I agree with a lot of that.

But hypothesis testing remains important because in some contexts with too little data that's about the best can do. For parametric tests, there are some cases when that's okay.

The asymptotic stuff is mostly okay: Can't figure out precisely what the darned thing will do for case n so let n go to infinity and maybe can see what happens. Then say, "for large n, this is about what happens" -- crude but better than nothing.

The central limit theorem and more says that the Gaussian is really important. Okay. Done. We know that. But, right, for too long too much of statistics made nearly a religion out of the Gaussian. Bummer.

Today happened to see the discussion panel at Stanford at

https://www.youtube.com/watch?v=hxXIJnjC_HI

It's fun stuff, with some big names.

They are laughing at ML: ML discovered statistics like Columbus discovered America. Columbus didn't discover America since when he landed millions of people were already living there. And when CS AL/ML discovered statistics, there was already a huge field there.

Moreover, the situation is reversed: Columbus brought better ship, etc. technology to the Americas than the Americas had, but CS AL/ML are bringing nearly all highly inferior technology to statistics, pure/applied math, etc.

CS AI/ML is nearly all new labels for adulterated old wine.

So, take some data on two variables, plot on an X-Y graph, fit a straight line, get the coefficients of the line as in first year algebra, and, presto, bingo, "The AI revolution is here!!!!", CS had had a machine "learn" the coefficients and they started with "training" data, that is trained the machine!!!!!! Where can I get one of those airline seat barf bags? Upchuck time!

Uh, I have a pretty good professional library; much of my house is lined with -bookshelves. The main topics are pure/applied math. Some of the books relevant to statistics include
(with TeX markup)

Alexander M.\ Mood, Franklin A.\ Graybill,
and Duane C.\ Boas, {\it Introduction to
the Theory of Statistics, Third
Edition,\/} McGraw-Hill, New York, 1974.\
\

N.\ R.\ Draper and H.\ Smith, {\it Applied
Regression Analysis,\/} John Wiley and
Sons, New York, 1968.\ \

C.\ Radhakrishna Rao, {\it Linear
Statistical Inference and Its
Applications:\ \ Second Edition,\/} ISBN
0-471-70823-2, John Wiley and Sons, New
York, 1967.\ \

Henry Scheff\'e, {\it Analysis of
Variance,\/} John Wiley and Sons, New
York, 1967.\ \

Yvonne M.\ M.\ Bishop, Stephen E.\
Fienberg, Paul W.\ Holland, {\it Discrete
Multivariate Analysis:\ \ Theory and
Practice,\/} ISBN 0-262-52040-0, MIT
Press, Cambridge, Massachusetts, 1979.\ \

Stephen E.\ Fienberg, {\it The Analysis of
Cross-Classified Data,\/} ISBN
0-262-06063-9, MIT Press, Cambridge,
Massachusetts, 1979.\ \

Leo Breiman, Jerome H.\ Friedman, Richard
A.\ Olshen, Charles J.\ Stone, {\it
Classification and Regression Trees,\/}
ISBN 0-534-98054-6, Wadsworth \&
Brooks/Cole, Pacific Grove, California,
1984.\ \

R.\ B.\ Blackman and J.\ W.\ Tukey, {\it
The Measurement of Power Spectra:\ \ From
the Point of View of Communications
Engineering,\/} Dover, New York, 1959.\ \

William W.\ Cooley and Paul R.\ Lohnes,
{\it Multivariate Data Analysis,\/} John
Wiley and Sons, New York, 1971.\ \

Maurice M.\ Tatsuoka, {\it Multivariate
Analysis: Techniques for Educational and
Psychological Research,\/} John Wiley and
Sons, 1971.\ \

E.\ L.\ Lehmann, {\it Testing Statistical
Hypotheses,\/} John Wiley, New York,
1959.\ \

E.\ L.\ Lehmann, {\it Nonparametrics:
Statistical Methods Based on Ranks,\/}
ISBN 0-8162-4994-6, Holden-Day, San
Francisco, 1975.\ \

Jaroslav H\'ajek and Zbyn\v ek \v Sid\'ak,
{\it Theory of Rank Tests,\/} Academia,
Prague, 1967.\ \

Sidney Siegel, {\it Nonparametric
Statistics for the Behavioral Sciences,\/}
McGraw-Hill, New York, 1956.\ \

Donald F.\ Morrison, {\it Multivariate
Statistical Methods: Second Edition,\/}
ISBN 0-07-043186-8, McGraw-Hill, New York,
1976.\ \

Harry H.\ Harman, {\it Modern Factor
Analysis: Second Edition, Revised,\/} The
University of Chicago Press, Chicago,
1967.\ \

George E.\ P.\ Box and Gwilym M.\ Jenkins,
{\it Time Series Analysis --- Forecasting
and Control: Revised Edition,\/} ISBN
0-8162-1104-3, Holden-Day, San Francisco,
1976.\ \

Jean-Ren\'e Barra, {\it Mathematical Basis
of Statistics}, ISBN 0-12-079240-0,
Academic Press, New York, 1981.\ \

So, what is really significant recent ML is adding to this quite old material? How much of the good stuff in that material has CS AI/ML even read and understood so far? Uh, what am I missing? I can think of a little but not much.

CS AI/ML going for applications of statistics is a lot like Stanley Tools, long in the hammer, screwdriver, saw, drill, and nail gun business, going into the residential construction business building, selling new houses and claiming that they have something new! That is, because they make good nail guns they conclude that they are the best at building houses. They know nothing of excavation, masonry, framing carpentry, windows, doors, roofing, plumbing, electrical, HVAC, dry wall, painting, circular stairs, walnut paneling, landscaping, or even the building codes, but they've got some good nail guns!

The math I derived and published in multi-dimensional, distribution-free anomaly detection has next to nothing to do with any of those books above; instead, I did original work and drew from ergodic theory, abstract algebra, and a classic result of Ulam. For the math for my startup, it's also original and even farther from those books above. In both cases, the core results are presented as theorems with proofs. Such math is mostly not what I'm seeing in CS AI/ML.

I DID see some cute, recent work in analysis, maybe from ML, of the over fitting problem; I don't need that work for my startup, but I do intend to go back and read that work.

My main points are:

(1) If AI/ML have some applied math tools that are solid, good, and new, terrific. Then those cases will add to the many thousands of such tools already on the shelves of the research libraries.

(2) The most important paradigm for
a solid future for such tools is new,
solid, correct, and powerful
theorems and proofs building on
solid material in math. That is,
we want better stuff than is
already in the libraries.