Any time someone mentions "ability", you should ask "... to do what?"

If you're looking for ability to find new algorithms and prove their correctness, I probably win. If you're looking for ability to build a robust application (which is a key point to me -- I'm working on online backups, and the central point of backups is that they do NOT lose data, even if hardware failure occurs) I might win. If you're looking for ability to create an engaging Web 2.0 site, I definitely lose.

I'd assume that what YC means by "ability" is "ability to create whatever you've said on the application form that you intend to create" -- which in my case was an efficient, robust, and secure online backup system, but for most applications would be an engaging Web 2.0 site.

EDIT: Incidentally, it didn't even occur to me to mention the Putnam on the YC application form. For the "high level of ability" question I pointed towards my BSDCan'05 paper concerning stealing RSA keys on Intel CPUs with HyperThreading via an architectural side channel.

Dude, if I won the Putnam I would invent some letters that signified that fact and put them after my name. Heck, maybe in front of my name.