Of those who will be graduating with degrees in physics this year, about half will go on to further study. Perhaps surprisingly, of the other half, about one-fifth will soon be starting work in the financial sector. According to a report published last year by the Institute of Physics, of those in employment one year after graduation, a job in “finance” was second only in popularity to a job in “education.” Furthermore, many of those who stay on to doctoral level and beyond eventually leave academia to work in the financial sector, often at senior levels in investment banks.

Then again, perhaps it is not surprising that so many physicists wind up working in finance. After all, they are good at using mathematics to solve real-world problems and the money is good. There is more to it than that, though. There are mathematical links between physics and finance that go back at least to 1900, when Louis Bachelier wrote his Theory of Speculation, in which he used the mathematics of a random walk to analyse fluctuations on the Paris stock exchange.

Five years later, the same ideas were used by a young Albert Einstein to explain why pollen grains zigzag when they are suspended in water. His explanation invoked the idea that very large numbers of tiny molecules are responsible for kicking the grains around. This was a crucial insight and provided one of the earliest convincing confirmations of the existence of atoms.

To make the parallel with the financial markets, we might say that stock prices are kicked around by myriad unknown factors in the marketplace. Today, these ideas have been developed into a means of computing the value of sophisticated financial instruments and the management of risk.

As a particle physicist, I work with systems containing just a few particles so I can keep track of the ways they interact with one another. Things spiral out of control when we try to study systems with a large number of components because it is then impossible to keep track of everything. A simple system might be a gas, in which case the components would be the constituent molecules. Although we do not know what the individual molecules are doing, we can make statistical statements; we can speak of the average speed of a molecule or the average distance between a pair of molecules.

Thinking about large collections of particles like this led the physicists of the 19th century to the field of statistical mechanics and to a precise understanding of what is meant by concepts such as “temperature” and “pressure.” In the 1950s, understanding the statistical properties of electrons in semiconductors was exploited to invent the transistor, the tiny switch used to build the logic circuitry that underpins the operation of the microchip.

By backing away from the near-impossible challenge of understanding a complicated system in every detail, the strategy is instead to focus on the more modest goal of computing the odds that the system will behave in a particular way. Precisely the same ideas are used to model the financial markets. The most famous equation in finance was published in 1972. The Black-Scholes equation provided a means to value “European options,” which is the right to buy or sell an asset at a specified time in the future. Remarkably, it is identical to the equation in physics that determines how pollen grains diffuse through water.