On Being Smart

∗

Nabil H. Mustafa

What is the crucial qualit y imp ortan t for succeeding in graduate sc ho ol? I will provide a few

examples that suggest that: i) The answ er is not in telligence – a minim um of in telligence,

suc h as what every one reading this article has, is suﬃcient for succeeding in an y graduate

sc ho ol, ii) it is ... hard w ork. I ap ologize for the disapp oin tmen t.

Here is what some of the great mathematicians, after ha ving done work considered the very

p eak of human thought, think ab out the factors in their success:

Grothendiec k, Fields Medalist 1966 : ‘Sinc e then I’ve had the chanc e, in the world of

mathematics that bid me welc ome, to me et quite a numb er of p e ople, b oth among my “elders”

and among young p e ople in my gener al age gr oup, who wer e much mor e bril liant, much mor e

“gifte d” than I was. I admir e d the facility with which they picke d up, as if at play, new ide as,

juggling them as if familiar with them fr om the cr ad le – while for myself I felt clumsy, even

o aﬁsh, wandering p ainful ly up an ar duous tr ack, like a dumb ox fac e d with an amorphous

mountain of things that I had to le arn (so I was assur e d), things I felt inc ap able of under-

standing the essentials or fol lowing thr ough to the end. Inde e d, ther e was little ab out me

that identiﬁe d the kind of bright student who wins at pr estigious c omp etitions or assimilates,

almost by sleight of hand, the most forbidding subje cts.’

Gauss : ‘If others would but r eﬂe ct on mathematic al truths as de eply and as c ontinuously as

I have, they would make my disc overies.’

The reason why I give credence to these remarks is that i) while b oth Grothendiec k and

Gauss were considered amazing geniuses by their contemporaries, ii) b oth w ere not exactly

kno wn for b eing mo dest (Grothendieck said: ‘In the history of mathematics, I have pr o duc e d

the gr e atest numb er of new ide as’ , and Gauss w as famous for putting do wn other mathemati-

cians). This, together with the fact that even at graduate schools in the US which attract

the b est and the brightest of studen ts, the drop-out in computer science is ov er 50%, should

suggest that other factors play a larger role in determining success or failure. In my opinion,

a rather large reason for failure is the follo wing, rather fragile, learning psychology .

∗

This article is more a collection of interesting quotations with m y commentary . This has the added

b eneﬁt of providing references for those in terested.

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