[deathanatos]

> Babai (the author) has a very small Erdos number

Let's quit beating around the bush: he has the smallest possible Erdős number[1]. If you don't presently have an Erdős number, or wish to improve your Erdős number for bragging rights, co-authoring a paper with him (or any anyone with an equivalent Erdős number) is the best possible outcome. (Obtaining an Erdős number of one is sadly no longer possible.)

[1]: https://en.wikipedia.org/wiki/Erd%C5%91s_number

[dietrichepp]

Smallest possible for living humans. One person, notably, had a lower number, but he is no longer with us.

[hyperpallium]

It's weird that you're downvoted. Just to clarify

> Paul Erdős has an Erdős number of zero.