Grothendieck Primes

A post on Geomblog reminds me of the following gem from the second of the AMS Notices articles on Alexander Grothendieck.

One striking characteristic of Grothendieck’s mode of thinking is that it seemed to rely so little on examples. This can be seen in the legend of the so-called “Grothendieck prime”. In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right,take 57.”

All mathematicians should make sure to keep this story in mind for the next time someone asks them to help balance their checkbook. Real, breathing, cutting edge mathematics has very little to do with the kind of tedious number-crunching that is standard fare at high-school level.

PS: Getting to the main point of the Geomblog post, I have to concur with Suresh that mathematicians do not make the best material for dramatic television, and that the best one can expect from "Numb3rs" is for the math guy to play the "deep" but geeky foil to our straight-shooting, down-to-earth main lead; nor am I alone in this opinion ...

Comments

[Don Lloyd]

Abiola,

---In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right,take 57.”---

I'm confused as to what the point of the story is. It was clear until I realized that 57 is NOT a prime number.

Regards, Don

[Delmore Macnamara]

Don (assuming you are not being ultraironic), that 57 is *not* a prime is precisely the point - partisans of "abstract nonsense" (I use the phrase affectionately) are often surpisingly unfamiliar with the actual facts of arithmetic.

At Edinburgh there is an algebraic topologist, Dr Andrew Ranicki. He used to cover many blackboards with (to me) unfathomable proofs in his lectures, but never in the obvious sequence i.e. higher boards before lower ones, left before right. He was prevailed upon by the student representative to number his boards so that the slower students could follow the correct sequence. He agreed, but it is debatable whether his efforts helped much; a typical numbering would be 1,1,3,4,6,5,...