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chriswarbo

> What's the point of spending "time" (brain cycles) on such problems?

What's the point of anything?

> Is it just a mathematician's version of brain teaser?

All of mathematics can be characterised as "brain teasers". Make of that what you will.

> What useful development comes out of such?

I'm not qualified for this particular example. However, it seems quite number-theoretic, and number-theory has given us such "practical" things as asymmetric encryption and universal computation (Turing's famous paper from 1936 was titled "On Computable Numbers", after all).

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> What's the point of anything?

Not that I disagree with you, but some things have an impact on people's quality of life: nutrition, healthcare, and psychological well-being.

> ... but some things have an impact on people's quality of life: nutrition, healthcare, and psychological well-being.

I would perhaps classify that as "immediate" impact, not "lack of impact".

Number theory has driven computer science, calculus, statistics, and so on.

CS, calculus, stats... they all drive (for example) "nutrition". For example, how do you know what a "vitamin" is? How do you measure it? How do you quantify it's effects on the body (and mind)? A whackload of analysis DEPENDS on number theory for us to understand almost everything about the natural world!

It's a big world, not everyone needs to be a farmer/doctor/psychologist so some people who have other skills do other things. Sometimes those other things help. A lot of time they don't. For better or worse we live in a society.

I'd say there's a strong case that this has a positive impact on the psychological well-being of anyone who's interested in number theory.

Perhaps not that many people in the world understand the formulation of the problem, but then not many people "get" abstract art, either.

Psychological well being is definitely improved if people could work on something they like and get praised/rewarded for it. And I believe that is way people could get interested in something. Best engineers I know of, had got into their field because they are driven by solving problem just for the sake of it.

So? What is the point of living?

:-)

Farming provides food. Predicting the probability of water spontaneously combusting, while interesting, provides much less food.

You know what does though? Irrigation. You know what allows you to optimally irrigate so you don't waste money that you could be spending either on growing more crops or your family? Maths.

Only a fool pretends the ground floor of a house is worthless because they live on the second floor.

I'm not saying Math is useless, I'm saying there must be tiers for topics in how useful they are such that someone can say "Hey, that's pointless!" and one can't follow with "Therefore all things are pointless". Or, that allow me to rank niche topics in their usefulness.

Irrigation is very important. Now, is Irrigation Maths more important to us as a species than Terrence Taos work on spontaneously combusting water? Probably! Would it be more useful to have PhDs be funded in optimizing food routes between countries after climate change over game theory applications for blackjack? Probably!

Unfortunately, no. Maths is so vast that what might seem a trivial and silly brain teaser can turn out to unlock a massive problem in a seemingly completely unrelated subfield of mathematics, and we won't know until someone discovers that link.

What someone might call "a silly little brain teaser" today could actually result in a breakthrough paper weeks (or centuries) from now in a different subfield because someone far smarter than us realized that part of the problem they were working was actually analogous to a number theory related problem that was simplified, even a tiny bit, by this solution. (Hell, Nash built his entire career on spotting those kind of links and then telling other mathematicians to focus on working out the individual pieces)

Maths plays out over "we don't even know how long or short" time scales. What's the use? We don't know, it's probably completely useless. Until someone suddenly realizes that it's not.

>Now, is Irrigation Maths more important to us as a species than Terrence Taos work on spontaneously combusting water? Probably! Would it be more useful to have PhDs be funded in optimizing food routes between countries after climate change over game theory applications for blackjack? Probably!

I imagine you would be equally annoyed at Euler in 1736 when he was wasting his time with bridge brain teasers (and invented graph theory in the process) instead of solving bubonic plague or optimizing irrigation. Science just doesn't (in general) work the way you propose.

And the majority of science sit in empty libraries with maybe a single citation by a postdoc trying to write enough papers to get the next postdoc...

Sounds like you forgot that's literally everything niche until a post doc or tenured mathematician goes "yo hold up. This tiny proof (helps) solve(s) X". And now their name's in the science history books.

OP didn't say all math was useless, just this math, which yes is most likely completely useless.

The interesting thing about the question is that there really aren't any right or wrong answers.

People pointing out that maths is full of advancements that had no immediately identifiable use at the time, but that came to be useful later, is correct. Yet it doesn't even begin to answer the OP's question.

I doubt very much that many people choose to pour their lives into endeavours that they don't particularly enjoy just because some hypothetical person at some hypothetical future point in time might hypothetically find a hypothetical use (hypothetically ;P).

The answer is that "value" presupposes the question "valuable to who and why?"

Newton invented Calculus because he had an immediate use for it. Other mathematicians pour themselves into solving problems because they enjoy it and find a lot of reward in the prospect of solving a previous unsolved problem. Both are "valuable", just to different people for different reasons.

Yeah it's fine for mathematicians to amuse themselves, the problem is when they demand salaries to do that and taxpayers like OP rightfully ask "whats in it for me?" And when the answer is "IDK but maybe in a century we might have a problem this math is useful in solving" then it's not surprising that no one wants to fund pure math research. It's not the 20th century anymore when math research was going to meaningfully improve someone's life through the invention of things like electrical devices.

Yeah, if you force other people to pay for something then you had better offer them an attractive value proposition. Though public funding of mathematics and other sciences is not what I thought we were discussing :)

In which world do you think mathematicians are raking in taxpayer money? Mathematics requires very little funding: a blackboard, some chalk, a pen and paper, a desk, some coffee. That's it.

Thats a pretty myopic view of history there champ.

The pragmatic, practical perspective here is that funding the egg heads has had incredible outcomes (and its so cheap too), so dont let the simpletons shake the golden goose down just because they don't understand anything they cant fuck, fight, or eat.

You described my thinking very well, and much better than I. Thank you

They were trying to solve a real world problem using this kind of math, and then decided it'd be easier to improve upon the math itself than to continue to pound at the problem - so by definition, I'd say you're absolutely wrong here, or they never would have started this proof in the first place.

Until it's not, because someone suddenly realizes that a seemingly completely unrelated problem in a completely different subfield that's holding up a major proof is actually analogous to a problem where this result removes a bunch of roadblocks.

That's the problem with math from a "so what is this good for?" perspective: we don't know yet, but we sure have a litany of instances where seemingly useless proofs had a profound impact anywhere from weeks to centuries later.

>Predicting the probability of water spontaneously combusting, while interesting, provides much less food.

Unless you can make a prediction that water will combust in low energy conditions, in which you can use this combusting water to generate excess power. Then use that power to compress nitrogen into ammonia, and then use that product as fertilizer.

The British show Connections went over how completely different things sometimes 'connect' and bring fruitful new ideas.

The problem space of reality has emergent behaviors that are not (easily?) predictable. Sometimes you have to iterate large portions of it.

What is the point of providing food? Surviving? Existing? Is that the highest achievement? Is remaining breathing for a few more seconds the greatest goal?

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