Right. They are overwhelmingly merely heuristic. The methodology is to guess, with heuristics, and then try it and find out (TIFO method) on real data, maybe adjust, and use it when it appears to work. There's next to nothing in theorems and proofs before hand that show that the manipulations will be powerful or yield valuable results.
There is a long history of good applied math where, once the theorems are proved, there isn't a lot of doubt about how the real world application will go. E.g., (1) GPS, (2) the earlier version for the US Navy, (3) error correcting coding for, say, satellite data communications, (4) phased array passive sonar, (5) optimal allocation of anti-ballistic missiles to incoming warheads, .... There's much more making good applications of math, e.g., Wiener filtering, the Neyman-Pearson result in advanced radar target detection, in cases of engineering where, once the engineering is done, there's not a lot of doubt about how good the practical results will be. No guessing. No TIFO. Low risk. High payoff. E.g.,
http://iliketowastemytime.com/sites/default/files/sr71_black...
As designed, unrefueled range 2000+ miles, altitude 80,000+ feet, speed Mach 3+, never shot down. Just as planned. Just as clear from the engineering, based on quite a lot of applied math.
Uh, for (5), really don't want to have to use the TIFO method! Instead, want to know with high confidence before someone pushes a big red button.
> So applied math researchers aren't expensive?
For evaluating the cost of a startup, commonly pay the founder $0.00 per year until there is revenue or at least funding. :-)! Sorry 'bout that.
E.g., I worked in artificial intelligence at IBM's Watson lab. Part of the work was to monitor the health and wellness of server farms and their networks. No theorems. No real guarantees of the power of the data manipulations or the value of the results. I did an upchuck, derived some new math, and published it. The math says that we know in advance the false alarm rate. The AI work didn't. The usual approaches to machine learning don't do such things because they don't approach the work as assumptions, theorems, and proofs.
For Ph.D. applied mathematicians (I am one) at Google, once Google ran a lot of recruiting ads, and I sent them a resume and got a phone interview.
They asked what my favorite programming language was, and I said PL/I. Apparently the only acceptable answer was C++. It was clear enough that my answer of PL/I essentially ended the interview.
Why PL/I? It has some total sweetheart scope of names rules. The exceptional condition handling is super nice (get an implicit pop of the stack of dynamic descendancy with just the right clean up). The data structures are nearly as powerful as classes and much faster in execution. Threading (tasking) in the language. Pl/I does really nice things with automatic storage -- C doesn't. And there's more.
C++? We know the history: Unix was a baby Multics, on an 8 KB DEC box. C was a dirt simple language, no runtime. All function calls for every little thing, e.g., string manipulations -- the first version of PL/I was like that, but the later versions compiled such things and were much faster. PL/I does just wonderful things with arrays, but C doesn't really have arrays.
Then C++? That was, along with Ratfor, an example of Bell Labs liking pre-processors. So, C++ was a pre-processor to C. Instead, PL/I was carefully designed.
My selection of PL/I over C++ was not wrong.
Google laughed at my naming PL/I. The laugh is on Google. Uh, Linux is a version of Unix which was a baby version of Multics which was written in, may I have the envelope, please (drum roll), right, PL/I.
It was clear that my Ph.D. in applied math and experience were of no interest at all. None. Zip, zilch, zero. C++? Sure. Ph.D. in applied math? Nope -- worthless.
Okay. It was Google's decision. But, now I get to make a decision: I'm not impressed by the power of the role of math at Google. At QUALCOMM, maybe. At Renaissance Technologies, sure. At Google, nope.
I still prefer PL/I to C++. Sorry 'bout that! But I wouldn't want to use either language in production now.
Now I program on Windows, not Linux, and on Windows I use the .NET Framework. To do that, for a language, I have just two leading choices, C# or the .NET version of Visual Basic (VB). The difference is mostly just the flavor of syntactic sugar, and I prefer the more verbose flavor of VB.
For FB, I never applied -- it seemed totally hopeless.
I'm doing my own startup, right, based on some applied math I derived as in my post here.
A few weeks ago I got all the code running I first planned to do. Now that the code is running, I see a few tweaks. Then I will load some initial data -- have been having fun collecting some. Then on to alpha test, beta test, going live, getting publicity, users, ads, and revenue.
Hopefully people will like the results (from the math, although users will not be ware of anything mathematical); if so, then I stand to have a nice startup.
Much of my confidence in the work is the theorems and what they say about the power of the data manipulations and the resulting value of the results.
Math is supposed to be useful. There's a long track record that it can be. I studied math hoping it would be useful, and I believe that it is for my project.
Doing some applied math might seem unusual, but it's not "crazy". The unusual part indicates an opportunity.
A "name"? For my work so far, I've not needed a static IP address so have not paid extra for one from my ISP. So neither do I have a domain name yet.
I won't get a static IP address or a domain name until just before I go live, ASAP.
My startup is for Internet search, discovery, recommendation, curation, notification, and subscription for safe for work Internet content where keywords/phrases work at best poorly.
My project might become a big thing.
The user interface is just a simple HTTP, HTML, CSS Web site, also simple enough for smart phones.
So, my software takes in data, manipulates it, and sends the user the results. The crucial core of the manipulations is from some math I derived based on some advanced prerequisites I got mostly in grad school.
Right, the users will see the results but not be aware of any of the math. What the user does with the Web site and the results they get back will seem intuitively reasonable and maybe even natural, but actually doing the data manipulations in a way with good promise of good results is a challenge, one that I addressed mathematically.
The theorems give good evidence that with some good data the results for the users will be good. Given what I'm betting on this project, I want the good evidence, up front, long before TIFO results, traction, etc.
My main use of italics is a common one, mark a word as being used in a sense maybe not the same as in a literal dictionary definition and, thus, needing some caution, reinterpretation, and/or apology.
You don't think CV, ML/DL, VR are worth pursuing? Or are you saying that those are not "mathematically" technical? If the latter then you are decidedly wrong as proven by any number of research teams at MSFT/FB/GOOG etc...
>Not really expensive.
So applied math researchers aren't expensive? Tell that to every PhD Mathematician at Google/FB.