
Terence Tao's General Exam  - kenjackson
http://www.math.princeton.edu/graduate/generals/tao_terence
======
shadowmatter
I did a math minor at UCLA, and he taught the upper-division linear algebra
class I took. He didn't like the book, so he decided to write his own lecture
notes, which formed a book unto themselves. They're still available online at
<http://www.math.ucla.edu/~tao/resource/general/115a.3.02f/>. If you ever have
the itch to learn linear algebra, read them, they're quite excellent.

It was pretty obvious at class and obvious hours he was crazy smart -- but I
had no way of knowing he was Fields Medal smart. But unlike other crazy smart
professors I've had, he's a very gifted teacher as well. I mostly learned by
reading the books and considered the lectures as an ancillary learning aid,
but his lectures were very illuminating. I'm glad he now has a blog to teach a
wider audience at <http://terrytao.wordpress.com/>, but unfortunately most of
it is beyond what I can understand. If you're a math die-hard, be sure to read
that.

~~~
pagefruit
One awesome and pretty understandable blog post of his is a layman's
introduction to Quantum Mechanics, using Tomb Raider as an analogy:

[http://terrytao.wordpress.com/2007/02/26/quantum-
mechanics-a...](http://terrytao.wordpress.com/2007/02/26/quantum-mechanics-
and-tomb-raider/)

------
busyant
Just an FYI: the General Exam is the qualifying exam used to determine whether
a graduate student (usually in his/her 2nd year) can continue on and complete
his/her Ph.D. thesis. It's designed to test general knowledge (hence the name)
in your field of study and sometimes the depth of your knowledge related to
your thesis.

Different schools have different names for the exam. Sometimes it's written,
sometimes it's oral...sometimes it's both. Depends on the school and the
department.

In many instances, if you fail the exam you are booted from the Ph.D. program
and given a "terminal" master's degree.

~~~
btilly
_In many instances, if you fail the exam you are booted from the Ph.D. program
and given a "terminal" master's degree._

In many others, if you fail the exam (or exams - in my case they just rolled
this into the quals) you are booted from the program _without_ a masters
degree.

I once spent a month teaching someone topology from scratch so that he could
pass a qual he needed to get a PhD in combinatorics.

------
neworder
I absolutely love the ending:

"After this, they decided to pass me, though they said that my harmonic
analysis was far from satisfactory. :("

especially when compared to the Fields Medal citation, where Tao is awarded
the medal "for his contributions to partial differential equations,
combinatorics, harmonic analysis and additive number theory".

Seems he did learn a bit of harmonic analysis in the meantime.

~~~
a3_nm
... or that this sort of exams don't measure correctly the ability to get
Fields medals.

~~~
tomrod
I find this true in many PhD fields (and their relative measures of success)

------
sramsay
What's so striking to me, is how similar the exam is (in range, pace, and
tone) to the Ph.D. oral exams I took for a doctorate in English (years ago).
That same rhythm. The minute you start to set forth an argument, they get you
off onto something else. A lot of times, you're groping for the question.

Few people walk away from them feeling like they did well, but later, you have
a sense of accomplishment just for having done it at all.

~~~
telemachos
I did a Ph.D. in Classics, and I had the exact same feeling of "Oh, right, I
remember that." This form of exam was the last part of our A exams (A exams =>
after coursework but before being allowed to start a thesis; B exam =>
dissertation defense). Hadi Jorati's[1] review sums it up for me: "as soon as
they feel you know something they will move to something else!"

They sent me out of the room to discuss whether or not I passed. The door
stayed closed long enough that I became pretty nervous, but it turned out that
two of them were arguing about what they wanted to set as my dissertation
topic. By the time they called me back in, I was a wreck. (I paid them back by
choosing neither of those two topics.)

[1]
[http://www.math.princeton.edu/graduate/generals/jorati_hadi2...](http://www.math.princeton.edu/graduate/generals/jorati_hadi2.txt)

------
tptacek
Advice: next time you feel an urge to frustration or mockery of non-computer-
professionals, pull this up and start reading it from the top.

And this is the _general_ exam.

~~~
jarekr
I obviously won't doubt the genius of Terrence Tao, but reading about PhD
level research from any other discipline without knowing a yota about it would
leave exactly the same impression, even from a lesser scientist. Of course
some people are incredibly smart, but there is no need to mythologize their
abilities without having any understanding of what they have actually done.
Thus I think such an article can only have value for people who at least
vaguely understand the mathematics involved.

~~~
idle_processor
_a yota_

an iota

~~~
StavrosK
The pronunciation of γιώτα (iota) in Greek is, actually, exactly "yota", so
I'll allow the nonstandard transliteration.

/resident Greek

------
tokenadult
You can see notes about the general exams of many other famous people who have
studied math at Princeton at the base URL:

<http://www.math.princeton.edu/graduate/generals/>

I discovered this link years ago and enjoyed reading accounts of math learners
about what they knew at the beginning of their graduate studies.

"This page is maintained by Alison Miller," who just happens to be the first
United States woman to win a gold medal at the International Mathematical
Olympiad.

The report of Kiran Kedlaya

[http://www.math.princeton.edu/graduate/generals/kedlaya_kira...](http://www.math.princeton.edu/graduate/generals/kedlaya_kiran)

(which will be a familiar name to some readers here) is laugh-out-loud funny.

~~~
pagefruit
Another funny one (also by a familiar name, though perhaps not as much in
contest math circles) is Manjul Bhargava's:
[http://www.math.princeton.edu/graduate/generals/bhargava_man...](http://www.math.princeton.edu/graduate/generals/bhargava_manjul)

In this case, the funniness is for the totally opposite reason: sounds like
Bhargava totally crushed his exam.

Also, is anyone surprised how well everybody seems to remember the details of
their exams?! I suspect I'd barely remember anything afterwards...

------
savrajsingh
The Princeton Math Department is where I first learned that I should not take
a course with "Advanced" in the title unless I wanted to major in the field. I
learned that one the hard way.

------
Cyph0n
I read the whole thing, and it surprisingly turned out to be pretty
interesting (even though I didn't understand a thing).

I had to look up who the guy was afterwards though. A smart fellow indeed.

~~~
bdhe
_A smart fellow indeed._

He is one of the few people I know who has an insanely prolific online
presence. His blog, What's New (<https://terrytao.wordpress.com/>) has
hundreds of detailed articles on various math topics and occasionally I find
myself using it as a beginner's reference to detailed topics. He's also
published his blog posts as books. It is astounding how one person can produce
so much intellectual output! This is in addition to his mathematical papers
and books (<https://terrytao.wordpress.com/books/>)

~~~
lamnk
Come on, he is a prodigy. The only person I know that have matched impressive
ingenuity is Stephen Wolfram.

Great, now after reading their bio, i'm feeling more depressed ... sigh

~~~
robertk
I hope that was facetious.

~~~
tzs
What part do you hope was facetious?

~~~
fictorial
The part about Wolfram.

~~~
william42
Wolfram was a child prodigy and is very smart. Even the very smart are prone
to crackpottery.

------
raldi
Can someone provide some context for this? (Besides Terence's Wikipedia page.)

~~~
kenjackson
Terence Tao was 18 I believe when this takes place. He had completed about a
year of graduate work at Princeton when took his General Exam. An oral test to
proceed with his PhD at Princeton. It's apparently a tradition at Princeton to
write up your experience with the general exam, and here is Terence Tao's.

I wish I had written up my writtens (in CS) after I had taken them, but
unfortunately now I just recall a question or two -- not that anyone would
want to read mine. :-)

------
rfurmani
It's not that impressive, he performs okay. I hear he spent the first few
years mostly playing games, until he finally buckled down and got a thesis
out.

~~~
rfurmani
I can understand getting downvoted for tone, but I disagree with the
downvoting as I was just trying to state facts. The thought process here seems
to be: Terry Tao is a brilliant researcher, therefore why he wrote here must
be great. I thought one of the tenets here is that work should stand on it's
own value and not on who did it, especially when so young. The typical
Princeton student would do better on this, and if you really want to see a
good one you can check Bhargava, Venkatesh, etc. I was going to go through
this qual and give examples but nearly every paragraph has something bungled.
It you have any particular questions, I'd be happy to respond

