How to Make $1 Million with Math: The Quant

In 2024 one firm most people have never heard of posted 20.5 billion dollars in net trading revenue — nearly double its 2023 figure of 10.6 billion — and roughly 13 billion dollars in net income. It has no retail app, no branch on your high street, and fewer than 3,000 employees. That firm is Jane Street, and on those numbers it out-earned the entire trading desks of Bank of America and Citigroup.

Spread 13 billion dollars of profit across fewer than three thousand people and you get more than four million dollars of net income per employee — generated not by salespeople or dealmakers, but by mathematicians pricing risk. This is the highest-ceiling answer to the question this series keeps asking: what is the most lucrative way to turn being good at math into money? It is also the most honest opposite of the actuary. The actuary is a high floor. The quant is a high ceiling, and a low floor to match.

Jane Street is a proprietary trading firm: it trades its own capital rather than managing yours, and it makes its money as a market maker, quoting a price to buy and a price to sell thousands of securities at once and capturing the tiny spread between them, millions of times a day. On some measures it handled more than ten percent of North American equity volume in 2024.

It is not alone. Citadel Securities, a separate market-making giant, executes north of twenty percent of all US equities trading and around thirty-five percent of US retail order flow — a serious fraction of every stock trade an ordinary American makes passes through its models first. Next to these prop shops sits a second cluster: the quantitative hedge funds. Two Sigma runs more than 60 billion dollars (above 70 billion by late 2025); D.E. Shaw manages around 65 billion.

Whether they call themselves prop shops, market makers, or funds, they share one trait. The people who generate the returns are not traders shouting on a floor. They are researchers writing code and mathematicians modelling probability. This is the world you enter when you become a quant.

"Quant" is not one job. Inside a modern trading firm the work splits three ways, and the split matters because it decides which degree you need and how you get paid.

The quant researcher (QR) is the scientist. They hunt for a statistical signal — a faint, repeatable pattern in years of market data that predicts, a little better than chance, which way a price will move — and turn it into a model. This is the most credential-heavy seat; researchers often hold a PhD in mathematics, physics, statistics, or computer science.

The quant trader (QT) runs the strategies in live markets, manages risk in real time, and decides how much capital to put behind each signal. Traders lean on probability and fast mental arithmetic more than deep theory, and many are hired straight out of a strong bachelor's or master's. The quant developer (QD) builds the machine everything runs on — the low-latency systems that execute an order in microseconds. Developers are elite programmers, usually with a computer-science background, and at the top firms they are paid like the researchers and traders they support.

There is a second axis that shapes both the math and the money: buy-side versus sell-side.

The sell-side is the banks — Goldman Sachs, Morgan Stanley, J.P. Morgan. Their quants mostly price and hedge derivatives, so the math is the continuous-time toolkit: stochastic calculus, partial differential equations, the Black-Scholes world and everything built on it. It is intellectually deep, relatively stable, and the pay is good but bounded.

The buy-side is the hedge funds and prop shops — Jane Street, Citadel, Two Sigma, D.E. Shaw. Their quants are chasing an *edge*: a strategy that actually makes money, priced in statistics and machine learning rather than PDEs. The buy-side is where the eye-watering numbers in this essay live, and it is also where the variance lives. Sell-side is a career. Buy-side is a career with a lottery ticket stapled to it.

Strip away the job titles and every quant is doing one thing: turning uncertainty into a number they can bet on. Three pieces of mathematics sit under almost all of it.

The first is expected value — the probability-weighted average outcome of a bet. If a trade pays outcome x with probability p, its expected value is the sum across every possible outcome:

A market maker does not need to win any single trade. It needs a positive expected value and enough repetitions for the average to assert itself. Which leads to the second idea. A single trade with a razor-thin edge is almost pure noise; the edge only becomes visible when you repeat it. For a strategy with mean edge mu and volatility sigma, repeated N times, the signal-to-noise ratio grows with the square root of N:

This one relationship is why high-frequency firms want millions of trades a day: a tiny per-trade edge that is invisible over ten trades becomes a near-certainty over ten million. The third idea measures how good a strategy really is once you account for its risk. The Sharpe ratio is the return above the risk-free rate divided by the strategy's volatility:

A Sharpe ratio near 2 is the rough bar to run your own book at a top multi-strategy fund — it says your returns are large relative to how much they wobble. Probability, stochastic calculus, statistics and machine learning, optimization: those four fields, plus the ability to write the code that applies them, are the entire toolkit. Everything else is detail.

The firms filter for exactly that toolkit, and the filter is famous. A quant interview is not a conversation about your résumé; it is a timed math exam.

The first round is almost always probability and brainteasers — expected-value puzzles, conditional-probability problems, betting games where you have to compute the fair price on the spot, often under a clock and out loud. Mental arithmetic matters: firms like Jane Street are known for rapid-fire estimation and probability games precisely because they mirror the job.

Later rounds add coding — usually Python, with C++ a strong plus for anything latency-sensitive — and, for researcher roles, statistics and modelling. The through-line is that the entrance exam and the job are the same skill. If you cannot price a simple bet quickly, you do not get to the second round.

There are two well-worn roads in.

The first is the elite STEM undergraduate: a strong degree in maths, physics, or computer science from a target university, ideally decorated with the signals these firms trust — a high finish in a mathematical olympiad, a Putnam score, competitive programming. This route leads most naturally to trading and development seats, where firms hire at the bachelor's and master's level and train you.

The second is the PhD, the standard entry ticket for research seats, where the job is genuinely inventing models from data. The template for this whole world was set by Jim Simons, the geometer whose Medallion Fund famously hired astronomers, physicists, and codebreakers instead of bankers — his story is its own essay, and the firms in this piece are his intellectual heirs. You do not need to be Simons. But you do need to convince people who think like him that you can find a signal in noise.

So, concretely, what does this pay? The honest answer comes with a heavy caveat: quant firms do not publish salaries, so the numbers below are assembled from self-reported data (levels.fyi) and recruiter ranges, not company disclosures. Treat them as well-informed estimates, not audited figures. The pattern, though, is consistent and steep.

A few of those numbers deserve unpacking. New graduates at the top prop and high-frequency firms really can start near half a million dollars all-in, because pay is overwhelmingly bonus-driven — a modest base plus a bonus tied to how much money you or your desk made. As a reference point, self-reported Citadel quant-researcher compensation on levels.fyi runs from roughly 336,000 dollars at entry to about 642,000 a few levels up, with a median near 396,000.

The real prize is the last quant row. A portfolio manager at a multi-strategy fund like Citadel or Millennium typically keeps fifteen to twenty percent of the profit their book generates. On a large book, that is where the numbers run from one million into eight figures. The contrast row is there on purpose: a Fellow actuary, the high-floor career from the companion essay, tops out around 150,000 to 220,000 dollars with almost none of the risk. Same underlying skill, opposite risk profile.

Which brings us back to the number in the title. On the actuary's path, one million dollars in cumulative earnings is a milestone you reach steadily in your early thirties. On the quant's path, the arithmetic is almost embarrassingly fast. If your all-in compensation is around 400,000 dollars a year — the low end of a new-grad trading or research seat at a top firm — then cumulative earnings cross one million dollars in year three:

Push the annual figure up to the 600,000-to-800,000 a developer or a strong trader can reach, and you clear a million in cumulative pay inside two years of leaving university. No graduate degree is strictly required for the trading and development routes, no company to found, no personal capital at risk.

This is the fastest legal conversion of raw mathematical ability into money that exists. Which is exactly why it is also the most crowded and the most brutal.

Everything above is the ceiling. Here is the floor, and it is not soft.

The first catch is variance. On the buy-side, your bonus is a share of the money you made, so a bad year is not a smaller raise — it can be a bonus near zero. The second is competition. These seats are among the most contested jobs on earth; a single new-grad trading class at a top firm may be pulled from tens of thousands of applicants, and the people you are competing against are olympiad medalists and PhDs.

The third catch is the hard one: up-or-out. A portfolio manager who breaches a drawdown limit — often a loss of just five to ten percent on their book — can be cut immediately, book liquidated, seat gone. Annual PM turnover at the big multi-strategy funds is estimated in the region of fifteen to twenty percent a year. The same feature that lets a good year pay millions lets a bad six months end the career. Burnout is common and openly discussed; the hours are long and the pressure is relentless.

This is the precise mirror image of the actuary. The actuary has a high floor and a modest ceiling: very unlikely to be poor, unlikely to be ultra-rich. The quant has a low floor and a spectacular ceiling. You are trading stability for the size of the prize.

Quant vs. actuary vs. data scientist — which should I pick? Same raw skill, probability and modelling, pointed at three different risk profiles. The actuary is the high-floor, high-stability choice (Fellow pay roughly 150,000 to 220,000 dollars, and it barely moves in a recession). The data scientist is the most flexible and portable. The quant pays the most at the top by a wide margin, with far more variance and far more competition. Pick the quant if you want the maximum ceiling and can genuinely stomach the downside.

Do I need a PhD? For a research seat, usually yes — that is where models are invented from data. For trading and development seats, often no; a strong bachelor's or master's from a target school, plus proof you can do fast probability and write good code, is the standard route.

Is it AI-proof? AI is a tool these firms already run on; machine learning *is* the research. It changes what a quant does more than whether the job exists — the edge simply moves to the people who can build and direct the models rather than run them by hand. The demand is for the mathematician who understands the machine, not the one who competes with it.

Is it worth the stress and the up-or-out? For some people, emphatically; for most, honestly, no. If day-to-day thrill and an uncapped upside matter more to you than stability, and you can treat a lost seat as a risk rather than a catastrophe, the quant path offers rewards almost nothing else can match. If the thought of a zero-bonus year or a sudden exit keeps you up at night, the actuary next door is quietly earning a very good living with none of it.