Counterexample: Consider the simple, first order, linear, ordinary differential equation initial value problem

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

I was feasting on picnic pork shoulder BBQ in Memphis when I saw that and with freshman calculus (never took it, taught it to myself, started on sophomore calculus) got the closed form solution. Don't even need a course in differential equations, variation of parameters or any of that!

Well, one Saturday morning my solution kept the two representatives of FedEx BoD Member General Dynamics from walking out; they cancelled their plane reservations back to Texas and stayed; FedEx was saved from going out of business.

So a little bit of math work helped a major business!

Yup, gaps, that's the usual situation.

But, early in my education, I didn't know those facts of life about gaps, etc. and believed that the stuff I was studying in math and physics would be useful, to make money, for a house, wife, kids, etc.

But, naive or not, in the end I got a good education in pure/applied math. Now I'm less naive.

But, now I'm an entrepreneur: I can pick a good real problem -- as we know, good problem selection is important for success. And there's no law against my drawing on all I learned in pure/applied math to derive some new math to get the first good solution to an important problem.

I did that for zero day monitoring of server farms and networks, but for success, the $ kind, I was in effect depending on others to make the practical application. I had some high quality flour but was not starting Domino's Pizza.

So, being too naive too often in the past, I decided to go to where the money was, to have a Web site that would get a lot of traffic, run ads from ad networks, get lots of clicks, and get paid by the click -- be 100% owner.

How to do that? First, pick a problem. Really, pick a pair of problem and a solution, but, to keep it simple, first pick a problem. Right, if in the second step can't find a good solution, then loop back and pick another problem.

So, there's the Internet and computing, both not nearly fully exploited. And there's ballpark 5 billion people on the Internet. Maybe in the more developed countries that can support good ad rates, there are maybe 400 million good Internet users.

So, then, find a problem these 400 miliion or 5 billion people would very much like to have solved, want a new solution on average once a week, and will be willing on average to look at screens from my Web site for 30 minutes a week and, there, see maybe 50 ads with decent ad targeting. Multiply that out, and it's a successful business. Get optimistic and excited multiplying that out and get an estimate that it's the first $1 T business.

Heck, get on average 24 x 7 one user a second, and it's a nice life style business -- plenty for house, wife, kids, etc. (uh, i've never had money enough to buy a house -- I'd like to be able to buy a house; I'm not joking about that, not even a little bit; if I'd had money enough to buy a house my wife might still be alive; I want money enough to buy a house; I know with 100% certainty I will never have money enough to buy a house unless I start, own, and run my own successful business -- period.).

So, I found such a problem. It's not solved worth a darn -- the best solutions totally suck. The solutions are so bad no one even suspects that there could be a solution and, thus, fails even to notice the problem.

Well, a solution is not trivial: Routine applications programming won't work. That AL/ML would work is a LOL joke. The applied math for a solution is not on the shelves of the libraries. So, I found some new math for a new solution. The work was not too difficult -- I've done high quality, new math before.

I never had any trouble; get good at understanding the theorems and proofs and working the exercises in books by Halmos, Rudin, Fleming, Coddington, Royden, Loeve, Neveu, Breiman, Bertsekas, Hadley, Herstein, Hildebrand, Cinlar, Nemhauser, Zangwill, Luenberger, Simmons, Kelley, Suppes, Tukey, etc. and then maybe will be able to do publishable work in math.

Then I wrote the software. It appears to run fine. I wrote the software in Microsoft's Visual Basic .NET -- looked, still looks, like a fine approach to me. So, no LISP, no functional programming, no particular concern about object oriented architecture, ignored JavaScript, nearly ignored CSS, never used an HTML div element, no attention to languages intended to make high levels of parallelism easy and automatic, ignored the model, view, controller Web software architecture, just typed into my favorite text editor and never used an interactive development environment, had no problems with debugging (it was enough just to write little trace messages to the Web site log file), just kept it simple. Seems fine to me.

I'm on the way to going live and getting revenue.

I'm a sole, solo founder, entrepreneur. I can do math and write code; there's no law against it; I don't need permission; and maybe my work will make money -- I believe there is a huge chance.

If people like my work, then I'll be rich.

Yes, on the gaps, one of my Ph.D. dissertation advisers told me with high concern that I should consider how long it takes to get original research into practice. Immediately I told him "I'll put it into practice right away.". That's what I'm trying to do. Uh, he assumed that I wanted to be a college prof; nope, I wanted to make money, the green kind, in business, the green money making kind.

Gap between academics and applications? Not for me, now. Sure, I suffered from that gap, but now I look at the flip side and see a big opportunity.

Software development isn't zero sum. Just because AI/ML companies are valuable it doesn't mean what you are doing can't be too.