As for whether Pi is such a big deal, I would say that it is.

You can define a circle as being the set of all points that are distance r from point (x,y). That’s the simplest shape you can have in geometry. You can define it with just three numbers. Even a line needs two sets of coordinates.

And pi is the ratio between the circumference and the diameter of a circle. It’s exactly the same for any perfect circle in the universe. If that number were three, we’d memorize the formula and think nothing of it. But it’s not three. It’s this irrational neverending number that we can compute to billions of digits but will never be able to define precisely.

The thing is, though, that it’s not a number we made up. It’s a number that exists - not in nature - but in the very fabric of mathematics itself.

So if space aliens in a distant galaxy plot the points that are a given distance from a central point, and they take the ratio of the circumference to the diameter, their answer will be the same as our answer.

Also, I think the fact that it is infinite has captured our imaginations over the centuries. It never ends and it doesn’t repeat, so all possible finite combinations of numbers are in there somewhere (see the quote in the original post). It’s also a puzzle that mathematicians can continuously solve. They’ll never reach the end, so they can eternally challenge themselves to go farther. This can be seen as a marker of intellectual (including now technological) progress.

But how do they compute it? How do they know they’re right? That part still eludes me.

http://www.angio.net/pi/piquery

type in 4261564 and it starts at around the 28,000,000th place or so of PI…