So pi is an irrational number. That means no ratio of 2 numbers can exactly define it. 22/7 is quite close, other fractions can get closer, but none can be exact.

Pi is also a transcendental number. That means, in a sense, it is as irrational as it can be. The digits of it’s decimal expansion/representation (is 3.1418…) aren’t just infinite, but each digit is unpredictable and appears random.

So how do we know what pi is? Well, there are many, many, many ways of calculating a precise value for pi. One of them is an infinite series. That is, you come up with a formula that you can apply an infinite number of times, and each time you expand on that equation, you get a little closer to the true value of pi.

Sangamagrama Madhava came up with this formula for it:

Because the minus 1 on top is raised to a (modified) power of n, the sign flips with each added step. So the approximation of Pi will over and under estimate the value by an ever-tinier amount with each added step.

He came up with that formula as he was working out the formula for arc-tangent (a useful operation in trigonometry).

The scientists in the article came up with something similar but their source was trying to simplify the equations of string theory. In the process, they came up with another way to calculate pi.

I’m afraid my math knowledge is not up to the task of assimilating and explaining a brand new string theory paper, so I’ll have to leave off details here.

Agreed, but that makes me wonder if it’s cool because I don’t understand it.

Math peeps - ELI5?

I think the math is beyond me, but the subscript notation seems to be defined on page 2 as the Pochhammer symbol, a_b = Γ(a+b)/Γ(a).