TITLE: Alternate proofs of Quillen's theorem on formal group laws and MU
QUESTION [11 upvotes]: This is related to this posting:
complex cobordism from formal group laws?
but not entirely the same.  I'd like to know if there are any proofs of Quillen's theorem that $\pi_* (MU)$ is the Lazard ring (home of the universal formal group law) other than Quillen's.  Specifically, is it possible to prove the result without a deep understanding of the structure of $H^*(MU)$ as a module over the Steenrod algebra?

REPLY [4 votes]: Jacob Lurie taught a course at Harvard in the spring of 2010 which included a slick proof of Quillen's theorem. I'm pretty sure Steenrod operations are not mentioned at all. The course page is here, and the notes which include this proof are in lecture 7. Also, the proof of Lazard's theorem (on the structure of the Lazard ring) in lectures 2 and 3 is very cool.