John Voight visited Emory last week and introduced me to the crazy LMBDB (L-functions, modular forms, and related objects database). (He also introduced me to the awesomeness of Fucsian groups.)
Contrast with this quote by Borcherds:
If you ever find yourself drawing one of those meaningless diagrams with arrows connecting different areas of mathematics, it’s a good sign that you’re going senile.
(From this great post by Scott Carnahan about Lafforgue’s work.)
Technically, these aren’t arrows between areas of math, but between mathematical objects, so its legit. Fun features:
1) If you hover over an arrow it tells you what the connection is.
2) The biggest selling point for me (and this came up in conversation with John, he wasn’t just gloating about his involvement in this awesome project) is the computations over number fields other than Q.
3) If you go to the page of a particular elliptic curve, it returns the isogeny graph. (Featuring conductors up to 299998!)
4) On a page for an L-function, it will even verify the Riemann Hypothesis. (Scoll to bottom.) It computes this in real time too. You can see a little, almost invisible progress bar in the top right corner.
5) I generally really like super hyperlinked mathematical things. (E.g. I LOVE the stacks project and its recent interface update.)