Yesterday, while reading the comments to this post by Lance Fortnow, I learned that Mihai Pătraşcu, the author of three accepted papers at FOCS 2006, is a first-year graduate student, and submitted the papers when he was still an undergraduate at MIT! He was also the co-recipient of the best Best Student ICALP Paper for 2005.

Earlier this year, Jacob Fox (MIT) won the Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student. (See this link.) The prize citation mentions that:

Jacob Fox’s research exhibits a formidable ability to get to the heart of the issues in the problems at hand, and the ability to develop extremely ingenious and novel techniques. In addition to being able to solve problems posed by others, Fox has also excelled at finding topics all by himself, formulating novel conjectures and approaches to solutions. His accomplishments are shaping his areas of research, and are of extraordinary promise for the future.

If you want to read about one of the things he has done, look here. (Make sure you don't miss Dana Scott's feedback to that post!)

I am always overawed by these accomplishments from young researchers, and wish both Mihai and Jacob the best of luck in fulfilling their exceptional promise. However, no matter how gifted they are, it is a fair bet that this won't be easy. They will have to show a lot of appetite for hard work and guts in doing so. Keep it up guys!

Before closing, and in Football World Cup spirit, let me suggest that you have a look at this short movie by Marcus du Sautoy, professor of mathematics at Oxford University, where he uses football to explain the proof of Euclid's theorem to the effect that there are infinitely many prime numbers. Marcus du Sautoy is the author of the excellent book

*The Music of the Primes*. Check it out, if you have not read it already.