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Comment by ubj | Hacker News Reader

Neural networks were first prototyped in the 1950's [1]. How practical was it to study them back then?

Aleksandr Lyapunov's theory of stability for dynamical systems, which forms the bedrock for much of control theory, was first proposed in 1892 and went unnoticed until the 1930's [2]. How practical was it for Lyapunov to study that topic?

It's virtually impossible to predict which mathematical tools will be "practical" or "useful" in the future. The point is that if someone needs the tool down the road, they'll have access to the solution due to the efforts of these mathematicians.

[1]: https://en.wikipedia.org/wiki/Neural_network#History

[2]: https://en.wikipedia.org/wiki/Lyapunov_stability#History

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Many other fields too.

Mendel's discoveries weren't appreciated until after he died. When Narinder Singh Kapany invented fiber optic cable in the 50s he had no idea it would lead to revolutions in computer networking, gastroenterology, and other fields.

And the entire works of Church and Turing…

Or the guy who just wanted to extend the works of Aristotle, and created binary...

Leibniz did that from memory, although the stoics deserve the credit for propositional logic (which can be reduced to a collection of truth tables). and contrary to popular belief Boole actually extended Aristotle’s syllogisms (reduced the conventional syllogisms to computation using matrices of 1s and 0s) rather than create a today’s binary logic.

> It's virtually impossible to predict which mathematical tools will be "practical" or "useful" in the future

On a long enough timeline, you're right! But if we limit ourselves to, say, the next 5,000 years, it gets a lot easier to accomplish. ;)

How does limiting the timeline to 5,000 years enhance our ability to predict the future?

The more you limit your timeline, the easier is is to predict the future. That's why we only have 10-day weather forecasts.

Good point, maybe a better way of phrasing it would have been "It's virtually impossible to predict which tools will _not_ be useful" :)

Fast Fourier transforms, complex numbers, complexity classes, etc. are clearly useful. It's much harder to rigorously claim that a result will _never_ be practical or useful.

Just to be clear, I think it's fair to say that a result isn't _immediately_ useful. But who can say whether or not it will have a more practical application down the road? Only time will tell.

there is a huge chance this advancements could be invented maybe in more efficient form when need and time come.

Proofs (both results and techniques) are a mathematician's ammo. It is not good strategy to wait for a war to start before building ammo.

And then you open ammo storage when you need it and see it is polluted by 99.9% of irrelevant garbage.

Math is like code: technical debt makes moving forward much harder.

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