Of those who will be graduating with degrees in physics this year, around a half will go on to further study (doing a PhD is the most popular option). Perhaps surprisingly, of the other half, around 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". Trailing behind those two are jobs in "scientific and technical industries", in "government" and in "energy and the environment". Furthermore, many of those who stay on to PhD 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 Frenchman 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, much smaller than the pollen grains, 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 and because the number of particles is not too great I can keep track of the ways they can interact with one another. Things rapidly spiral out of control whenever we try to study systems with a large number of components because it is then impossible to keep track of everything. Notice the generality of the language – we speak of "systems" and their "components". 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 by physicists at Bell Telephone laboratories to invent the transistor, the tiny switch that is 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, in which case the "system" could be the price of an asset and the "components" would then be the range of things that can influence its price. The most famous equation in finance was published in 1972 and is named after American economists Fischer Black and Myron Scholes. 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.

Intellectual connections such as these are why so many physicists are interested in problems in finance and, in part, why so many have been recruited into the financial sector. It also helps that physicists tend to be good at computer modelling and working with large data sets.

The March 2013 edition of Nature Physics was devoted to the latest academic research into the links between physics and finance. Much of this is in the emerging area of "complex networks", which aims to describe the behaviour of systems containing a number of interconnected discrete elements. Complex networks are known to have a very wide range of applicability: a biological cell can be viewed as a network of chemicals linked through chemical reactions; the world wide web is a network of webpages connected by hyperlinks; and food webs are used by ecologists to model the relationships between different species. Financial institutions collectively form a network and, by understanding the global properties of the network, it is possible to gain key insights into its function.

One such insight is that the greater diversification of risk might actually increase systemic risk, not decrease it, as one might naively think. The idea dates back to a short paper published in Nature way back in 1972 by former chief scientific adviser to the government Robert May, entitled "Will a large complex system be stable?". The paper was set in the context of population stability in ecological networks and, in simple terms, it is the idea that by complicating matters we increase the numbers of ways something can go wrong. Using networks, it also becomes possible to understand how the use of leverage by competing institutions can push a market network towards financial collapse and to assess which institutions are systemically important. It isn't just a case of being "too big to fail" – an institute's position within the network matters too.

The network idea brings together the analysis of many superficially very different systems. In the words of Andy Haldane, the executive director for financial stability at the Bank of England, speaking in 2009: "Seizures in the electricity grid, degradation of ecosystems, the spread of epidemics and the disintegration of the financial system – each is essentially a different branch of the same network family tree."

The recent financial crisis has highlighted the need to better understand how the global markets work. Theoretical developments in statistical physics and complex systems may be able to help.