[sja]

While I agree that it is vital for a practitioner know the mathematical basis behind what they're doing in order to maximize their chances of success, I find your current argument lacks substance.

You argue that there is a vast amount of solved problems in tomes of "pure" mathematics. But this doesn't mean that any of those solutions are relevant and/or necessary to the problems people are working on.

Your "statistical test" argument is misleading. Machine learning techniques aren't designed to form such statistics, and judging them by their ability to do so willfully disregards the real world success many companies have found by using ML/AI to solve their problems.

Certainly, there are challenges that are waiting to have their solutions implemented from a rediscovered manuscript, but listing impressive-sounding statistical terminology doesn't demonstrate lack of value for machine learning/AI techniques. Furthermore, it doesn't even demonstrate value for the "pure" techniques you list. To clarify, I'm talking about real-world value, not just theoretical value (and again, I'm not arguing that such techniques don't have value, just that your argument isn't doing a good job communicating how such techniques have orders of magnitude more value than ML/AI).

[graycat]

AI/ML now is too often just heuristic curve fitting. Okay, with good training data and then testing data, can get some utility that way. So, if that's the best can do in the context, okay. A secret in old applications of regression model building, that idea of cut the data in half, fit with one half and test with the other, was common and appropriate.

But we'd like to do better. Some of what is in statistics and applied math more generally will let us do better.

But the idea if dividing the data into training and testing is old. There's much more in the literature on how to build and evaluate models. E.g., there's analysis of variance and categorical data analysis (e.g., log linear).

E.g., for my startup, a guy gave a talk and said that can't do that, encounter four problems. He was right about the four problems. And if just look in elementary texts, yup, do see the four problems. But I'd already seen all four and worked up some theorems and proofs to get around all four, in the context of my real problem. The foundation of the theorems and proofs was mostly some advanced pure math. Without new theorems and proofs, I'd been stuck like he was.

In an important sense, the pure math guys are right: They are looking for the big, important structure and powerful properties, where all the furniture is in the room, turning on the lights so that can see all the furniture (A. Wiles), and that can be darned powerful stuff in practice.

> You argue that there is a vast amount of solved problems in tomes of "pure" mathematics. But this doesn't mean that any of those solutions are relevant and/or necessary to the problems people are working on.

Flour is a raw material. Some people can use it to make a fantastic Sacher Torte. Pure math can be regarded as a raw material. Some people can use it to get new, powerful, valuable results for real applications in practice.

> orders of magnitude more value than ML/AI

Those techniques are narrow and weak. The stuff long on the shelves of the libraries is much more broadly applicable and usually much more powerful. I've made a lot of applications of applied math, and not one of them would the AL/ML discussed these days be better and nearly never would be competitive.

[srean]

What 4 problems ?