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On Apr 14, 2024, at 6:42?AM, John Robinson via groups.io <profilecovenant@...> wrote:
I wonder what Lee & other math Wizards think of this?
John
Why AIs that tackle complex maths could be the next big breakthroughMathematical AIs show machine intelligence may emerge from unexpected pursuits
Read in New Scientist:?
I¡¯ve been thinking about writing about AI here ever since February 3, when John posted the following:
Harry, I¡¯m a guy that listens to hundreds of Audio Books, many Biographies, Autobiographies. ?Steve Jobs, Elon Musk, Charlie Munger, Ray Dalio, Tony Robbins and on and on it goes. ?I also listen to a plethora of investment works. ?I¡¯VE NEVER HAD ONE TOTALLY CHANGE MY THINKING like ¡°The Coming WAVE¡± by Mustafa Suleyman.
I added that book to my reading list, and finally finished it in the middle of March. I¡¯ve been mulling over it and several other ones ever since.
To greatly oversimplify, right now what we call AI is really a huge pattern search engine. We feed it a bunch of data and it correlates the data into a big collection of connected nodes. It is also programmed with rules that tell it how to traverse the nodes. With a huge set of input data and a rich rule set, there might be many ways to traverse the graph. Given a command, it chooses the path its rules deem most likely to result in a correct result. This process can require a huge amount of computing, if the data set is large and the rules are complex.
In mathematics, the computer is given a data set of known results in an area. For example, it might be given a huge collection of algebra equations and the steps to their solutions. It¡¯s also given the rules of algebra and logic. When you ask it to solve a new equation, it will look for something in its dataset that is similar the new equation. Since the thing in its dataset has a well-defined solution, it tries to use the same steps to solve the new equation. Programs such as Mathematica, Maple, and SageMath?have been doing this for many years. They can solve any equation from a high school algebra class and much more.
The problem that comes up is when the problem can't be twisted into something similar to something else in the data set, the program is stuck.
All the examples I know of where AI systems solved difficult math problems are similar to what I described above, except the training data sets are many examples of proofs, and the rules are complicated. With a diverse enough data set and a rich set of rules, the program might very well be able to construct tricky proofs of difficult problems.
In fact, quite a few years ago I read an article in Math Intelligencer (I think??) about a computer program that was taught the basic facts of Euclidean geometry, which form a nice and fairly simple closed system. The programmers just told it to start proving facts by wandering around its database and following the logic rules it was programmed to use. The result was hundreds of ¡°theorems¡±. Few of them were interesting and the interesting ones were already known¡ªwith a couple of exceptions. It did manage to find some new proofs of well-known theorems.
The moral to this story is that the computer didn¡¯t really come up with anything new, because it didn¡¯t have any new ideas, and this is the weakness with the AI mathematical proving programs. The great mathematicians are great because they came up with new ideas. The names we remember are Newton, Euler, Gauss, Cantor, Noether, Neumann, Turing, and many others, because they didn¡¯t just just prove hard things, they came up with unprecedented methods and ideas.
Today¡¯s AI programs are showing uncanny technical virtuosity in many areas, but they aren¡¯t yet showing originality.
Don¡¯t think what I¡¯ve written means I think AI is pure hype and just another tech bubble. It is doing some seemingly magical things, particularly in medicine, where it is already better than almost all doctors in spotting some heart problems and breast cancer. In both of these cases, the AI diagnosis is often earlier and more accurate than standard diagnoses, and the experts don¡¯t really understand what it¡¯s seeing.
Returning at last to the Suleyman book, I do think a lot of it is hype coming from an AI entrepreneur. He does a lot of hand-waving and has few details. I do believe his claim AI will have a profound effect in biology because it¡¯s the only way we know to make sense of the large databases of proteins and DNA. I am skeptical of his claims about the imminence of AGI (= artificial general intelligence).
L^2
The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man in the bonds of Hell.?¡ª?Augustinus
