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.
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.
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.
"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.
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.
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.)
Ooooh, you're getting me so hyped up for my PhD! I still have to finish my BS (which I'm starting this fall) and Masters before I can get there, but it excites me nonetheless.
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.
I think Terrence on his blog does a decent job as coming across as someone who is really smart but has got to that position in maths by spending a lot of time in some pretty narrow fields. He openly admits, like for example when P/NP stuff come up a bit maybe 6 months back, areas where he isn't an expert.
He could probably easily make his knowledge look even more impressive but is humble about what he does and doesn't know.
In my experience programmers don't mock mathematicians and other hard science and engineering specialists. They are seen as more or less peers. They tend to mock marketers, MBAs, sociology majors, etc.
"Hard" is a relative term, here. Surely physics is hard science. Most would agree with Chemistry. Biology? Well, okay...Psychology? No, now you're just--Sociology? The hell? How did we get here?
As far as people I mock--only those who think a liberal arts education will land them a good job with no other qualifications. The world needs historians (even of the art variety), anthropologists, sociologists, and even marketers. What it doesn't particularly need, however, is 70% of the college population pursuing those degrees when maybe 3% of the jobs out there are suited to them.
I agree with your basic point, but if you mean to say that some other set of exams (the non-general ones) were harder, I'm not so sure. For most places, there are two sets of exams: generals before you write a thesis and your thesis defense. In my experience, pre-dissertation general exams are significantly harder than the oral defense of a thesis. Most universities use them as a final weed-out phase before allowing people to even consider a thesis topic. As such, you have to demonstrate mastery over a far wider field than a dissertation might cover. For example, all of Math or Philosophy or English Literature or Romance Linguistics - often with chosen specialty sub-topics, so you end up having to worry about breadth and depth. By the time you get to the oral for your thesis, on the other hand, you are in such complete command of the material that defending your views (on that narrower scope) is relatively easy.
Also, in most cases, you won't be allowed to set a date for your dissertation defense unless the work as a whole is already passable.
Definitely my experience. I still have vivid nightmares about the general exam more than 10 years later. It was an 3 day x 8 hours per day written test with no breaks. If you wanted to eat, you had to bring food with you into the test room. Then there was the dreaded oral inquisition. Although I didn't appreciate it at the time, having survived the abject misery of the first 2 years of a physics Ph.D., everything else has seemed manageable in comparison. A few years ago, they changed the format of the written exam to a single 8 hour day. My thesis defense was a total cakewalk. Scheduling it late on a Friday afternoon was probably the single smartest thing I ever did in grad school.
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 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.
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/)
I was also surprised at the number of awards and honors he's acquired at an insanely young age. He even scored 760 on the SAT when he was only 8 years old!
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. :-)
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.
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
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.