
The 1980 Math Olympiad Program: Where are they now? - claywm
http://andrewgelman.com/2015/03/17/1980-math-olympiad-program-now/
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CurtMonash
When I told John Tate I was thinking of switching out of mathematics, his
response was in effect "Good heavens! If there's anything else you can imagine
doing, don't stay in math!" I later read that Wittgenstein had famously said
something similar about philosophy. (Context: I was 19 years old and finishing
up my PhD in math at Harvard. In that small department, Tate was not one of
the professors I knew well.)

In fact, I often feel pangs about not staying in academia. On the other hand,
I've been able to carve out a life with a big dose of public intellectual --
for want of a better or less pretentious term -- so that's cool too. E.g., I'm
repeatedly told that my blog is "required reading" for grad students in the
relevant areas of computer science ...

~~~
graycat
At least at one time and maybe still, there was a decently good living in
applied math within 100 miles of the Washington Monument in DC.

There early in my career, once I sent some resumes and in two weeks went on
seven interviews and got five offers.

Big topics were scientific engineering programming, numerical analysis,
especially numerical linear algebra, standard applied statistics -- hypothesis
testing, linear statistics, analysis of variance, curve fitting, etc. -- the
fast Fourier transform, digital filtering, power spectral estimation,
deterministic optimal control theory, linear and non-linear programming,
discrete and continuous time stochastic processes, Monte-Carlo, numerical
solutions of ordinary and partial differential equations, etc.

Some of these topics are part of mathematical EE.

At one time I my annual salary was six times what a new, high end Camaro cost.
My wife got to pursue her Ph.D. in essentially _mathematical sociology_ as
part of her desire to _save the world_ while we had big times at Thanksgiving
and Christmas, shopped in Georgetown for high end French wine and cheese, were
regulars with good tables at high end restaurants, went to lots of concerts
and plays, got a good piano for her and a good violin for me, got boxes of
fancy French pastries and sweet, sparkling dessert wines and on Saturday
nights pigged out watching old movies, went to Shenandoah for vacations, had
plenty of time for trips to families in Tennessee and Indiana, did some fancy
cooking at home, etc.

Of course the money was coming almost entirely through the US Federal
Government, mostly for US national security, e.g., via the US Navy, DARPA,
etc. But, still, there was money via the DoE, NIST, and more.

I went ahead and got an _applied math_ Ph.D. at Johns Hopkins, research on
stochastic optimal control.

My startup has at its core some applied math I derived based on some advanced
prerequisites I got mostly at Hopkins. The math is an advantage. If the
startup works, then the math will have been the key -- except for the math and
the basic business _idea_ , it's all routine, that is, the math is the only
thing really special.

Math can be used to say how to take data that is available and manipulate it
to get data that is valuable. Now there is a lot of data and means to
communicate, store, process, and display it, infrastructure software to make
the rest much easier, ads to run to get revenue, etc.

Except possibly for coding theory and cryptography, I don't know if there are
valuable applications of algebraic topology, algebraic geometry, algebraic
number theory, commutative algebra, etc., but for the topics I mentioned it
would seem that there is some practical value.

For some of what can be done with applications, there is a long dessert buffet
from the Hahn-Banach theorem and more in D. Luenberger, _Optimization by
Vector Space Methods_. One heck of a toolkit. Make just one good application
and retire, make a donation to a university, and get your name on a building.

Here's another possibility: Attack integer linear programming problems in
business. Focus on the problems that can attack with min cost flows on
networks with integer arc capacities. Why? Because it is just linear
programming; the simplex algorithm becomes really simple in that case; in
practice the simplex algorithm is fast beyond belief on problems large beyond
belief; and get integer programming for no extra effort -- if start with an
integer basic feasible solution, then the simplex algorithm will maintain an
integer solution and, if there is an optimal solution then will get an integer
optimal solution. Can use this in various resource allocation problems. For
more, use it as a linear approximation in nonlinear problems and for still
more enhance it with some Lagrangian relaxation. Show that P = NP? Nope. Make
money? Maybe.

~~~
hgibbs
I'm a third year maths student at the moment and having a bit of an
existential career choice crisis. I don't know if academia is for me, because
I don't think it is worth it unless you are top tier, and having done an
internship at a big bank neither does finance, mainly due to the stress. What
kind of resources or subject areas do you think are valuable to study while I
will have time? How lucrative is the industry in its current state and how
good current employment opportunities are?

~~~
graycat
For academics, for one possibility, look into B-schools: At the research
universities, the B-school _research_ requirement seems to be to publish
nearly anything. Some of the journals popular in B-school publishing have not
very high standards for quality.

The B-schools are basically forced by some standards efforts to teach some
courses that are essentially applied math.

One might guess that the B-schools want to be professional or clinical but,
instead, they tend to want to see themselves as _applied social science_ , and
social science has _physics envy_ and wants to be mathematical. Their favorite
math is linear statistics. So typically there's a lot of such statistics in
the research at B-schools. And typically the B-school profs are not very good
at math or statistics.

B-schools also want to dabble in computing -- if you can teach some courses in
computing, even as electives, then you might get liked for that.

No doubt some B-schools would like someone who could teach courses in
_financial engineering_ , say, with Brownian motion, stochastic integration,
Black-Scholes and generalizations -- basically the Brownian motion solution to
the Dirichlet problem. So, if you like mathematical finance, then maybe teach
it in a B-school.

DC may still be a good area for applied math: So, submit a Civil Service
application and also send copies to the usual suspects -- NIST, various DoE
labs, various DoD labs, various groups interested in economics or mathematical
finance, that is, maybe the Federal Reserve (also try the regional Fed banks),
the Social Security Administration, etc. If you want, try NSA, CIA, DIA, FBI,
etc. -- no telling what they might want to do with some applied math. Also try
the JHU/APL.

There have long been lots of _Beltway Bandit_ shops because commonly Congress
gives the departments of the Federal Government more money to spend than full
time head count to spend it on so that a lot of the money and/or work goes
through companies. E.g., Edward Snowden worked for Booz-Allen or some such.

For technical jobs around DC, it used to be that the job ads in _The
Washington Post_ were good places to look.

There is a chance that Google, Facebook, Yahoo and some others are interested
in some projects that might be able to use some high end applied math. A
problem may be that the other workers there are not very good at math and,
really, make a mess out of the work, the opportunities, the positions, etc.,
and that can be bad for everyone.

It's not clear that everything in mathematical finance is a rat race. I doubt
that James Simons ran a rat race shop.

Houston has some important slots for optimization, e.g., as in the work of
Princeton Chem Eng prof Floudas. E.g., here's all the crude oil inputs we have
available and the costs, and here's all the prices for all the possible
refinery products. So, say what crude oil to buy and what products to sell to
maximize earnings. That's an old problem, but likely people are still working
on it.

The airlines have some very serious problems in fleet and crew scheduling, and
first cut it's integer linear programming. But with uncertainties, if you want
to handle them at all realistically, the formulations and solutions can become
challenging in all respects. A better solution can show its value just on the
computer and get taken seriously. For some airline spending $100 million a
month just on jet fuel, saving a few percent can pay for some nice computing,
work, etc.

Maybe look at what the operations research people are doing these days in
scheduling for trucks, airplanes, cargo ships, etc.

No doubt Amazon, Wal-Mart, etc. have some good problems that are
generalization of the old _transportation_ problem -- the one Kantorovich got
a Nobel prize for. Now we regard that problem as least cost flows on a network
and use the simplex algorithm to solve it and where a basic feasible solution
corresponds to a spanning tree of arcs on the network.

My view is that broadly now being handy with probability and probabilistic
modeling of real situations is valuable, not that you can expect anyone else
to know this so that, really, all you can sell are results, not the _work_.

E.g., with the Kolmogorov definition of a random variable, a function from a
measurable space to the reals measurable with respect to the Borel subsets of
the reals and a sigma algebra on the measurable space, go get a number, any
number, and then regard it as the value of a random variable, that is,
intuitively, one number among others that might have been observed. Now you
know the first step in analyzing any given data -- call each number the value
of a random variable. Then look for some assumptions, independence,
orthogonality, or other relationships among the random variables. Keep the
weak law of large numbers at your side -- that is, get some independent,
identically distributed _samples_ and take an average. There's more! Uh, the
set of all real valued random variables X so that E[X^2] is finite forms a
Hilbert space. The inner product is (X,Y) = E[XY]. So, yup, that completeness
holds is a bit amazing, but it does and the proof is mostly just the Minkowski
inequality from the inner product. Then in a Hilbert space we can do
projections, and they are approximations, e.g., least squares.

Currently the Internet ad people and their ad targeting should be an
opportunity to do some valuable applied math.

For what to study beyond the usual ugrad and Master's pure/applied math, I'd
say the _math sciences_ , the math of operations research or systems analysis
or electronic engineering. So, linear algebra, numerical linear algebra,
linear systems of various kinds, optimization (linear, integer linear, non-
linear, network linear programming), etc.

My view is that soon computing will run aground due to running out of any
additional utility from just their usual intuitive and heuristic approaches to
solving practical problems and need math. But don't hold you breath.

Maybe you can have a good, long term career, say, long enough to have kids and
get them through college, at some one organization. Maybe. Maybe for some DoD
lab. Maybe.

Otherwise I have to suspect that in the end you will have to be a
_businessman_ where you think of the product/service, develop it, deliver it
to your customers, and get the revenue. Then you get to use whatever math
helps without trying to talk some non-mathematical manager into letting you
try, and then you just deliver the results, not the math itself, to your
customers.

In the short term, I'd suggest get a job for a salary, keep one foot in
pure/applied math, keep the other foot in computing, try to make a career out
of the job, but really expect to have to do, and, thus, to look for a way to
do, a startup based on applied math and computing. There you just use the math
as an advantage, maybe the crucial core -- still the rest that is more routine
is also important.

For how "lucrative", essentially that's up to you! Broadly, can't really
expect someone else to create a good job in applied math for you. Instead, you
have to create the job you want and then take that job, do well with it, and
build a career. You can do this starting a pizza shop; with math and
computing, they should be advantages. E.g., with some abstract algebra applied
to coding theory, A. Viterbi built Qualcomm.

If you know someone who knows someone, then maybe could get into some niche
slot somewhere, maybe on the staff of a committee of Congress.

~~~
hgibbs
Cheers, I really appreciate that you took the time to write this all out. I am
glad that there seem to be so many options.

~~~
graycat
Here's an example of _applied math in industry_ :

FedEx had candidate investor General Dynamics (GD), and GD had sent two of
their guys, one aero engineer and one finance guy, to _help_ FedEx. FedEx
needed the GD investment.

At one point, the Board wanted some revenue projections. I wasn't asked to get
involved and didn't want to, but no one had any ideas of how to do the
projections except just draw a free hand line on a graph based on hopes,
dreams, intentions, guesses, etc.

So, I thought: We know (1) the current revenue. We know (2) the revenue when
the planned service to 90 US cities with 33 airplanes is full. So, the
_projections_ are roughly how interpolate between (1) and (2).

For how the interpolation will go, we have (3) current customers and (4) the
rest of the customers we will have when we have (2) and are full.

Then say that the _growth_ is from current customers (3) talking to the rest
of the customers (4). That is, the rate of growth is directly proportional to
the number of (happy) customers (3) talking to the rest of the customers we
will have (4).

So, let t denote time in days with t = 0 corresponding to the present. Let the
revenue at time t be y(t). Let the revenue from (2), being full, be b dollars
a day. Then at time t, the growth rate is y'(t), that is, d/dt y(t). So, we
have that

y'(t) = k y(t) ( b - y(t) )

How 'bout that! Maybe it's so simple it's almost just a joke, but the rest of
the ideas floating around the office are much worse!

So, sure, it's an initial value problem for a first order, linear ordinary
differential equation but, really, is so simple can just use freshman calculus
directly and find the closed form solution, right, some exponentials I omit
here.

So, on a Friday the Senior Vice President (SVP) for Planning and I got out
some graph paper, picked a value for k, and drew the graph.

The next day, Saturday, I was in my office, and at noon I got a phone call
asking if I knew about the revenue projections. Well, the SVP was traveling,
and, yes, I knew. So, I was asked if I could come over to the HQ offices and
explain. So, I got in my Camaro hot rod and drove over.

When I got there, people were unhappy. The two GD guys were standing in the
hall with their bags packed.

I was led to the graph, given a time, and asked to reproduce the value on the
graph at that time. So, I had brought my HP scientific calculator, punched the
buttons, and got the value on the graph. I did that a few more times, and
people started to be happy again.

It turned out that the Board meeting had been that Saturday morning; the graph
had been presented; and the two GD guys had asked how it had been calculated.

Well, all the FedEx people there tried to figure out how the graph had been
calculated and went on for a few hours without success, and then GD guys lost
patience, got plane reservations back to Texas, went to their rented rooms and
packed their bags, and as a last chance returned to the HQ offices to see if
FedEx had an explanation for the graph. FedEx was about to die.

That's when I arrived and explained the graph.

The FedEx guys stayed, and FedEx was saved.

I never got thanked! Really my impression was that the rest of the top of
FedEx had concluded that I'd been dangerous, maybe had 'hooked' the company.

And I'd never been invited to the Board meeting. So, I began to conclude that
my contribution was so resented that the top of FedEx would rather see all of
FedEx go under than let me help.

The promised FedEx stock was already 18 months late. I was in Memphis while my
wife was in her Ph.D. program at Johns Hopkins near our home in Maryland. So,
to heck with FedEx -- I went home and to Hopkins for my Ph.D.

So, that's an example of _applied math_ in US business! E.g., I was the only
one around who still knew freshman calculus! And, heck, I'd never even taken
freshman calculus, had studied it on my own and started with sophomore
calculus!

A broad lesson is, for anything very technical, have a tough time just making
a contribution in the middle of a lot of operational and management people who
forgot freshman calculus -- such people will feel out of control and
resentful.

So, instead, for technical contributions, need an appropriate _organizational
structure_ , maybe be in a research division and out of the main line
operations or management, maybe be a respected external vendor, maybe be in a
_profession_ complete with legal liability and licensing, etc. And charge a
LOT.

Of course, broadly, the flip side of such technical incompetence, at the level
of just freshman calculus, should be an opportunity!

There were several other cases where I did some good technical work on an
important problem but resentment by others and competitive office politics
kept me from getting credit or actually blocked my contribution. In the field
of _organizational behavior_ , such politics is called _goal subordination_ ,
that is, someone finds it in their interest in the company to hurt the
company, _subordinate_ the good of the company to their own good.

Broadly, being a really good technical contributor among a lot of less
technical people is a great way to create enemies who will sabotage your
career, not friends who will help it.

So, net, usually have to make a technical contribution from outside the
_pecking order_ of the organization. That is, be a vendor.

Still better, just sell a product or service the customers will like but where
the customers need not be aware of anything technical in the work.

~~~
hgibbs
What kind of companies would be good to get practical experience in this area?
In my experience the bridge between theoretically and actually apply
mathematics is very hard to cross. Having started working mathematically
recently it seems to me that even though I can propose a solution which isn't
the best, they are usually better than what is currently available. Is that a
common experience as a working mathematician.

That story about FedEx is hilarious!

~~~
graycat
Part II

For what companies to go to to get going on a career in such applied math, I
can't think of any. Mostly people and their organizations would rather waste
money than get involved with mathematicians doing work only mathematicians
understand.

Again, if want to make math pay, just sell the results, usually as a vendor
outside the customer.

If are inside the company, then likely no good work will go unpunished.
Basically to be successful, you will need the strong personal support of the
CEO and hopefully the Board -- literally. And the CEO will routinely have to
go around and break 2 x 4s over the heads of recalcitrant middle managers to
see if they are just asleep or really dead -- otherwise those middle managers
can sabotage you with high determination and creativity.

E.g., twice I saved FedEx from going out of business and had much more that
would have saved FedEx maybe tens of millions of dollars a year, but I got
flack and push back and contempt and none of the promised stock.

Such are some of the challenges in getting _stuff done_. But successful people
have been overcoming challenges, some much worse than I faced at FedEx, for
many centuries.

Now that you know about the possibilities of some of the absurd challenges,
don't be surprised. Really, one of the best rules is just to keep your good
technical work essentially a secret until you have a solution that is just too
darned good to refuse, and then pull back the curtain, let people see the
results and also see that it's too late to fight with you.

Better still, just provide such results as a business and _own_ the business.
E.g., in some cases, just do the work for free, show the results, and then
announce "You can have this for your real operations for a fee of only 15% of
the savings."

Once there was an in-house research group that was successful. It was for
WestVaco paper -- think specialty papers, e.g., coated papers for milk
cartons. So, they had Ph.D. chem eng guys running their plants in jungles,
etc., that is, where the trees were, but it was a family owned business with
HQ in NYC.

The research shop was in Maryland, and I got an explanation from them: Each
year Research went to NYC for their budget. Always the CEO, family guy,
offered much more money for the Research shop than the shop was willing to
accept (first-cut, good budget situation!).

Why? The rules: Research picks their own projects. Projects tend to run from a
few months to a few years. One project in 10 gets to operations. When Research
has a project ready for operations, they approach the relevant operational
managers. In the first three years, savings are allocated half to Research and
half to the operational unit. After three years, all the savings are allocated
to the operational unit. With this accounting, Research was returning $3 to
the company for each $1 in their budget. So, sure, HQ wanted to increase the
budget, but Research didn't want to have to find ways to return $3 for each
extra budget $1 so didn't want a bigger budget!

It is just crucial that the CEO is supporting such in-house innovation. The
rules are also important.

Ah, while I was in grad school, to make enough money to support my wife and I
while we both finished our Ph.D.s, I took a job at a DC area _think tank_
working for the US Navy.

At one point our _problem sponsor_ group wanted an analysis of a special,
worrisome _scenario_ of global nuclear war but limited to sea -- they wanted
to know how long the US SSBN fleet could survive if it was just held in
reserve and didn't shoot its missiles with nuke warheads. And they wanted the
results in two weeks.

Gee, two weeks to model global nuclear war limited to sea! How generous! Good
that they were not in a real hurry! Besides it was good timing since the day
after the due date my wife had already gotten us reservations for a vacation
at Shenandoah!

Well, there was a guy B. Koopman who in WWII had written a report OEG-56 on
finding things at sea. So, given A and B wandering around at sea, when might
they have an _encounter_? Well, Koopman took the area of the sea, the two
velocities, and the detection radius and came up with an arrival rate for a
Poisson process. Hmm ....

So, list the Red forces and Blue forces (the US SSBNs were part of the Blue
forces), that is, list airplanes, helicopters, destroyers, battleships, attack
submarines, etc., the speed of each, and the detection radius. Then have a
table with a row for each Blue weapon type and a column for each Red weapon
type and the detection radius and, if there was an encounter, the probability
that one, the other, or both died.

Now tap lightly with an independence assumption (maybe not wildly
unjustified), realize that a sum of independent Poisson processes is again a
Poisson process with arrival rate the sum of the contributing arrival rates,
and get for the _state_ of the war a continuous time, discrete state space
(very large from a combinatorial explosion) Markov process _subordinated_ to a
Poisson process. So, yes, there is a closed form solution as a matrix
exponential for the transition probabilities from state to state, but that
matrix exponential is absurdly large. Instead using Monte Carlo to run off,
say, 500 sample paths was easy. I typed in the code.

Prof J. Keilson did a technical review. He said, "There's no way you can
fathom that enormous state space.". I said, "At each point in time, say, 10
days into the war, the number of SSBNs remaining is a random variable.
Moreover it is bounded so has finite expectation and finite variance. So, the
law of large numbers applies. So, run off 500 independent, identically
distributed samples, add them up, divide by 500, and get the expectation
within a gnat's ass nearly all the time. Really the Monte Carlo puts the
effort where the action is.". He agreed with me and passed my work.

The Navy got their results on time, and my wife got her vacation on time.

Later I was told that my work had been sold to a leading US intelligence
agency. I could tell you which one, but then I'd have to ...!

I thought that the whole effort, which ignored so much maybe crucially
important detail, was close to a joke, but, surprisingly, the output did look
reasonable. Also, the two weeks was also so short it made the whole exercise
next to absurd, another joke.

The group I was working for didn't trust me to get results on time so had
another person working independently. Well, at the end of the two weeks, the
other person had nothing at all. So, I'd won.

Office politics: One guy said "You write nice computer programs" and otherwise
I got no thanks but just some jealousy, contempt, and silence. So, soon
afterward when I'd gotten my Ph.D., I wanted to leave and did.

Again, no good deed need go unpunished.

Again, own the business, use math as an internal _secret sauce_ and
technological advantage, and sell just the results.

~~~
hgibbs
Thanks. I really appreciate you taking the time to write so much. Honestly,
this seems to be the best description of potential careers that I have ever
gotten and I feel so much more assured about my choice to study Maths now. It
is also really interesting to hear about how colourful such a career could be!
You sound like, despite the politics, you have had a really interesting career
and have done the kind of things that I would exactly like to do!

Again, thanks so much. One last question, what are you doing with your life
right now? It seems like you have had a pretty broad career and I am
interested in the end game. If you are retired, what is your lifestyle like
and in particular how has your career impacted your life as a retiree.

~~~
graycat
Part II

For now, sure, I know some math and can stir up some more, and I know some
computing and can learn more.

So, I've got a 1.8 GHz AMD single core processor, Windows XP Professional SP3
(I have an official copy of Windows 7 Professional on DVD but have seen no
great reason to go to all the trouble to install it and rebuild all my
software _environment_ yet), three hard disks, 100 million files, .NET
Framework 4.0, a good text editor (KEdit), Visual Basic .NET (comes with the
.NET Framework), ASP.NET, ADO.NET, IIS (low level Web server), SQL Server
Express, etc.

I thought, why not go after about 2/3rds of Internet search, the _safe for
work_ part served at best poorly by looking for keywords/phrases?

So, how to do that? Not with just routine software! And not with anything
commonly talked about for _search_!

I stirred up some math, typed the theorems and proofs into Knuth's TeX, worked
up a _scalable architecture_ , and typed in the software.

Maybe I should have used Redis, but instead I thought that writing my own
session state server would be faster than even understanding Redis. So, my
session state server is single threaded ("Look, Ma, no concurrency problems"),
for faster lookup rates is trivial to run as several instances as in
_sharding_ , and is just some TCP/IP sockets, some de/serialization of
instances of my session state class, and uses two instances of a .NET
collection class. Simple.

It's fast! A server for less than $1500 should be able to keep session state
for an hour of inactivity for each user and do the session state work for
sending 5000+ Web pages a second. Two standard racks should be able to handle
session state for the world.

The rest of the software is also readily scalable also from just simple
sharding.

Currently I have one bug in one Web page \-- it's not handling session state
just right! But I have the fix in code in another Web page and should copy it
over today!

My _interactive development environment_ is just KEdit with about 100 macros
and some careful use of file system directories.

I'm using SQL Server only to record the data from the users and for the
results of some _batch_ computations; at one point I actually do make use of a
_transaction_ ; the data for the searches is drawn from SQL Server with a
batch program (run it maybe once a day); some solid state drives (write
rarely, read thousands of times a second) should do wonders for the data for
the searches.

I was about to fix the bug in the Web page but took some opportunities to
gather some good initial data. The site will start _focused_ and only slowly
grow to be comprehensive -- right, at first do some things that don't scale
and please some niche group of users a lot instead of trying to please 2+
billion users a little.

Currently the database has only some meaningless data I put in for first
testing of the software. It's about time to load in some of the good initial
data I have. Then give a _critical review_ , go live, etc.

It's getting there.

All the work uniquely mine has been fast, fun, and easy, but the whole project
has taken far, far, far too long. Why? I worked through about a cubic foot of
books and 6000+ Web pages of documentation of Windows, .NET, Visual Basic
.NET, ASP.NET, ADO.NET, SQL Server, etc.

The main problems: (1) Badly written, obscure documentation (worst bottleneck
in the future of computing); (2) computer viruses; (3) SQL Server installation
bugs destroying my boot partition requiring rebuilding starting with the XP
DVD (barbed wire enema with an unanesthetized upper molar root canal
procedure); (4) SQL Server management and administration (e.g., a week of
throwing stuff against a wall to see what sticks just to get a SQL Server
connection string that will let code for a server side Web page connect with
SQL Server); (5) clean, smooth means of system backup and recovery (including
for both user data and bootable partitions); (6) Sony DVD drives that quit for
no good reason (and inability to buy more IDE DVD drives).

Good stuff: (1) KEdit and its macro language; (2) the scripting language Rexx
(Microsoft's PowerShell may also be terrific but have yet to move to it); (3)
NTFS (fantastic); (4) Visual Basic .NET design, functionality, speed of
compilation, compiler error messages, minimal bugs (sweetheart language); (5)
what ASP.NET does when it compiles a Visual Basic program (enough for a really
nice IDE); (6) NTBACKUP (once understand how to use it, e.g., _do_ have to ask
to save "system state", whatever the heck that is, or the saved copy,
restored, won't boot -- learn this and how to get around it the hard way,
weeks of work); (7) XCOPY; (8) the tools to have server side Web page code
write to a log file; (9) Firefox (except for virus vulnerabilities); (10) the
classes in the .NET Framework (once learn how to learn about them and use
them); (11) Adobe Acrobat (except for virus vulnerabilities); (12) the ability
of XP to find device drivers and recognize new devices; (13) Microsoft's anti-
virus Safety Scanner (if only from CP67/CMS and Multics, there should be no
virus vulnerabilities, but since there are the safety scanner is terrific to
have); (14) Knuth's TeX; (15) the Western Digital Passport Ultra 2 TB USB
drive!

I'm not retired or _retiring_! Likely I'm still 100% unemployable at anything
that would pay enough to let me keep a car going to commute to the job. Y
Combinator and VCs want nothing to do with me.

But if I can get my Web site up to a search a second, on a server for about
$2000, I will be in decent shape financially and on the way to _organic
growth_ for my business and much more.

Then I'll get a nice house, a building for some cars, at least one Corvette,
visit the rest of the family still alive, take off two weeks to pig out on
lobster in Maine, get some good grape juice from between Beaune and Dijon, do
some cooking, give some dinner parties, go to concerts and operas, continue
with the business, go to seminars on mathematical physics, etc.

I'll implement and deploy my server farm monitoring techniques and maybe spin
it off as a separate business.

I have some guesses for some approaches to _real AI_ and might try to
implement those.

And I will get a kitty cat! We'll see!

Good luck on your work with math. Maybe what I typed in here will help; I wish
I'd known all that when I started.

~~~
lightcatcher
Writing this as a reply rather than an email because there's no contact info
on graycat's profile.

Hi graycat,

I'm an applied math & CS undergrad at Caltech and I love all of your posts,
especially the ones about how data center scale computing really needs to
embrace statistics. The FedEx stories are also excellent. I'm personally
interested in high performance computing and machine learning, but I'm also
interested in solving "real problems" and like how you seem to focus on the
actual value of the applications. I love the feeling of engineering solutions
to mathematical problems, and this seems to be something that you also enjoy.

I'd really like to hear more about your career, research, and also the startup
that you're working on. I'd be very happy if you shoot me an email at
eric@ericmart.in

Best, Eric

------
lmm
> According to one online source, Jeremy was a “Harvard-educated maths genius
> whose computer models alerted the bank to how small levels of defaults would
> quickly turn apparently sound assets into junk,” leading Goldman to start
> selling off at the end of 2006. OK, whatever.

Are you kidding me? This is huge; this is what prevented the financial crisis,
as bad as it was, from turning into something much worse (it's "bad" for a
bubble to pop, but it's worse for it to keep growing and pop later). This guy
made the difference between billions of dollars going into houses that people
couldn't afford and weren't worth the cost, and that same money going into
productive investments. He probably contributed more to humanity than the rest
of the list put together, with the possible exception of the other Goldman
guy.

I know everyone thinks their own field is the most important, and I love
academic maths, but goddam the snobbery towards the people who did something
more directly useful with their talents is irritating here.

~~~
learnstats2
If you're a talented mathematician who thinks that the financial industry is a
net positive for society, you're most probably already working in it. It
undoubtedly pays the best and generally recruits talent.

So, if you're a talented mathematician not working in that industry... it's
reasonably likely you've made a conscious decision not to work there - perhaps
because you don't agree that it's directly useful to society.

There's a reason why the financial industry has to pay the highest salaries.
It's surely not out of generosity.

~~~
davmre
Lots of people just don't think of financial modeling as a particularly
interesting or beautiful area of math (this is of course a matter of taste).
You could believe that finance is socially useful, and yet prefer for selfish
reasons to work in algebraic geometry instead.

~~~
trhway
>Lots of people just don't think of financial modeling as a particularly
interesting or beautiful area of math

I kind of surprised how those things are frequently mixed together. The math
is a science while various industry modelling is an application of the
known/established tools/skills. It is like designing a drill vs. actually
drilling a hole. (note: i have an MS in Math (3.8 GPA) from one of the top
Russian schools)

------
yodsanklai
I played a similar game some time ago. I looked up people from a nationwide
(French) elite math program. Most people where either university professor in
Math, CS or theoretical Physics, or they were working in finance. Two opposite
environments it seems.

I wonder how their lives is in the financial industry. I imagine finance as a
demanding and stressful environment, driven by big egos, commercial types. How
do these math geniuses fit there? what level of freedom do they have in their
job? in term of schedule, things they work on and so on...

~~~
imgabe
> demanding and stressful environment, driven by big egos

The same is true of academia, from what I understand, just less money.

~~~
yodsanklai
Not really, or at least it doesn't have to be. Some ambitious and competitive
persons may work very hard to publish more papers than their colleague. But
for those that don't feel like playing this game and are immune to the
comparison with more prolific researchers, it is possible to work very little
in a low profile institution.

~~~
screwedup
I imagine that's true once you get tenure, but not before.

------
carlmcqueen
I have to admit, when I started reading this I thought the places they'd be
would be a lot different. Not sure why I had such weirdly high expectations.

~~~
lmm
Sounds like they're in pretty prestigious positions to me. Lots of professors
publishing papers, and a couple working for the biggest name in finance; only
one ordinary-sounding job ("web developer in Boston"). What were you
expecting?

If anything I was surprised so many of them had done so well. I was on the UK
squad for a few years and most of my friends from then seem to have ordinary
jobs at companies you've never heard of (like me).

~~~
carlmcqueen
I think I expected NASA-esq types of jobs.

While the hedge fund landing zone is very typical of the math grifted grads, I
expected a higher % in PHD/professor world then were listed.

~~~
ska
"grifted grads" \- Freudian slip?

------
NTDF9
As an aside, I find it curious that so many mathematicians, programmers and
others associated with logical professions be interested in music. I was
relieved to see Olympiad guys from before my birth showing similar traits.

~~~
nilkn
This is totally a tangent, but I've also noticed that juggling is very popular
in math circles.

~~~
eru
There's a special branch of knot theory, I think braid theory, that describes
juggling patterns.

------
sz4kerto
Good friend of mine was finalist around the early '90s. He know has a totally
simple 'senior dev' job at one of the big SV company's service centre. One of
the things that keep reminding me that success depends on so many things, hard
math skills are one of them.

Unfortunately, I'm a guy with a very bad impostor sindrome, and a) whenever I
see guys like him in worse/intellectually less challeging jobs than me I think
I must be just lucky b) whenever I see guys like him I think I must be
useless. :)

~~~
Moshe_Silnorin
Does he consider himself a failure? Some percentage of very intelligent people
just don't care about "success". They have rich inner lives and hobbies and
interesting friends, if they can find some. It could be that he's found a job
that doesn’t cause him much stress, that he excels at compared to his
colleagues, and allows him to pay for the pleasures of being alive. Much of
pure math is the pursuit of difficult problems that may or may not be of any
use to anyone. You ever hear this line: "Winning the Fields medal tells you
two things about a person, that they were capable of achieving great things
and that they didn't."

It's not clear to me that he would have contributed more to the world had he
become some high-status academic.

Different goals lead to different outcomes, regardless of innate ability.

~~~
sz4kerto
One always has to look at the whole person to understand whether he performs
relatively well or not. The guy I was talking about is extremely risk averse.
That makes steep careers quite difficult. But all in all, he's probably a
happy person. Another example: MENSA says I'm way inside the top 1% when it
comes to IQ tests (I didn't want to say 'intelligence'). I don't think I'm in
the top 1% most successful people in my current environment, but that's all
right as I'm coming from a poor village from a postcommunist country, and
everything that comes with it (lack of good education, etc.). So compared to
that, I'm doing all right, but naturally it's very difficult to catch up with
people who could go to Stanford or Oxford. Not because it's difficult to learn
the 'hard science stuff' \-- I interviewed many Oxbridge guys and they're not
that better than the others when it comes to hard tech/science knowledge.
However, they're much better in social skills, self-confidence, usually have
better network, family connections, etc. And those things matter a lot.

And I'm a big believer of luck and randomness. Since I've got a kid I wonder
how do we even survive, life is so risky, starting from the birth itself.

Anyway, I think perspective gives you more happiness. At least it did for me.

~~~
Dewie
> And I'm a big believer of luck and randomness.

Indeed. Like, for example, being born with a high IQ?

~~~
sz4kerto
Yes, absolutely. Brains, geolocation, family, this is all just blind luck.

------
shamefulbronze
I participated in the IMO around 2000. Now I work as a software engineer, but
I've never lost my love of mathematics. In fact, I still consider myself a
mathematician, but instead of seeking inspiration from the physical world
(physics) I seek inspiration from the practice of computer programming. This
approach has already yielded homotopy type theory, but I think that this is
the tip of the iceberg.

------
nickysielicki
Listening to Jordan ramble at the bottom was really fun, seeing his
personality come through. He taught me my discrete class just a year ago, I
got so lucky.

------
graycat
For the criterion of the title, i.e., "where are they now?", from the article
and more, sadly, it sounds like a _Math Olympiad_ is not a very good way to do
well on the criterion.

Why not very good? Because it looks like the students are given what, for the
criterion, is poor direction and use of time and effort.

E.g., when I look at my education in math and its use in applications, most of
the best of the education had nothing to do with anything like a contest,
especially a contest in the early and mid teens. Instead, the best education
was well selected, well presented material into the best work in math, e.g.,
via the best authors -- Birkhoff, Halmos, Rudin, Royden, Neveu, Tukey, Kelley,
Suppes, Simmons, etc.

Or, my impression of _encouraging_ kids in their early and mid teens to pursue
math is to give them some _enrichment_ material such as Pascal's triangle,
some number theory, various puzzle problems, a lot of recreational math, etc.
Why? Because mostly the people directing the efforts and selecting the
materials are not very well educated in math.

In simple terms, to have kids do well on the criterion in the title is just to
have the kids proceed along the main line -- get through the standard high
school material in algebra and geometry, with some applications to high school
chemistry and physics, and then move on to a fairly standard college major in
math -- calculus, modern algebra, linear algebra, advanced calculus, ordinary
differential equations, advanced calculus for applications, partial
differential equations, point set topology, measure theory, functional
analysis, probability, statistics, stochastic processes, etc.

Then that background promises to be good for a good answer 30 years later for
the criterion "where are they now"?

~~~
SamReidHughes
It seems to me like plain regression effect. Also your argument makes no sense
because most or virtually all of those people had all that standard math
curriculum too. You'll find that "is a professor" is very well correlated with
"wants to be a professor" among that set.

Edit: Pascal's triangle??? Sorry but if you give some mopper Pascal's triangle
they'll have already heard about it or invented it themself.

~~~
graycat
The question was where are the people now who did well in Math Olympiad in
middle and high school.

Good grief: Lots of people in middle and high school get pushed into math
competitions such as the Math Olympiad but don't go on to be math majors in
college and grad school.

My point is that the middle and high school Math Olympiad directions basically
don't help people be good at math later in life or good at anything later in
life. So, bingo, presto, people who were good at Math Olympiad show little or
no good effect later in life.

But if want to study some math that has a chance of having a positive effect
later in life, then follow what I outlined.

Net, sadly, Math Olympiad and other middle and high school math competitions
are unpromising for doing any good later in life. Such middle and high school
efforts would, could, and should be helpful but not by pursuing recreational
math, etc.

Seems totally obvious to me -- sorry you don't agree.

Difference of opinion is what makes horse races.

~~~
SamReidHughes
You proposed enrichment materials such as number theory puzzles and other
recreational mathematics. That's already what the math olympiad contests
consist of.

> Good grief: Lots of people in middle and high school get pushed into math
> competitions such as the Math Olympiad but don't go on to be math majors in
> college and grad school.

This isn't true at all. Most people in high end math contests are just smart
and do no preparation. They just accidentally scored high on the AMC. A lot do
some practice for fun, because the contests are fun. Possible exceptions are a
handful of people at Philips Exeter++ and maybe Thomas Jefferson High School,
I'm not familiar with that dynamic. Contests like the ARML are oriented around
making local friends more than anything. At the most local levels it's like,
some high school teachers will corral their students into doing a contest at
the nearby college one afternoon.

For example some friends of mine in the Philadelphia area thought it would be
neat to enter the Harvard/MIT math contest (which is way more fun and
difficult than the Temple School of Actuarial Sciences contest or Drexel's).
It was the kids telling their parents they were doing this, and deciding to
practice for it. I think the same happened with a group of students in Albany.

++and they were recruited after performing well on middle and elementary
school math contests that parents are completely unaware of.

~~~
graycat
> You proposed enrichment materials such as number theory puzzles and other
> recreational mathematics. That's already what the math olympiad contests
> consist of.

No, I did just the opposite: I said that others proposed such materials; I did
not propose them but criticized such proposals. Again, for a high school
student to be pushed into seeing lots of tricky things in Pascal's triangle,
attacking number theory exercises, doing recreational math won't do the
students much good in later life -- so as in the title of this thread, we
won't expect to see many such students successful in math later in life.
Instead, the efforts there in middle and high school will rarely come to
anything.

Helping middle and high school students do better in math than what is in just
the usual courses would, could, and should be doable and done, but the path is
not recreational math, etc. but, instead, as I outlined, just proceeding with
the main line of math education -- rush through the high school math of
algebra and geometry, likely also trig, and then get a college calculus book
and dig in.

E.g., the high school math teachers I had were eager to say that we "were not
ready for calculus". Nonsense. It was the teachers who didn't know calculus.

I very much would have rushed ahead had I had some good guidance. Eventually I
knew enough to rush ahead when I was a college freshman: I'd had four years of
math, grades 9-12, at a relatively good high school but for my college
freshman year went to a state school that was cheap and close enough for me to
walk there and back. They wouldn't let me take calculus but pushed me into a
course beneath what I'd already done in high school. So a girlfriend told me
when the tests were, and I showed up for those. The teacher said I was the
best math student he'd ever had -- in no very real sense was I _his_ student!

I asked to be permitted to start calculus but was turned down. So I got a good
book and dug in. I did well (in high school mostly I'd been teaching myself
from the books and sleeping in class anyway). For my sophomore year I went to
a good college with an excellent college math department, started on their
sophomore calculus, from the same text used at Harvard, and did well.

I'm hot on this stuff about what middle and high schools do to good math
students: My eighth grade arithmetic teacher gave me a D and took me aside one
on one and fervently urged me never to take anymore math. In some significant
ways, my father was good at education and just laughed.

That eighth grade teacher didn't have a clue about what math was: For the
actual _math_ , I'd done well in her class. What I did poorly on was
multiplying two four digit numbers, and the reasons were (1) my handwriting
was sloppy (common for boys), so sloppy I didn't get the columns lined up and
then added wrong for the final answers, (2) my _clerical ability_ was just
awful (common for boys), (3) I understood the ideas right away but never
worked on the _clerical_ skills to get correct answers, (4) my parents never
urged me to work to get right answers (my father had some high-end views of
_education_ and just wanted me to learn, especially out of interest, and
didn't care at all about grades, and I did learn).

But in the ninth grade, the teacher saw right away that I was his best
student, and he sent me to the state math tournament. In the summer after the
11th grade I was sent to an NSF math and physics program.

So, net, I was a good math student, was very interested in math, was eager to
race ahead, but the school did a poor job helping me.

There is a little more to the story: When the SATs came back, I was called out
of study hall to get my scores, from the same teacher I'd had in the sixth
grade. Nice woman. Sweet. Ignorant! She, along with most of the rest of the
teachers, thought I was a dunce. So, she read me the Verbal SAT score -- 538.
She said "Very good". BS! It sucked! But she was sweet. She may have thought
that I would get 250 or some such!

Then she looked at my Math SAT and hesitated. She looked worried. Confused.
She said "There must be something wrong." Then she said the score was 752 and
"That's uh, uh, very good.". Darned right it was good. But she was correct
that there "was something wrong" and had been for 4, 6, 12 long, wasteful,
painful years.

I had had no idea what the SATs were about and had made no effort to prepare.
But I finished the Math SAT early, checked my answers, and still had 15
minutes. I'd _very_ much like to know what the CEEB thought I'd missed. Maybe
they _scaled_ the scores and didn't give anything much higher.

My Math SAT was second out of a grad class of about 180, which is about right
from the statistics, 2.5 sigma above the mean of 500. The #1 guy beat me by a
few points. The best student in the grad class was a little behind me -- he
went to MIT and burned out his fuses in his freshman year.

I was a good math student, had been eager to rush ahead in math, physics, and
chemistry, but I'd had poor guidance. So, I'm hot on grades 6-12 continuing to
give good math students bad advice. So, here I say, mostly, for the actual
Math Olympiad competitions, waste of time. To do well with math, just go down
the main road to a ugrad math major as I outlined. Simple. And to heck with,
say, learning to play Nim in Courant and Robbins, _What is Mathematics_ ,
about Pascal's triangle, etc.

Yes, I'd learned about Pascal's triangle. So when I was in grad school and had
been pushed into a silly ugrad class in probability, the prof went all
arrogant and emphasized that due to the factorials it can take some really
long precision arithmetic to calculate even relatively ordinary binomial
coefficients. BS: Just work in from one side of Pascal's triangle and never
see a factorial. Indeed, I raised my hand and stated so in the lecture. I'd
long since written software do to just that.

Next he did a sloppy job explaining the glory of the central limit theorem,
and I dropped the course. But I was taking and grading in the Neveu measure
theory level course at the same time, my first official course in probability,
and did well. E.g., I was the only student who showed that there are no
countably infinite sigma algebras.

The schools who want to send their good math students to Math Olympiads are
likely also doing a poor job helping their students. Then, as in the title of
this thread, in later life we mostly won't see much effect from such high
school efforts.

Net, my hot button is that the schools in grades 6-12 don't know enough math
to do well helping their students eager to race ahead in math.

> > Good grief: Lots of people in middle and high school get pushed into math
> competitions such as the Math Olympiad but don't go on to be math majors in
> college and grad school.

> This isn't true at all.

Of course it's true: E.g., you gave some examples of how high school teachers
try to get some of their students into such competitions, i.e., "push" the
students. That's _lots_ of students, and in college math is not a very popular
major. So, lots of middle and high school students in math competitions don't
major in math in college, just as I claimed.

For more, you mentioned some activities at the college level; I was addressing
the high school level. Sure, college students who do well on the Putnam are
likely college math majors who are taking math very seriously. Again, I was
addressing high school.

~~~
consz
Why are you acting as if these contests do a poor job training kids? The OP
never suggested that -- in fact, it seems nearly all of them grew up to be
very successful. Your stance seems to be in direct contradiction of the
evidence offered in the original article.

~~~
graycat
The article implied that the Math Olympiad work didn't much result in
significant results 30 years later from the work in math for the contest.

You are correct that the OP didn't directly say that the "training" of the
"kids" was poor.

My view of such high school math competitions is that they waste the time and
effort of the students and, otherwise, with good guidance, there would be
significant results from the efforts 30 years later. In this sense, then the
training was a "poor job".

But the OP did not say that directly -- that's my interpretation, heavily from
what I saw used as efforts to have some high school students do _better_ in
math -- the efforts were a waste of time for all concerned and because the
people directing the efforts didn't know enough math.

~~~
consz
I'm still not following. In what way are there not significant results from
the kids in the contest? They almost all seemed to have had significant
success.

------
coroxout
In case anyone else is interested but didn't make it all the way through the
comments on the blog page, a commenter notes that Miller Puckette of Max/PD
music software fame was one of their coaches a year or two later.

------
roblm
So, really don't like Goldman, huh?

------
adaml_623
> Dan Scales: Am I misremembering this name? I can’t find anything on Google.

I don't know who Dan Scales is but if you can't google someone nowadays then
they might just work for the government ;-)

