Wall Street?

I was in NY and close enough to NYC. I'd just published a paper in anomaly detection in complex systems, gave a talk at the main NASDAQ server farm, and later at Morgan Stanley. No real interest.

Sent a copy of my anomaly paper to a hedge fund, got an interview, was asked by one of their junior people "If know the correlation between A and B and that between B and C, what about A and C"? Okay, maybe: Start with the cosine of the sum of two angles???

Asked them for a reference on investing math -- did already know about the old Markowitz work, the efficient frontier, the role of quadratic optimization, about to do more with stochastic differential equations for the Black-Scholes work -- got the book they mentioned, saw that its math was all junk, and didn't follow up with the A and C contact, a mistake.

Did send a resume to Simons.

Looked into deterministic optimal control, Athens and Falb, talked with Athens, later talked with an Athens student who knew something about Simons and claimed that he hired mostly Russian mathematicians. So gave up. A mistake. I was naive.

Later, of course, Simons explained that he liked people who, say, via math but any math, had shown some ability, and I had some evidence I could have shown. My Math SAT was high enough that maybe I even beat Simons?

I was naive: Assumed that a carefully written resume was necessary and sufficient and that anything else was superfluous and unwelcome.

Nope: In practice in the real world, keep trying different things. Do send reprints of published papers. E.g., when I was at Georgetown, computer center staff and teaching computer science, a prof had some teaching software as a front end to the IBM SSP (scientific subroutine package) and in testing found that two of the IBM routines were too slow and the third had poor numerical accuracy. So, I wrote plug compatible versions -- used some (n)ln(n) software and some tricky double use of memory to replace the n^2 software and used some Forsythe and Moler work to fix the accuracy problem -- seemed too simple to me, but COULD have sent Simons that work. Once did get a lecture on differential geometry from a student of A. Gleason and had a copy of some S. Chern notes -- could have studied those and sent something to Simons. How'd I know Simons knew Chern??

There is a recent remark: "Don't give up. Keep plugging".

I was naive. Knew much more about math and computing than people and personality.

Since WWII, the US military has pushed hard to have more -- students, professors, and research -- in math and science. In high school, taught myself the math, learned the physics at a glance, otherwise goofed off (had a girlfriend drop dead gorgeous), but did well on the state standardized tests, so got sent to summer math/physics enrichment programs. I swallowed the bait hook, line, and sinker. I'd recommend:

"Always look for the hidden agenda."

"Believe none of what you hear, half of what you see, still that will be twice too much."

"Who you know can be more important than what you know."

There were some opportunities to "know" some powerful people, but I was naive.

My Ph.D. advisor was a nice guy, but I got to him after the fallout of a bad civil war in the faculty and never much talked with him. For my dissertation, some applied math, and had the main idea on an airplane flight before the Ph.D. program, in the first year wrote a 50 page first draft, later cleaned up the math, used Fubini's theorem in a short proof that my math was optimal, wrote some illustrative software, typed in the paper, showed it to my advisor and the rest of the department, had a famous guy a Chair of an orals committee to review the dissertation, and graduated. My advisor and one of the faculty (connected in DC and later President at an Ivy) knew a LOT about politics, but I was naive.

For a while, my career, in computing but with some math on the side, e.g., the FFT and digital filtering of Navy sonar signals, was going well, so I got the Ph.D. in applied math just to do better in THAT career and with ZERO intentions to be a professor or do academic research. That career direction was MY idea, mine alone, ..., a BAD situation!!! I was naive.

Naw: The WaPo period was before my Ph.D. The ads were for computing -- math not mentioned. For some years, the career was computing but with some math, e.g., the FFT (fast Fourier transform), ....

I never wanted the Ph.D., what I learned there, the research I did there, to be the basis of a career. Instead, before the Ph.D. I had a good career going with computing and, at times a crucial help, some math, and went for the Ph.D. ONLY to do better at THAT career. For my career, the day I entered the Ph.D. program was a BIG step down, and what I'd learned about optimization was, in a word, WORTHLESS.

My main point here is on the word "applied" for optimization: I was well qualified, and happened to publish some research in optimization, but discovered that "applied" optimization was not the basis of a good career. Here I'm just reporting that fact. I doubt that there is still any real career opportunity in "applied" optimization.

So, a book title with "Applied" Optimization is to me a outrage.

I wasn't stuck on "optimization". For a while worked in the first wave of AI (artificial intelligence via the Rete algorithm). Then published in mathematical statistics. I was perfectly willing to mow grass, shine shoes, ..., do anything that would support me financially, be reasonably safe, and not seriously illegal but discovered that "Ph.D." on the resume blocked any such. Thought about taking "Ph.D." off the resume but was afraid that I'd get into trouble due to the gap in time.

Here my point, complaint, warning, contribution to others, is: My long experience was that there is nearly no career in "applied" optimization. A second point could be, outside of academics, a Ph.D. can hurt your career. Try leaving it off your resume. A Ph.D. might be worse for your career than a felony conviction; no joke (my legal history is totally clean).

In life, we are forced to make important decisions without good information. In my career, at times I did well, and at times I didn't.

E.g., by middle school it seemed accepted and true that education helps, more education helps more, education in the STEM fields is the best, a Ph.D. is the best education, and, thus, a Ph.D. in a STEM field should be really good, e.g., easily enough to buy a house and support a family.

Truth: Nope, too simple. I couldn't take care of my wife, kitty cats, get a job, any job, at all, ANY job, got run out of the house by the Sheriff with guns.

With a BS "With Honors" in math, I got strongly recruited. With a Ph.D. in applied math, including optimization, I got strongly rejected.

Yup, it hurt. I was manipulated, lied to, and hurt.

"psychological burden": Maybe those are the right words. But millions of people have suffered worse, e.g., The Great Depression, wars, Covid in the family, and much more, and still did well.

Don't know the solution in general.

For me, now, still good in math and computing, with .NET, etc. got a Web site, with some math at the core, running easily enough, and intending to go live, get some viewers, run simple ads (standard sized rectangles), and make some money. In this, want to remain anonymous and not be a public person.

And want to OWN the business. Have someone list what papers I need to file for a business, an LLC, etc. Get an accountant. Get and receive revenue. In simple terms, add up the expenses and keep the rest. Eventually sell the business and pursue, say, mathematical physics.

I believe I get fully what you are saying.

At one point, we need a correction: The optimization was to schedule the fleet for FedEx. They were spending big time money on the airplane operations, and a better schedule, saving even 1% of that, would amount to maybe $millions a year, at any rate, money worth saving and where, in comparison, my work cost peanuts. At FedEx at the time, the 1%, the automation of the fleet scheduling, the business planning potential, made the project worthwhile.

The "decision maker" was F. Smith, founder, COB, CEO. My office was next to his. On paper I reported to a Senior VP, but in reality reported directly to Smith. Smith wrote a memo giving the optimization problem to me -- I still have a copy. The project was approved, and by passing all the executive considerations you mentioned. The project was not "killed". Instead, due to (a) commuting between Memphis and Maryland where my wife was in her Ph.D. program, (b) wanting to stay in Maryland, where I'd done the best work for FedEx and saved it the first time (access to consultants and time sharing computing), (c) the Senior VP I was reporting to telling me there "was no money in the budget for me", and (d) the promised stock very late, I left for the Ph.D.

I got Smith to approve the project by explaining "Integer linear programming set covering" to him for this application: (i) Take all or a reasonably large subset of all the reasonable tours from Memphis and back. All the planes were the same, French Falcons, .... (ii) For each tour, program standard means of evaluating flight times and costs and find the cost of the tour. Throw out some tours for however goofy reasons, e.g., can't fly over this city at that time of day. Note, some of the costs and constraints were really goofy, way beyond what could be converted to software even for non-linear integer programming. Such is the magic of set covering enumeration.

(iii) Intuitively regard each tour as a piece in a jigsaw puzzle where have lots of extra pieces, each piece has a cost, and want to cover. "set covering", the board exactly at minimum total cost. That's when Smith understood the work well enough to approve it as my project. Considering what airplanes cost, my project was not very expensive.

(iv) Now have a 0-1 integer linear program with one row for each city and one column for each tour. In a column, a row i = 1 to 90 is 1 if the tour serves city i and a 0 otherwise. The cost of that column is just the cost of the tour. The right side is all 1s. The constraints are all >=. With 90 US cities, there were only 90 rows in the linear program. So, use some LP (linear programming) software to get solutions feasible and optimal or nearly so. At some point if necessary just use old branch and bound. Worth a try. My computing was VM/CMS time sharing on relatively large IBM mainframes.

"1% is a fraction of inflation." Maybe you are saying that CEOs should have optimization involved only for super big aspects of the company, like Ike's work on D-day, and ignoring a 1% reduction in the cost of M1 rifle ammunition. Well, not then at FedEx. Fleet operating costs were by far the biggest expense of the company and .... Even for D-day, such a 1% reduction might have been worthwhile but to be handled by some Colonel and not Ike!!

Your other points seem to be correct. One response is when working for US national security, some of the problems were "strategic" for the US and where ... would be as you describe "advising" "options" at no higher than some mid-level uniform in the Pentagon and not for the POTUS. But for my work in the commercial economy, I never was trying to advize the CEO of some $800 billion company on some crucial decision. And I didn't work on enough problems to encounter many of the considerations you listed.

Again, my main point here was just the "applied" optimization in the book title in the OP. My experience, academic, military, commercial, student, professor, research and applications, indicates that outside of the US military there is nearly nothing real about "applied" optimization -- optimization applications are nearly like hen's teeth.

Maybe Amazon, Walmart, Google, Microsoft, and a few of the largest companies have an office of planning and analysis on the organization chart reporting to some VP for something or other and there occasionally develop/run some optimization models, but I never saw any evidence of such. Sure, such an "office" would have to do the TLC of the CEO you mentioned. I'd guess that such an "office" would get their optimization done with a lot of contact with some professors, but the only professors I ever saw doing any such work were the few I contacted. I just didn't see any credible evidence of "applied" optimization in the US commercial economy.

Now, in the last 10 years or so, everything about such optimization -- data collection, data manipulation, word processing for the math, the basic desktop computing, statistical tools, and, sure, Gurobi, etc. are just MUCH better. Soooo, maybe now the US commercial world is ready to exploit optimization like Dantzig, Kuhn, Tucker, Arrow, Hurwicz, Nemhauser, etc. intended. Maybe.

If I got an offer, now, for such work I'd turn it down and stay with my startup. (a) You're talking too much in office politics; that's not one of my specialties; and I have none of that in my startup. (b) I know the math for my startup, all nicely written up with TeX, but I'm rusty on a lot of the rest of math. E.g., for Lagrangian relaxation I'd look at my notes for the last time I did that. For some of the classic integer programming on graphs, I'd go for my grad school notes. For anything in probability, I'd want to review the Radon-Nikodym theorem and conditional expectation, all the standard theorems on convergence of random variables, etc. (c) From the time I got the offer, I'd have to start spending my money, and I might get fired before I even got that back -- such a job would be a gamble where I could lose money significant for me.

Again, my post here was just to object to "applied" for optimization. No way am I looking for a job; not now; not any more; not again. Instead I'm staying with my startup.

Fine. But I'm still not finding the private planes, yachts, mansions, or even houses with wife and children of people with careers in "applied" optimization. Computing, startups, venture capital, lots of careers. "Applied" optimization? In the years after my Ph.D., I didn't hear of them. As I was teaching optimization in a business school, the phone didn't ring. The phone did ring for some statistics, one from a company with sales districts and one from a law firm.

I'd strongly encourage you to leave academia for at least 2 years, preferably a little more -- and go intern, or work at, at least 2 or 3 different companies. This will benefit your mental health, working practices, and sense of perspective.

Academia is full of superstitions and misunderstandings about 'industry', and is an ideologically closed system designed to present itself and its practices as of the highest value. Including, as mentioned here, hijacking 'industrial values' (such as utility, applicability, etc.) and presenting itself with them.

This is in part a straight deception: academics need to lie about this to governments and other funding agencies in order to get funding. And in part naivety, their sense of 'application' is so far removed from any, that they are poor judges of it.

Enabling these deceptions is, of course, that academic output does occasionally have an impact over longer time horizons. But it is more the case that something written ~30 years ago will today find some use by a small team somewhere -- which might have a lot of impact, but isnt on the scale or time lines you'd need for your research today to give you an ROI.

Indeed, as you'll see if you're in industry long enough, there is often something very suspicious and deceptive about the values of various research communities. Even when researchers are told: no one cares about this, this does not have the value you say it does, this isn't a real problem etc.-- they continue. Why? Because they aren't interested in solving problems people have, they are interested in whatever puzzles are current within their community.

If you want to solve real problems using research, it is better to go out and undertand what problems people actually have, then go back into research aiming to help them.

Once you have postulated BigInt as available, the mathematician is going to make a rational approximation for phi using the continued fraction expansion that they know by heart (because of its “simplicity”).

late to discovering proofs and thereoms, only a little bit late to apply them to real world problems.

If you think it is you should read up on linear algebra, specifically its use in finite difference equations and how that relates to linear differential equations.

The astonishment doesn't get less, but it shifts from Binet's single formula to the exponential map, and maybe the fundamental theorem of algebra (or generalisations).