Some of the greatest scientific discoveries of all time have happened on accident – or at least, have been discovered while the scientists was looking to find something else.

I’m not sure this discovery will be remembered in that category, but finding a new way to write Pi still is pretty interesting.

Pi’s expansion goes on forever and there is no way to predict which number comes next; even NASA only bothers learning around 15 digits.

That said, there are ways to express the constant exactly, if you’re tricky – and that’s exactly what a team of Indian Institute of Science physicists have done.

In fact, they have found a way to express pi that has so far gone completely unnoticed by mathematicians and scientists – but totally on accident, says Aninda Sinha, one of the paper’s co-authors.

“Our efforts, initially, were never to find a way to look at pi. All we were doing was studying high-energy physics in quantum theory and trying to develop a model with fewer and more accurate parameters to understand how particles interact. We were excited when we got a new way to look at pi.”

The idea of an infinite series comes down to a sum (or product) of the terms of an infinite sequence. They can be extremely useful for calculating the digits of pi, and are also very satisfying to look at, says mathematician John Joseph O’Connor.

“One of the earliest infinite series for pi was that of Wallis, and one of the best-known seems to have been first discovered by James Gregory. These are both dramatic and astonishing formulae, for the expressions on the right are completely arithmetical in character, while pi arises in the first instance from geometry. They show the surprising results that infinite processes can achieve and point the way to the wonderful richness of modern mathematics.”

The search didn’t stop there, though.

“From the point of view of the calculation of pi, however, neither is of any use at all. In Gregory’s series, for example, to get 4 decimal places correct we need about 10,000 terms of the series.”

This new formula is fast, though. It’s related to Gregory’s series but arrived at through different means. This means they were able to vary a certain constraint to maximize its efficiency.

“While the Madhava series takes five billion terms to converge to ten decimal places, the new representation with 𝜆 between 10 and 100 takes 30 terms.”

They think they know why no one has noticed it before now, too.

“Physicists and mathematicians have missed this so far since they did not have the right tools. These were only found through work we have been doing with collaborators over the last three years or so.”

Science is always advancing.

And more answers are always coming to light.

If you enjoyed that story, check out what happened when a guy gave ChatGPT $100 to make as money as possible, and it turned out exactly how you would expect.