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Comment by capnrefsmmat | Hacker News Reader

I'm curious how you would replace mathematics with programming. My undergraduate thesis project involves a lot of programming, but I also had to determine that I can detect anomalous gamma spectra through some linear algebra, a correlation matrix, an assumption of Poisson-distributed counts, and a chi^2-distributed anomaly statistic. This gives me a statistically well-founded way to detect anomalies.

Would you have me replace this process with some sort of automated machine learning, hoping it could produce better results than a special-purpose algorithm?

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Even if your argument is true, that maths is needed for that particular task, it doesn't justify teaching it to 99% of people. Also, the math you mention could have been taught as a set of computer programming functions (taught in a few hours) rather than how it's traditionally taught (as s semester long class or sequence of classes).

Black box machine learning might have given you better method than your whatever you're currently doing. And it would be done in a automated manner, with human effort just focusing on collecting data. I'm assuming whatever you're done is being done/has been done by many 1000s people as well. That's a tremendous waste of time. Even if the method you outline is better than what machine learnig would have found, it only needed to be done once (or a few times - marketplace) and exposed as an api.

The point of my thesis is that it has not been done by anyone else before. In fact, I had to do the mathematics because previous work in the area required too much training data to be effective for mapping; it is simply not viable to require dozens of training passes through an area before I can begin to detect anomalies.

My algorithm works because it uses assumptions from the physics of the problem -- the assumption of Poisson-distributed counts.

Well, I can't argue with the specifics of your problem since I don't know about it (but the general point that this doesn't justify the current maths system for 99% of people).

However, at some point in time, computers will be taking over all human abilities (if you believe that AI is inevitbale). At what point will that occur? It's my strong suspicion that we have already reached that point and any evidence to the contrary is simply that people aren't trying automated methods (I believe that machine learning can solve any problem that humans can solve, and furthermore, this wouldn't require more computing power than we already have).

How do you choose the black box if you don't understand the problem? It's not as if there exists a single black box for all possible problems.

That's missing the point entirely. I'm pretty sure you don't know the exact materials and the process for making the shoes you might be wearing. There are probably no shoe factories left in america. They same applies to the black box machine learning, very very few people need to know of what goes on under the hood. edit: I don't know if you changed your comment, but black boxes exist that can solve any problem (neural nets for example).

That might be true for some very general (or common) problems (though I have doubts about that as well), but it can't possibly be true for a specialized problem such as the one described. How do you train a model if you don't understand the problem? You can't just say "unsupervised learning" and expect your algorithm to come up with a full understanding of the physics involved.

(And no, I have not edited my comment.)

I agree with you, I just feel like that is basically the understanding of variables (names of concepts) and not maths. So, you need to understand what measurements to take/can be taken, and then set up that system and feed it to the black box machine learner.

Now, there still need to be some people who understand how things work in detail, but this is much smaller than what is being taught (most k12 do not need to know maths or physics or chemistry etc). They do need practice in abstract thinkng and this would be much better done with programming (a playful, creative, logical, and useful activity).

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