he would learn quant trading if starting from scratch. His central claim is blunt: quant is not about stock picking or having opinions on earnings. It is a math discipline, and a serious learner can reach an entry-level threshold in about 18 months if the sequence is followed in order.
A five-stage progression built around math
The roadmap starts with probability, then moves through statistics, linear algebra, calculus and optimization, and finally stochastic calculus. The author argues that nearly every problem in quantitative finance can be reduced to one question: what are the odds, and are they in your favor? That is why conditional probability, Bayesian updating, expected value, and variance come first. He pairs the reading with practical assignments, including solving textbook exercises, simulating coin flips, and coding a Bayesian updater.
Statistics comes next, with a warning that many apparent discoveries in market data are just noise. He focuses on hypothesis testing, p-values, the multiple comparisons problem, Bonferroni correction, Benjamini-Hochberg false discovery control, regression, and maximum likelihood estimation. The message is clear. Most beginner strategies do not survive contact with rigorous testing.
Why matrices and optimization sit at the center
In the linear algebra section, the author treats matrices as the machinery behind portfolio construction, PCA, neural networks, covariance estimation, and factor models. For a universe of 500 stocks, he notes that the covariance matrix contains 125,250 unique values, while portfolio variance can be written as w'Σw. He recommends running PCA on S&P 500 returns and building a Markowitz mean-variance optimizer from scratch.
Calculus and optimization are framed as the language of change. Prices move, volatility shifts, correlations break, and distributions evolve over time. That makes derivatives, Taylor expansions, gradient descent, and convex optimization core tools rather than abstract math exercises. The proposed assignments include implementing gradient descent by hand and solving a portfolio optimization problem with trading-cost constraints.
The real threshold: stochastic calculus
For gemchange_ltd, stochastic calculus is the line between a data scientist interested in markets and a true quant. This section introduces Brownian motion, the idea that (dW_t)^2 = dt, Itô’s lemma, Delta hedging, and the derivation of the Black-Scholes equation. He walks through the hedging argument step by step and lists the Greeks — Delta, Gamma, Theta, Vega, and Rho — as the practical sensitivity measures traders must understand. The study plan calls for deriving Black-Scholes independently and comparing closed-form pricing with Monte Carlo simulation.
Polymarket and LMSR enter the picture
The post also extends the roadmap into prediction markets. The author describes Polymarket as one of the most interesting markets in the world and uses it to connect probability, information theory, convex optimization, and integer programming. He outlines Robin Hanson’s logarithmic market scoring rule, or LMSR, and points out that its pricing function is effectively a softmax. Prices always sum to 1, remain between 0 and 1, and the market maker’s maximum loss is capped at b×ln(n).
Jobs, compensation, and interviews
On careers, the article breaks quant work into four roles: Quant Researcher, Quant Developer or Engineer, Quant Trader, and Risk Quant. It also singles out AI/ML quant roles as the fastest-growing area, citing 88% annual growth in financial-sector AI/ML hiring in 2025. For top U.S. firms, new graduates are placed in a total compensation band of $300,000 to $500,000. Mid-level roles are listed at $550,000 to $950,000, senior positions at $1 million to $3 million+, and star traders or PMs at $3 million to $30 million+. Mid-sized firms are put at roughly $250,000 to $350,000 for new grads. The post also says Jane Street’s average employee pay reached an annualized $1.4 million in the first half of 2025.
The hiring process is described as resume screening, online tests, phone interviews, and a Superday with 3 to 5 consecutive rounds. For mental math, the recommended benchmark on Zetamac is 50+. The author adds that some Jane Street interview questions are intentionally difficult enough that even interviewers may not finish them cleanly, with the focus placed on collaboration and how candidates use hints.
Tools, data, and reading list
The toolkit spans pandas, polars, numpy, scipy, xgboost, lightgbm, pytorch, cvxpy, QuantLib, statsmodels, NautilusTrader, and vectorbt. The post says Polars can run 10 to 50 times faster than pandas on large datasets. Data sources range from yfinance, Finnhub, and Alpha Vantage to Polygon.io and Bloomberg Terminal, with Polygon.io priced at $199 per month and Bloomberg Terminal at about $32,000 per year.
The closing takeaway is not about speed. It is about sequence, estimation error, and mathematical fluency. Tools are now widely available, the author says, but judgment is not, and math remains the deepest moat in quant finance.