
Interview with Terence Tao - mikevm
https://docs.google.com/document/d/1rinL25rC8LnMTzZcGjg1axT-0r-oiCnoKKH1DLQlmVA/edit
======
IkmoIkmo
Thanks for posting this. Salient point for me was the following bit I'd never
considered before, but explains quite well the feeling I've had about testing
for a long time.

 _There’s a great observation called Goodhart’s Law that basically says any
metric becomes useless once you start using it for control purposes. So the
SAT, for example, is a good general test of academic aptitude. But since it’s
used so much for admission to college, kids are trained and coached. They
spend lots of time and effort, specifically to improve their SAT score at the
expense of a well-rounded education, to the point where [the SAT] may not be
such a good guide to general academic excellence, even though it used to be
before students started optimizing_

~~~
shamney
Test preparation does not do much to increase SAT scores:

"For students that have taken the test before and would like to boost their
scores, coaching seems to help, but by a rather small amount. After
controlling for group differences, the average coaching boost on the math
section of the SAT is 14 to 15 points. The boost is smaller on the verbal
section of the test, just 6 to 8 points. The combined effect of coaching on
the SAT for the NELS sample is about 20 points."

[http://nepc.colorado.edu/files/Briggs_Theeffectofadmissionst...](http://nepc.colorado.edu/files/Briggs_Theeffectofadmissionstestpreparation.pdf)

~~~
eggnet
I went through the Princeton Review many years ago and it improved my score by
about 200 points.

Maybe I'm an outlier, but I can tell you this: nobody would pay for or go
through the course if the expected boost was 20 points.

On the other hand, if I hadn't taken the Princeton Review, I'd have done
something else to prep. And who knows how much I'd have been able to improve
on my own.

------
2muchcoffeeman
_A: I used to have more. When you work and you have family, it’s tough. When I
was younger I used to watch a lot anime and play computer games and so forth,
but I have no time for these things anymore._

He taught in Australia for a little while. I was in one of his classes and I
watched some Roruoni Kenshin with him. He was probably the best math lecturer
I've had. But I was a poor student.

~~~
Chinjut
I can't put my finger on exactly why, but this was the most interesting answer
for me (not in the specifics of anime and computer games, but just in the
ubiquity of the winnowing of interests over time due to career and family
pressures; even Terence Tao didn't start out all-math, all-the-time!).

------
stiff
_I mean you need a certain amount of base mathematics so that you can learn
everything else quickly. But once you have the foundation, it’s fairly quick._

Shame the interviewer did not proceed to ask him what he considers this
foundation to be, I think the question almost suggests itself.

~~~
timsally
I wouldn't presume to answer for Terry Tao but such a foundation certainly
included the usual topics covered in qualifying exams at top departments. For
example, Princeton:
[http://web.math.princeton.edu/generals/topic.html](http://web.math.princeton.edu/generals/topic.html).
Now that I'm looking at it, these topics actually align fairly nicely which
what Chicago requires first year graduate students to take:
[http://www.math.uchicago.edu/graduate/grad_first_year.html](http://www.math.uchicago.edu/graduate/grad_first_year.html).

If you're looking for some interesting reading, Princeton actually posts
write-ups of each student's qualifying exam
([http://web.math.princeton.edu/generals/index.html](http://web.math.princeton.edu/generals/index.html)),
including Terry Tao's
([http://web.math.princeton.edu/generals/tao_terence](http://web.math.princeton.edu/generals/tao_terence)).

~~~
yummyfajitas
I wouldn't suggest focusing on qualifying exam topics unless you need to pass
a math qualifying exam.

In modern mathematics, particularly applied mathematics, these are NOT the
most useful topics. That's just how things have always been done, and no one
wants to argue about changing them in faculty meetings. See also the language
exam: [http://web.math.princeton.edu/~templier/language-
exam.txt](http://web.math.princeton.edu/~templier/language-exam.txt)

In my former career I never once used topics covered in "abstract algebra"
(note that I'm distinguishing linear algebra from abstract), a common
situation among analysts. Most people outside of analysis never use complex
variables.

The only common core of topics I can identify that nearly every mathematician
I know uses is:

Measure theoretic probability (this intersects with real analysis)

Linear Algebra

Algorithms and optimization (this is less common than the above two).

~~~
dominotw
I learnt how to do proofs and what proofs really mean in my abstract algebra
class. I still use abstract algebra to refresh my math skills.

~~~
yummyfajitas
I learned proofs in a numerical analysis class. That doesn't mean a budding
algebraist should study numerical analysis, it means you will learn how to do
proofs in any rigorous math class.

~~~
dominotw
Sorry didn't mean to imply that one needs to learn abstract algebra to do
proofs. Was just mentioning my experience as it was course where I really
enjoyed doing proofs.

------
krat0sprakhar
_The funny thing about mathematics is that you don’t work with regular numbers
so much. I never see a 37, I see ‘n’ –a lot of what I do involves a big number
n that goes to infinity. Never any specific number._

An interesting answer to probably the most common question that mathematicians
are asked. Radiolab[0] covered this and the significance of "favorite/lucky
numbers" in a podcast a couple of months back.

[0] - [http://www.radiolab.org/story/love-
numbers/](http://www.radiolab.org/story/love-numbers/)

~~~
arketyp
Asking a mathematician for their favorite constant is like asking a painter
what their favorite color is. I like Tao's diplomatic answer.

~~~
wolfgke
I'd rather say something like "Fischer–Griess monster" (it is a constant in
the set of finite simple groups). Surely a constant, but not a numerical one.
The interviewer will probably change the topic immediately for not becoming
embarrassed. ;-)

Surely a less diplomatic way than Tao's, admitted.

------
mathattack
Perhaps the best thing of the article is his willingness to do an AMA on
Reddit. :-) Fingers crossed!

------
graycat
For the thinking about SATs, there's a standard situation not commonly
discussed:

Get a lot of multi-dimensional, empirical data and find some pattern, maybe an
equation, that fits. Okay.

But does this equation have to work in practice? Not really: The empirical
data may not have actually represented all the possible _dynamics_ of the real
system. So, when apply the equation, might not have maintained some crucial
conditions that held when found and fit the data.

Or, e.g., looking at academic performance data and SAT scores, etc., have a
lot of multidimensional data and might find a fit. But the data collected
might have been done with some unstated, unclear _conditions_ and not have
included all cases that could occur. So, this fit might not hold when those
conditions don't hold. So, applying the fit in reality where the conditions
are free to change might make the fit poor.

Or, if someone pulls too hard on the electric power cord of their vacuum
cleaner, then they will have a broken vacuum cleaner. Well, that would be true
for women like the mother of a girlfriend I once had! But not for me! I just
did a little work with a screwdriver and pocket knife and fixed the problem.
Maybe I impressed the mother of the girl! I was 14, the girl 12, and the
prettiest human female I ever saw in person or otherwise. Maybe it was good I
impressed the mother!

So, a _condition_ of the good fit was that I was that the user of the vacuum
cleaner didn't know how to repair some broken electric power wiring; that
condition held for the mother but not when she had a drop dead gorgeous, sweet
daughter with a boyfriend whose father had long since been teaching him about
basic work with hand tools.

For the SAT scores, early on might argue that so far in practice they really
did capture _real, pure academic ability_. Even if that was true, that need
not mean that SAT scores really have anything very important to do with _real,
pure academic ability_ and that some students, maybe most students, could,
with some additional _conditions_ , do well on the SATs and not have the
coveted _ability_.

Standard, old problem in multidimensional data analysis!

------
rpdillon
I like his response regarding strong AI. The idea that it is a moving target
might have been expressed before, but I thought he formulated it very well:

"The funny thing about AI is that it’s a moving target. In the seventies,
someone might ask “what are the goals of AI?” And you might say, “Oh, we want
a computer who can beat a chess master, or who can understand actual language
speech, or who can search a whole database very quickly.” We do all that now,
like face recognition. All these things that we thought were AI, we can do
them. But once you do them, you don’t think of them as AI."

~~~
saint-loup
"Every time we figure out a piece of it, it stops being magical; we say, Oh,
that's just a computation"
[http://en.wikipedia.org/wiki/AI_effect](http://en.wikipedia.org/wiki/AI_effect)

------
3rd3
_So I think, almost by definition, we will never have AI because we’ll never
achieve the goals of AI or cease to be caught up with it._

Never is such a long time. Maybe he is biased as an educator, i.e. not to
discourage thinking because a machine might do it for you at some point in the
future?

~~~
nl
I think you missed the point. He's saying we won't the goals of AI because: "
_it’s a moving target_ "

For example: " _In the seventies, someone might ask “what are the goals of
AI?” And you might say, “Oh, we want a computer who can beat a chess master,
or who can understand actual language speech, or who can search a whole
database very quickly.” We do all that now, like face recognition. All these
things that we thought were AI, we can do them._ "

This is very true.

~~~
arketyp
I'm beginning to suspect Turing consciously captured the moving target
definition when he conceived of his famous test.

~~~
crimsonalucard
The Turing Test is a fixed target though.

As far as I know there are no limits on how intelligent something will get.
Exploring the limits of AI is like trying to find the biggest possible number.

