3 ms·

Part I I tried a grad math department and didn't like it: (1) In a course in real analysis, early on the prof discussed some set theory. The summer before I'

by graycat 10y ago

Part I I tried a grad math department and didn't like it: (1) In a course in real analysis, early on the prof discussed some set theory. The summer before I'd had an NSF thing in axiomatic set theory, Suppes, von Neumann, an appendix in Kelley, etc. His first test had a problem, and at the last minute I saw a solution and wrote it down. He called me on the carpet -- nasty guy. I apologized for using little omega for its usual meaning without defining it, and then he saw that my solution was better than his and I was off the carpet. Bummer. He was too quick to cut me off at the knees. (2) Course was in Kelley, General Topology. As a ugrad senior, I'd lectured a prof once a week and covered all of it except the last chapter on compactness when I cut out to finish my honors paper [The typing was so hard that from rolling the carriage a half step my left arm hurt for a year!] But the course in grad school, same book, was beneath me. I turned in a stack of solved exercises and was a nice guy -- I didn't submit any I'd done in ugrad. Waste of time. (3) There was an abstract algebra course from Herstein's book -- by then nearly all beneath me. E.g., my ugrad honors paper had been on group representation theory which is heavy linear algebra and abstract algebra stuff. I solved some exercise in ring theory and got sent to a full prof. The only thing new in the course for me was Galois theory, so I studied that some weekend and took an oral exam for the course. Waste of time. I wanted the math for math-physics but didn't see how to get that there. Certainly not Galois theory. There were some good ways but not with the courses they put me in. The specs for the q-exams were a disaster -- the faculty committee had a political train wreck. Bummer. I got recruited by the NBS&T in DC. Getting to DC then was the land of milk and honey for applied math. I got married, and she went for her Ph.D. We had a great time, good French cheese, some quite good French wine, lots of plays, concerts, trips to Shenandoah, etc. I got into descriptive statistics, multi-variate statistics, statistical hypothesis testing, numerical linear algebra, curve fitting, the fast Fourier transform, second order stationary stochastic processes, extrapolation, and power spectral estimation, optimization, the Navier-Stokes equations, did a lot of catch up reading in the basics, a lot more in linear algebra, multi-variate calculus, e.g., exterior algebra, and more. Kept busy. Had a great time. Also got into computing in a fairly big way. Got some nice items, e.g., two new cars, etc. My favorite book on my bookshelf, including for applied math, is J. Neveu, Mathematical Foundations of the Calculus of Probability. Worked in industry and saw some problems in combinatorial optimization, deterministic optimal control, and stochastic optimal control, identified a problem in stochastic optimal control and found an intuitive solution, applied to grad school in applied math. Got into Cornell, Brown, Princeton, and more. Independently in my first summer did the research for my dissertation in stochastic optimal control. Had lots of delays having to do with my wife and, then, our budgeting. In a rush, wrote some corresponding software in two months, much of it over Xmas at wife's family farm, and wrote and typed in the final dissertation in six weeks, stood for orals, and got my Ph.D. During Ph.D., did work in military systems analysis, some optimization, statistics, and Monte Carlo -- wrote the corresponding software. The day my wife got her Ph.D. she was in a clinical depression from the stress. To help her get better, I took a job I didn't want as a B-school prof in applied math (also played a leadership role in campus computing and did some consulting) but was near her home family farm that I hoped would help her. It didn't. I took a job in AI at IBM's Watson lab and did some optimization, mathematical statistics, and AI. My wife never recovered from her illness and died. Then I became an entrepreneur. I did some interesting work in two cases of optimization; thus I found good solutions to the customers' problems that they believed could not be solved; that I solved the problems scared them off. One solution turned out to be just linear programming on networks -- I was coding up the W. Cunningham variation when the customer ran away. The other problem was just some Lagrangian relaxation; I got a feasible solution within 0.025% of optimality in 500 primal-dual iterations in 900 seconds on a slow PC to a problem in 0-1 integer linear programming with 40,000 constraints and 600,000 variables -- scared the pants off the two top people in the customer's company. They had tried simulated annealing, failed, and concluded that no one could solve their problem; that I found a good solution, both the math and the software, scared them off. I looked into lots of stuff that didn't work out. Lesson: US national security, especially around DC, was, maybe still is, really eager for a lot in applied math -- optimization, stochastic processes, etc. In wildly strong contrast, I've seen no interest in business at all comparable, not even in Silicon Valley. The US DoD is often quite good at exploiting applied math; in comparison, business, in a word, sucks. The flip side of that suckage is, in some cases, an opportunity. Lesson: Business is still organized like a Henry Ford factory where the supervisor knows more and the subordinates are there to add routine muscle to the thinking of the supervisor. Sooooo, US business just HATES anyone who knows more than any of the supervisors about anything relevant to the business, and one can about count all the good cases of applied mathematics in business without taking shoes off. Business CAN make good use of specialized expertise and does with lawyers, licensed engineers, and medical doctors. Each of these, however, is usually outside the usual organization chart pecking order, is often from an outside service, in a research division, in a staff slot off the C-suite, etc. Each of these has a profession that is crucial; applied math doesn't. Bummer. In business, an applied mathematician who shows the company how to save 15% of the operating costs is a lose-lose to the C-suite: If the project flops, then it was a waste, and anyone in the C-suite who signed off on the budget has a black mark. If the project is successful, everyone in the C-suite feels that their job is at risk from the guy who did the good project. So, the C-suite sees any such project as a lose-lose situation. Nearly no one in US business got promoted for doing an applied math project successfully or got fired for not trying an applied math project. So, sure, to make money with applied math, go into business, your own business, as your own CEO, and own the business. Now some of the opportunities are closely related to the Internet -- take in data, manipulate the data with some applied math, maybe somewhat original and novel, spit out valuable results. Then monetize the results whatever way looks best. Use the math as a crucial, core, powerful, technological advantage, secret sauce. Don't expect the customers/users to see anything about the math -- just get them results they will like a lot. Do the other usual things when can -- viral growth, network effects, lock in, good publicity, own data, etc.

graycat 10y ago
Part II My software now is 100,000 lines of typing with about 25,000 programming language statements and the rest voluminous comments. About 80,000 of the 100,000 are for on-line, and the rest are for off-line, occasional batch runs for some of the data manipulations. There is some light usage of SQL Server. I am basing on Windows and the .NET Framework. For the Web site, that is Microsoft's IIS (Internet Information Server -- handles the TCP/IP Web site communications and much more leaving a nice environment for my code for the actual Web pages) and ASP.NET for the Web page controls (single line text boxes, links, check boxes, radio buttons, etc.). My Web pages and my code for the pages is just dirt simple -- Microsoft writes a little JavaScript for me, and I have yet to write a single line of it. There's no use of Ajax, no pull downs, pop ups, roll overs, overlays, icons, etc. The Web site is also dirt simple, a seven year old who knows no English and has only a cheap smart phone dirt simple. I wrote a little C code; am using some open source C code, and otherwise wrote all the code in Visual Basic .NET -- seems fine to me. The important stuff is the math I derived; given the math, the code is routine, and Visual Basic .NET is well up to the work. Since I don't like C syntax, I don't like the syntax of C#. Maybe someday I will convert to C#, but in an important sense Visual Basic .NET to C# is just converting to a different flavor of syntactic sugar -- indeed, IIRC there is a translator. So, I'm an entrepreneur working to sell the results of some math I derived. So, to do such a thing, think of a problem and a solution, write the code, sell the results. Of course, problem selection is a biggie. And want a problem that can solve and with own applied math with a better solution than available otherwise; want the software not too much to write; want the computing resources within what is reasonable now or soon (possibly considering the cloud); want the results to be a must have instead of just a nice to have for enough users/customers times money per each to make some big bucks. If you are a solo founder, then you get to avoid a common cause of failure -- founder disputes. As a founder, you SHOULD understand all the work, so if you are a solo founder you will! Don't expect any equity funders to write you a check until you have revenue significant and growing rapidly. Thus, as a solo founder with revenue significant and growing rapidly you won't accept their check. No one in equity funding has yet seen even 10 cents from applied math research; you won't get back even laughs. Ph.D. academics is really good at work that is "new, correct, and significant". Business just HATES anything really new or significant and has no idea how to check "correct". E.g., the information technology VCs keep looking for simplistic, empirical patterns and have no idea how to evaluate anything new. Really, their looking for such patterns is likely also just a publicity scam; instead, they want to invest money in a business where accountants working for their limited partners, who, if that is possible, know even less about math, can say that they made a good investment. In an analogy, they want to buy a ticket on a plane that has already reached nice altitude and is climbing quickly. Maybe the startup will take their money if there are five founders, all exhausted, all with all credit cards maxed out, and each with a pregnant wife. For a good applied mathematician -- with some original, powerful, valuable work, good at software, with a business with significant revenue growing rapidly -- to report to a BoD of business people, essentially anyone else in business, is a bummer. E.g., at an early BoD meeting you will outline an applied math project for some nice progress in the business, and about the time you get to sufficient statistics, an ergodic assumption, completeness of Hilbert space, the polar decomposition, something in NP-complete, or a martingale, the board members will soil their clothes, leave a smelly trail to the rest room, and then run screaming from the building. They will meet off-site, fire you, put the business up for sale for the cash in the bank, and be glad you are gone. Bummer. So, go into business for yourself. Or, don't expect anyone in business, who no doubt knows next to nothing about math, doesn't even remember sin' = cos, to create a job suitable for your talents, training, and business value in applied math. Heck, at one time in business, I saved a major company just by formulating and solving y'(t) = k y(t) (b - y(t)) The BoD was thrilled, but I scared the socks off the C-suite. That was the third time. The first time I wrote some software that pleased the BoD and saved the company. The second time I beat everyone in the C-suite at Nim -- I'd read the algorithm in Courant and Robbins. Scared the socks off the C-suite. Applied math in business is a wide open field -- nearly no one there now. So, you will be alone. You can trust the solid math you know, the solid, new proofs you write, and a lot in software, but no one will do anything but laugh until you have the big bucks in the bank; then, since you did something valuable they don't understand and know they could not have done, they will fear you and hate you; they will all agree and may gang up on you; they may attack you. The laughing is not nearly new: Just read the Mother Goose "The Little Red Hen"; that's still the case. There's a lot of good, foundational applied math code out there for optimization, statistics, etc. you might be able to exploit. In computing, operating systems, .NET etc., SQL etc. are astounding and from free to usually quite cheap. Nearly no one in business can identify, formulate, and solve even a problem that is basically just linear programming -- the competence in applied math in US business is, well, they forgot plane geometry. To expect them to derive some simple Lagrangian relaxation is asking for hen's teeth. As an applied mathematician in business, you will be essentially alone out there, in the nearly empty intersection of math and business. If you are successful, then you will necessarily also be exceptional, and necessarily nearly everyone who is exceptional is alone. My first server is an AMD FX-8350, 64 bit addressing, 8 cores, 4.0 GHz processor clock, 32 GB ECC main memory, etc. That's a lot of computing power for the money. Fill that up doing something valuable, buy 20 more, fill those up, and sell out for $1 billion or so. It's a heck of an opportunity.

by graycat 10y ago

graycat 10y ago

Part II My software now is 100,000 lines of typing with about 25,000 programming language statements and the rest voluminous comments. About 80,000 of the 100,000 are for on-line, and the rest are for off-line, occasional batch runs for some of the data manipulations. There is some light usage of SQL Server. I am basing on Windows and the .NET Framework. For the Web site, that is Microsoft's IIS (Internet Information Server -- handles the TCP/IP Web site communications and much more leaving a nice environment for my code for the actual Web pages) and ASP.NET for the Web page controls (single line text boxes, links, check boxes, radio buttons, etc.). My Web pages and my code for the pages is just dirt simple -- Microsoft writes a little JavaScript for me, and I have yet to write a single line of it. There's no use of Ajax, no pull downs, pop ups, roll overs, overlays, icons, etc. The Web site is also dirt simple, a seven year old who knows no English and has only a cheap smart phone dirt simple. I wrote a little C code; am using some open source C code, and otherwise wrote all the code in Visual Basic .NET -- seems fine to me. The important stuff is the math I derived; given the math, the code is routine, and Visual Basic .NET is well up to the work. Since I don't like C syntax, I don't like the syntax of C#. Maybe someday I will convert to C#, but in an important sense Visual Basic .NET to C# is just converting to a different flavor of syntactic sugar -- indeed, IIRC there is a translator. So, I'm an entrepreneur working to sell the results of some math I derived. So, to do such a thing, think of a problem and a solution, write the code, sell the results. Of course, problem selection is a biggie. And want a problem that can solve and with own applied math with a better solution than available otherwise; want the software not too much to write; want the computing resources within what is reasonable now or soon (possibly considering the cloud); want the results to be a must have instead of just a nice to have for enough users/customers times money per each to make some big bucks. If you are a solo founder, then you get to avoid a common cause of failure -- founder disputes. As a founder, you SHOULD understand all the work, so if you are a solo founder you will! Don't expect any equity funders to write you a check until you have revenue significant and growing rapidly. Thus, as a solo founder with revenue significant and growing rapidly you won't accept their check. No one in equity funding has yet seen even 10 cents from applied math research; you won't get back even laughs. Ph.D. academics is really good at work that is "new, correct, and significant". Business just HATES anything really new or significant and has no idea how to check "correct". E.g., the information technology VCs keep looking for simplistic, empirical patterns and have no idea how to evaluate anything new. Really, their looking for such patterns is likely also just a publicity scam; instead, they want to invest money in a business where accountants working for their limited partners, who, if that is possible, know even less about math, can say that they made a good investment. In an analogy, they want to buy a ticket on a plane that has already reached nice altitude and is climbing quickly. Maybe the startup will take their money if there are five founders, all exhausted, all with all credit cards maxed out, and each with a pregnant wife. For a good applied mathematician -- with some original, powerful, valuable work, good at software, with a business with significant revenue growing rapidly -- to report to a BoD of business people, essentially anyone else in business, is a bummer. E.g., at an early BoD meeting you will outline an applied math project for some nice progress in the business, and about the time you get to sufficient statistics, an ergodic assumption, completeness of Hilbert space, the polar decomposition, something in NP-complete, or a martingale, the board members will soil their clothes, leave a smelly trail to the rest room, and then run screaming from the building. They will meet off-site, fire you, put the business up for sale for the cash in the bank, and be glad you are gone. Bummer. So, go into business for yourself. Or, don't expect anyone in business, who no doubt knows next to nothing about math, doesn't even remember sin' = cos, to create a job suitable for your talents, training, and business value in applied math. Heck, at one time in business, I saved a major company just by formulating and solving y'(t) = k y(t) (b - y(t)) The BoD was thrilled, but I scared the socks off the C-suite. That was the third time. The first time I wrote some software that pleased the BoD and saved the company. The second time I beat everyone in the C-suite at Nim -- I'd read the algorithm in Courant and Robbins. Scared the socks off the C-suite. Applied math in business is a wide open field -- nearly no one there now. So, you will be alone. You can trust the solid math you know, the solid, new proofs you write, and a lot in software, but no one will do anything but laugh until you have the big bucks in the bank; then, since you did something valuable they don't understand and know they could not have done, they will fear you and hate you; they will all agree and may gang up on you; they may attack you. The laughing is not nearly new: Just read the Mother Goose "The Little Red Hen"; that's still the case. There's a lot of good, foundational applied math code out there for optimization, statistics, etc. you might be able to exploit. In computing, operating systems, .NET etc., SQL etc. are astounding and from free to usually quite cheap. Nearly no one in business can identify, formulate, and solve even a problem that is basically just linear programming -- the competence in applied math in US business is, well, they forgot plane geometry. To expect them to derive some simple Lagrangian relaxation is asking for hen's teeth. As an applied mathematician in business, you will be essentially alone out there, in the nearly empty intersection of math and business. If you are successful, then you will necessarily also be exceptional, and necessarily nearly everyone who is exceptional is alone. My first server is an AMD FX-8350, 64 bit addressing, 8 cores, 4.0 GHz processor clock, 32 GB ECC main memory, etc. That's a lot of computing power for the money. Fill that up doing something valuable, buy 20 more, fill those up, and sell out for $1 billion or so. It's a heck of an opportunity.