It first turned up in flood records for the River Nile. Then it was found lurking in data on natural phenomena ranging from avalanches to exploding galaxies. Now medical researchers think it will help in the fight against cancer – a simple rule of seemingly cosmic potency.

Known as a power law, it is a formula that captures links between, for instance, sizes of avalanches and how often they occur, or the brightness of galaxies over time.

The first such formula was identified more than a century ago by Harold Hurst, a Cairo-based engineer looking for patterns in the size and frequency of floods along the Nile. Scouring records, the Englishman found that the two were connected by a simple power law, so called because the formula included a number mathematicians call an exponent, or “power”.

Intrigued, Hurst examined the records of other rivers, and found the same law at work. Casting his net further, he found the same type of law applied to a host of other phenomena, from temperature readings at weather stations to sunspot numbers.

Not surprisingly, his claim to have found a single rule that worked for all of them sparked controversy. Yet, the evidence was so convincing that the power law became the basis for Egypt’s water supply policy and the design of the Aswan High dam.

Since then, the number of phenomena found to follow power laws has grown exponentially.

This month, researchers at the Institute of Cancer Research, London announced that mutations in tumours also obeyed a power law, with implications that could save lives. A team has created a mathematical theory for certain types of mutation in cancer cells, and it leads to a power law for their behaviour.

The researchers have compared the theory to data for more than a dozen types of tumours. The results, published in the current issue of Nature Genetics, show the theory correctly describes the evolution of many types of cancer. This opens the way to testing tumour samples from patients, checking to see if they follow the power law, and tailoring treatment accordingly.

Study co-leader Dr Andrea Sottoriva uses the analogy of a game of chess.

“The aim is anticipating the next move of the adversary, to ultimately win the game.”

Quite how big an impact this “law of cancer” will have remains to be seen. Not all cancers follow its dictates, but that in itself could prove to be another insight.

There is no doubt that discovering new laws is big news for any scientist. Quite apart from their practical value, they have often been a fast-track to immortality – the laws of gravity, mass and energy that gave Issac Newton and Albert Einstein their enduring fame.

But the emergence of such truly universal power laws – applying to a whole swath of phenomena – also poses great questions. Where do they come from, and how can we be sure they are valid?

The work of Dr Sottoriva and her colleagues on cancer is unusual in that they began with a solid theory, extracted a power law from it and then tested the law using real-life data.

That is the textbook way of doing science – theory, deduction and test. But most power laws have been identified from flipping this around and starting with data, then extracting a power law and only then trying to explain it.

It is an approach that carries real dangers, as demonstrated by the salutary tale of perhaps the most famous “universal law” of them all – the so-called Bell Curve.

Named after its shape when plotted on graph paper, the Bell Curve is famous for describing the prevalence of human traits, from height to intelligence.

Its contours reflect the fact that most people have near-average values of such traits, creating a central bulge, while values far from the average are far less likely, as reflected in its graceful slopes to either side of the bulge.

There is no doubting the beauty of the Bell Curve, and during the 19th century some influential scientists fell under its spell. They began to view the curve as a universal law of nature, and set about collecting data to prove it.

Everything from chest measurements to crime statistics seemed to follow its dictates. By the start of the 20th century, the evidence of its ubiquity was deemed so compelling that researchers had given the curve a new name – the Normal distribution.

To this day it remains among the best-known “laws” governing natural phenomena, and it is relied on by everyone from astronomers to Wall Street analysts.

Yet, even before it acquired its cosmic reputation, it was clear that the Normal distribution had serious limitations. Even supposedly classic examples of its power did not really follow its rules. Real-life data on the heights of people gave dented, dumpy-looking curves.

Its predictions about extreme cases were also way off. In 1905, American John Rogan was famed for being the tallest human being. He was 267 centimetres tall, a height that according to the Normal distribution was so extraordinary that Rogan simply should never have existed.

This hinted at the other major problem with the Normal distribution as a universal law. There were no good reasons for thinking it should be.

Even before the craze for Bell Curve hunting took off, mathematicians had uncovered the key “terms and conditions” needed to justify fitting the curve to data. Put simply, a case could only be made if the phenomena were the result of independent random effects adding together.

But it was often far from clear that this was actually the case. For example, the events that lead to stock market crashes are often anything but independent. As such, they are unlikely to follow the Bell Curve’s predictions.

The emergence of power laws has given scientists an alternative candidate for the title of truly universal law. Yet these, too, are not without their problems.

Many power laws have properties that defy attempts to extract them from data, the time-honoured way of finding them.

Meanwhile, mathematicians still have not found a grand theory allowing them to be derived from first principles.

Recent research hints at an intriguing link with the “terms and conditions” behind the Bell Curve, although the details have yet to be worked out.

When they are, however, they might lead to a whole set of cosmic laws whose power would put even the works of Einstein to shame.

Robert Matthews is visiting professor of science at Aston University, Birmingham