That probably doesn't help me.

The Riemann hypothesis has implications involving the distribution of prime numbers, but it is not a theorem ABOUT the distribution of prime numbers, it is a theorem concerning the complex zeroes of the Riemann zeta function, so while it does involve numbers, it is not really a theorem about numbers, it's a theorem about a particular function.

I didn't say it was THE central problem, if only because there is no such thing as THE central problem in any field, and never will be.

And despite the fact that there are many theorems that are called 'The Fundamental Theorem of...', there is really no such thing as a 'fundamental theorem', calling a theorem 'the fundamental theorem' is all hype, the especially ironic thing is how misnamed these 'fundamental theorems' are, the fundamental theorem of algebra isn't even a theorem about algebra, it's a theorem about Complex Analysis, the fundamental theorem of arithmetic is actually more of a theorem about algebra etc, and neither the fundamental theorem of Calculus nor the fundamental theorem of Galois theory have ever seemed all that 'fundamental' to me.

Aristotle, who didn't know any better, defined mathematics as the science of numbers, but this is definitely not true. I would define mathematics as the science of recognizing patterns. Every theorem can be reduced to the statement 'there is a pattern that I have recognized, and now I can prove that this pattern always holds.'

But it's the science of recognizing certain kinds of patterns. For instance, physics also concerns patterns - but physical patterns. Mathematics concerns mathematical patterns. I think defining it as "science of quantity" (which is actually how Aristotle defines it - and quantity is distinct from number for Aristotle) is fine if quantity is understood properly. Maybe that's because I work in a so-called concrete discipline within mathematics, though, since I'm a complex analyst (as opposed to an algebraist, a topologist, a geometer, or a functional analyst).

Ummm...that is completely circular, no pun intended.

Before about the middle of the 20th century, Physics was always considered a branch of mathematics, you may it concerns 'physical patterns' but all those patterns can be described mathematically, with equations. Now, many physics equations, Maxwell's equations or the Schrodinger equation, are quite beautiful and concern some insanely complicated mathematics. And I'm not even talking about stuff like Hermann Weyl's use of tensor analysis to describe relativity theory, which Einstein, with a great deal of exaggeration that many people misunderstand and take too literally said that 'I no longer understand my own theory' when it was written using Tensor analysis. So, you can't really draw the distinction between math on the one hand and physics on the other, they work together or not at all.

When I was in graduate school, I had a whiteboard in my office, a small one that I put on the wall for my use, and whenever I didn't have anything to do, I would write the Schrodinger equation on it or Maxwell's equations, and people would come by, undergraduates mostly, and say 'wow, those are some beautiful equations, is that what you do?' and I would just kind of laugh, not really affirming or denying their assumptions. Of course, I'm an algebraist, and Schrodinger's equation is a partial differential equation, so it is NOTHING like what I do, but I've always thought it was a beautiful equation, and so I left it up there for aesthetics even though it had nothing to do with my own research.

Okay, two questions -

How does solving this equation(whatever in the world it is) make the world a better place?

And this one - how will those to whom the "proof" is presented know that it is true? I mean, if they would have the ability to know that it is true, then they should have already solved it. For all they know, he could be blowing hot air in their ears and they wouldn't know the difference.

It's the same as with any other logical argument. If the premises are valid and each step of the proof follows from the premises and from all preceding steps, then the proof is valid. It's a lot easier to verify that this is the case than it is to come up with the right steps in the first place.

As for the first question, is not a demonstration of the reasoning power of the human mind a beautiful thing?

Art is beautiful, in the eye of the beholder.

At the risk of being labeled "Jerk of the Week" - a more beautiful thing would be to spend one's time helping another human being in a tangible way. I tend to look at things like this "Oh, looooooook at me. I solved this riddle" as a kind of thing with a tinge of sinful pride. I'm more impressed by people who spend their hours in front of an abortion clinic or in a soup line.....but that's just me.

I respectfully disagree with you on this point. A preoccupation with "useful" knowledge is not a sign of a healthy culture.

I've seen mathematics defined variously as a "science of measurement" (which I guess corresponds roughly to "science of quantity") and "science of relations" which is probably more how I view it (with the caveat that I'm not a mathematician and haven't been in the field since earning my B.S. nearly 25 years ago).

Can you explain, please (not that I disagree with you)


If all the people in the world ever thought this way and never wanted to concern themselves with what appears to be dry abstract knowledge, then the internet would never exist

Did you mean to say " A preoccupation with "useful" knowledge is not a sign of a healthy culture."

No, he didn't.

Okay, then I am misunderstanding what is meant by "useful" knowledge.

What is your understanding of "useful" knowledge?

I thought Father was referring to the preoccupation with mathematics as spoken of in the OP.

A society that only values useful ideas and knowledge is likely to be a society that values only useful people. Ironically, those people picketing the abortion clinic are more likely to value "useless" ideas than the people inside are.

Interesting.

You know, that is one of the criticisms that is leveled at pro-life demonstrators by those who are pro-choice, that we only care about the baby until it is born, and then we abandon the mother and the child. In other words, we value "useless ideas" such as being against abortion, but do not value people themselves by rolling up our sleeves and helping them. This isn't totally true, of course, but they do have a point when Republicans in Congress constantly vote for things which are harmful to the elderly, the poor, and those with serious life-issue problems.

That's not my point. Knowledge of the truth, is, all on its own, regardless of any practical applicability, a good thing and therefore can be pursued for its own sake. There is more danger, oddly enough, with practical knowledge which could easily be turned to bad ends (e.g., some forms of medical research) than there is with purely theoretical knowledge such as the Reimann Hypothesis.

How does you posting on the Internet make the world a better place? How does asking this inane question make the world a better place? If 'making the world a better place' is supposed to be our sole motivation for doing anything, then you, I and everyone else is going to have to lead completely different lives, aren't we? I mean, did you eat dinner last night? How can you possibly justify that when there are so many starving?

I tend to agree with your position, but it's problematic, because the question is precisely of which relations is it the science? For instance, it's not the science of the Trinitarian relations.