beautiful strange powerful fast mysterious seductive

It's just very beautiful.

Please inspect and admire it for a few moments, just as you would a famous painting in a gallery.

A mystical genius discovered it, but it's really pretty simple to understand, just whole-number arithmetic, high-school algebra, addition, multiplication, division, a square root.

Beautiful, and very strange. It's an equation for pi, so it must have something to do with a perfect circle, with roundness, circularity.

But what? What do these strange numbers have to do with circles? Where do they come from?

Particularly striking is how precise a value of pi it computes before it even begins to go to work, when n = 0.

But the equation will not be "true" -- the left side will not equal the right side -- until n = infinity, until the stuff to the right side of the Sigma sign (a fairly simple kind of sum) has been computed and summed and computed and summed an infinite number of times.

It's a map, a set of instructions to travel to Infinity. But of course Infinity is a Realm no human being has ever reached or can ever experience. Our world, our human experience is Finite. We know Many, we know A Lot, we know Thousands, Millions, Billions -- but we can never reach or experience or know Infinity. We can only imagine or guess what Infinity is like, what goes on there.

Srinivasa Ramanujan (1887 - 1920) was a self-taught Indian mathematician who spent most of his mental life in the Realm of the Infinite, and in the Realm of Pure Numbers. He had very little use for our familiar and finite world, and no interest whatsoever in any practical applications of mathematics.

Ramanujan told his Cambridge colleague Hardy that the Hindu Goddess Namagiri gave him many of his mathematical discoveries in dreams. He wrote them down when he woke.

Ramanujan discovered this equation around 1915 -- about 35 years before electronic digital computers existed. It belongs to a group of his discoveries which are still the most efficient, fastest ways known to compute the decimal expansion of pi.

pi is defined as the ratio of a circle's circumference to its diameter; but expressed in digits, pi is a decimal fraction which never ends, which can never be perfectly expressed. Around 1990, the Chudnovsky Brothers, refugee mathematicians from the Soviet Ukraine, used one of Ramanujan's equations to break the world's record of computing pi beyond a billion digits on a homebrew supercomputer they built from mail-order parts in their New York City slum apartment.

Arguably, computing more than a few dozen digits of pi is a useless task with no possible practical or real-world application. And yet, since even before Archimedes (an early pi precision record-breaker), the world's most brilliant mathematicians have routinely been mesmerized and seduced by the problem, not just to compute more digits of precision, but to squeeze mathematical meaning out of pi and to find new, more elegant, more powerful ways to compute it.

Googling 26390 will return dozens of websites about Ramanujan's pi equations, Ramanujan, and related mathematical lore about related problems; these are among the most esoteric, profound and strangest of all mathematical discoveries. While in England he fell ill with tuberculosis, but was awarded a doctorate from Cambridge University, and elected a Fellow of the Royal Society before he sailed home to die in India. India's premier center of advanced mathematical research is the Ramanujan Institute; Ramanujan himself has been honored on an Indian postage stamp.