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Excuse me for being a bit of a moron here, but why do we spend so much time, energy, and money trying to solve these weird mathematical questions? What's the pr

Excuse me for being a bit of a moron here, but why do we spend so much time, energy, and money trying to solve these weird mathematical questions? What's the practical application of any of this that can justify the cost?

Kranar 6y ago
It's a fair question mostly because of how effective math has been at solving practical problems, but honestly working on problems like these is usually due to a genuine appreciation and enjoyment of mathematics. I'd even say the majority of mathematicians study math strictly out of a sense of wonder and curiosity rather than towards a commercial application and that the vast majority of math research is not at all practical. The cost is justified due to a common shared interest in the subject, many other people are interested in math and pay people to work on it. It's not all that different than paying someone for music, or a painting, or to write a work of fiction. People get a profound sense of enjoyment and happiness from this work and are happy to pay the cost for the continued advancement of this field.
marcianx 6y ago
The article touches on this with: > k = x³ + y³ + z³ is what number theorists call a Diophantine equation — a kind of algebraic structure whose properties have fascinated mathematicians for millennia. “They’re rich enough to encode [other mathematical] statements that have nothing to do with Diophantine equations,” said Browning. “They’re rich enough to simulate computers.” More specifically, equations of such form come up in a proof of Godel's first incompleteness theorem. That being said, yeah, this effort is mostly a mathematical curiosity, mapping out the domain of knowledge of mathematics increasingly more completely. Sometimes an application comes about where either the solution or novel techniques used to arrive to the solution can become useful, but pure math research isn't typically driven by any existing applications as much as a "because it's there" attitude.
redis_mlc 6y ago
> Excuse me for being a bit of a moron here It's beyond being a moron - you're acting like a caveman. Math is the language of logic and science, and allows the world to express how everything works. Once a problem is solved mathematically, that can be used as a tool forever. You should be asking why HN has a weekly UFO post, or what will be accomplished in killing people by sending them on a one-way trip to Mars. The fact that you don't understand an enormous field like math should make you respect the people who can even more.
evgen 6y ago
Sometimes these weird questions can lead to more practical applications down the road, e.g. once we know how to do something it gets added to the toolbox and eventually used, somewhat like how Euler's totient was a cute mathemtatical curiosity until it became one of the important steps in RSA key generation and a very useful tool almost two centuries after it was discovered. It is also the case that sometimes knowing where the 'holes' are in these sort of stepwise math series' can itself reveal something deeper or more important. Like the fabled exceptions that prove the rule, knowing where a general rule does not work is sometimes an incredibly useful discovery.
brasetvik 6y ago
I'm sure a certain Joseph Fourier was asked that question too, quite some time ago. :)
deleted 6y ago
[deleted]
doublesCs 6y ago
Often we don't know the "practical" benefits that will come out of some specific line of investigation. But some people find it interesting to think about. I guess better than spending time playing with facebook.

Kranar 6y ago

It's a fair question mostly because of how effective math has been at solving practical problems, but honestly working on problems like these is usually due to a genuine appreciation and enjoyment of mathematics. I'd even say the majority of mathematicians study math strictly out of a sense of wonder and curiosity rather than towards a commercial application and that the vast majority of math research is not at all practical. The cost is justified due to a common shared interest in the subject, many other people are interested in math and pay people to work on it. It's not all that different than paying someone for music, or a painting, or to write a work of fiction. People get a profound sense of enjoyment and happiness from this work and are happy to pay the cost for the continued advancement of this field.

marcianx 6y ago

The article touches on this with: > k = x³ + y³ + z³ is what number theorists call a Diophantine equation — a kind of algebraic structure whose properties have fascinated mathematicians for millennia. “They’re rich enough to encode [other mathematical] statements that have nothing to do with Diophantine equations,” said Browning. “They’re rich enough to simulate computers.” More specifically, equations of such form come up in a proof of Godel's first incompleteness theorem. That being said, yeah, this effort is mostly a mathematical curiosity, mapping out the domain of knowledge of mathematics increasingly more completely. Sometimes an application comes about where either the solution or novel techniques used to arrive to the solution can become useful, but pure math research isn't typically driven by any existing applications as much as a "because it's there" attitude.

redis_mlc 6y ago

> Excuse me for being a bit of a moron here It's beyond being a moron - you're acting like a caveman. Math is the language of logic and science, and allows the world to express how everything works. Once a problem is solved mathematically, that can be used as a tool forever. You should be asking why HN has a weekly UFO post, or what will be accomplished in killing people by sending them on a one-way trip to Mars. The fact that you don't understand an enormous field like math should make you respect the people who can even more.

evgen 6y ago

Sometimes these weird questions can lead to more practical applications down the road, e.g. once we know how to do something it gets added to the toolbox and eventually used, somewhat like how Euler's totient was a cute mathemtatical curiosity until it became one of the important steps in RSA key generation and a very useful tool almost two centuries after it was discovered. It is also the case that sometimes knowing where the 'holes' are in these sort of stepwise math series' can itself reveal something deeper or more important. Like the fabled exceptions that prove the rule, knowing where a general rule does not work is sometimes an incredibly useful discovery.

brasetvik 6y ago

I'm sure a certain Joseph Fourier was asked that question too, quite some time ago. :)

deleted 6y ago

[deleted]

doublesCs 6y ago

Often we don't know the "practical" benefits that will come out of some specific line of investigation. But some people find it interesting to think about. I guess better than spending time playing with facebook.