I know how you feel, in a couple ways. My high-school guidance counselor looked at my middle school transcript and told me I might realistically aspire to go to a UC school (as opposed to a school in the Cal State system). (I ended up going to Harvard and Caltech.) On the other hand, the year I finished my Ph.D. (at the age of 29) one of my college acquaintances, a brilliant mathematician, became one of the youngest full professors in the history of Princeton University, and when my Ph.D. advisor was 29 he had already been a professor at Caltech for several years (after graduating top of his Caltech class, finishing a Ph.D. in three years at Cambridge on a Marshall Scholarship, and doing a postdoc at the Institute for Advanced Study).

Though I know I'm not (alas) at the highest level, I feel fortunate to be smart enough to know how smart I'm not.

N.B. The introduction contains a small non sequitur unless you happen to know the book's author. Here's a quick edit:

I once lent Xiaoguang "Mike" Li my copy of Probability Theory: The Logic of Science by E.T. Jaynes.

I know how you feel, in a couple ways. My high-school guidance counselor looked at my middle school transcript and told me I might realistically aspire to go to a UC school (as opposed to a school in the Cal State system). (I ended up going to Harvard and Caltech.) On the other hand, the year I finished my Ph.D. (at the age of 29) one of my college acquaintances, a brilliant mathematician, became one of the youngest

fullprofessors in the history of Princeton University, and when my Ph.D. advisor was 29 he had already been a professor at Caltech for several years (after graduating top of his Caltech class, finishing a Ph.D. in three years at Cambridge on a Marshall Scholarship, and doing a postdoc at the Institute for Advanced Study).Though I know I'm not (alas) at the highest level, I feel fortunate to be smart enough to know how smart I'm

not.N.B. The introduction contains a small

non sequiturunless you happen to know the book's author. Here's a quick edit:I once lent Xiaoguang "Mike" Li my copy of

Probability Theory: The Logic of Scienceby E.T. Jaynes.