Trading floors were once the preserve of adrenalin-fuelled dealers aggressively executing the orders of brokers who relied on research, experience and gut instinct to decide where best to invest.
Long ago computers made dealers redundant, yet brokers and their ilk have remained the masters of the investment universe, free to buy and sell wherever they see fit.
But the last bastion of the old order is now under threat.
Investment decisions are no longer being made by financiers, but increasingly by PhD mathematicians and the immensely complex computer programs they devise.
Fundamental research and intuition are being usurped by algorithmic formulae. Quant trading is taking over the world's financial capitals.
Mathematicians have long played a vital role in risk management at financial institutions, but their skill set is increasingly being used to make money, not just to stop losing it.
Firms are now employing gifted academic statisticians to track patterns or trends in trading behaviour and create formulae to predict future market movements. These formulae are then fed into powerful computers that buy and sell automatically according to triggers generated by the algorithms.
These so-called quantitative trading programs underpin all quickfire trades - known as high-frequency trading (HFT) - in which stocks can be held for just a matter of seconds.
They are also used in more traditional trading, where the holding period can be days, weeks or months.
Some are fully automated, but most require human oversight to ensure nothing goes too drastically wrong.
Scott Patterson, a Wall Street Journal reporter and author of The Quants, uses the analogy of a plane on autopilot, which can fly itself but where a specially-trained pilot can step in at any moment.
These programs are immensely powerful, constantly monitoring market movements, trading patterns and news flows and are capable of changing strategies within fractions of a second.
The most powerful even have artificial intelligence that can adapt strategies of their own accord.
No-one can be sure quite how successful these quant programs are, but as Mr Patterson says: "They have been around long enough now to assume they are extremely profitable".
Their proliferation would certainly suggest so. One commentator says two of the biggest HFT firms, Tradebot and Getco, alone account for about 15%-20% of all equity trading in the US.
As they are private companies, it is hard to know precisely how far their influence extends.
Indeed, a recent government-backed study in the UK estimated that between a third and a half of all share trading in Europe, and more than two-thirds in the US, was HFT.
"The vast majority of firms use quantitative trading," says Mr Patterson.
"It drives almost everything that goes on on Wall Street."
The impact and ramifications of quant trading are widespread, but ultimately unclear.
The UK study, commissioned by the Foresight programme, found that quant trading helped to reduce dealing costs and improve liquidity, and did not harm overall market efficiency.
In fact, it found that HFT and quant trading have "generally improved market quality".
However, it did highlight one important concern, known in the trade as self-reinforcing feedback loops.
This essentially means a small trigger leading to a series of similar events, each amplifying the last, until the overall impact is significant.
Imagine a share falls in value, triggering a sale on one quant program, pushing the share price even lower. This in turn triggers a sale on another program, pushing the price lower still, and so on and so on.
The problem is exacerbated by the fact that many programs run on the same formulae, and so are piling in and out of the same stocks.
Nowhere is this better demonstrated than by the so-called Flash Crash of May last year, when the US stock market plummeted 700 points in less than five minutes, wiping out about $800bn (£517bn).
When the auto-pilot switches were turned off and the systems overridden, order was restored and the market bounced back within half an hour.
An unfortunate one-off, some say. Others point to far more damaging consequences, citing quant trading as a key contributor to the massive sell-off in stocks in 2008 that saw the US market almost halve in value.
Hedge funds, they say, sold equities fast in order to balance heavy losses on their mortgage investments following the collapse of the US property market, triggering a domino effect across quant trading systems with devastating consequences.
The Foresight study found no direct evidence that automated trading has increased volatility in equity markets, but many disagree, Mr Patterson among them.
Stock market historian David Schwartz is another who is in no doubt that HFT has unsettled markets.
"I believe [certain types of HFT] cause a great deal of damage," he says.
"I've seen too many instances during the recent sell-off where a sudden spurt of frequent trades has sent share prices bouncing down."
The problem is proving it. No-one knows exactly who is making the trades, while the exchanges have no incentive to find out as they are making a great deal of money from them, Mr Schwartz says.
Others argue the problem is more fundamental. Mathematicians, they say, do not understand markets. They deal in absolutes, not the irrational human behaviour that drives so many investment decisions.
As one leading actuary says: "Prices are determined by supply and demand, not by mathematics."
Could it be, then, that academic statisticians are congenitally unsuited to the job they are being paid to do?
Paul Wilmott, a prominent lecturer in quantitative finance, has questioned whether they are "capable of thinking beyond maths and formulas".
"Do they appreciate the human side of finance, the herding behaviour of people, the unintended consequences?"
And if mathematicians do not, there is little chance the computer programmes they create will.
As the Foresight report concludes: "Future trading robots will be able to adapt and learn with little human input. Far fewer human traders will be needed in the major financial markets of the future".
No bad thing, some may say, particularly given recent cases of insider trading and fraud, but Mr Patterson is in no doubt that the proliferation of quant trading is both "inevitable and dangerous".
Far-fetched it may seem, given the widespread disdain in which traders are currently held, but if mathematicians and their algorithm programs prove a poor substitute, we could find ourselves clamouring for their return.