Don't Think Riemann Hypothesis Is Right Successor To Fermat.

David Sklansky · #1 07-22-2005, 02:01 AM

As far as I'm concerned, an unsolved math problem cannot have widespread appeal unless the general population can understand what is unsolved. Fermat's Theorem and the Four Color problem fit that bill perfectly. Riemann doesn't come close. So (in spite of its importance) I don't know why mathmeticans are building it up as much as they do. I don't think they realize that the question isn't getting much of a following from the masses.

There are hundreds of unsolved number theory problems that everyone can understand. However they don't have history attached to them. An exception is Goldbachs Conjecture. But it has the problem that to an average person, it is self evident, even if there is no proof. Once you get past the first several dozen even numbers it seems inconceivable that you will find one that isn't the sum of two primes.

Thus I am suggesting that the mathematical community shift its focus away from Riemann (when trying to get regular people interested in math by invoking something yet unsolved) and instead start talking about the other well known problem that almost everyone can understand (and wonder why it hasn't been solved.) I am speaking of course about the Twin Prime Conjecture.

ihardlyknowher · #2 07-22-2005, 03:19 AM

I must disagree here. I did my senior math project on a proof that the sum of twin prime pairs converges. Then went to law school. To make a long story short, my project was on my resume and I had to try to explain it to many prospective employers (who were all very bright). I have never seen eyes glaze over faster. This is not the way to get everyone interested in theoretical mathematics.

David Sklansky · #3 07-22-2005, 03:23 AM

Are we talking about the same thing? Is there or isn't there an end to twin primes. Like there isn't for single primes. I'm not expecting people to understand the answer. Just the question.

ihardlyknowher · #4 07-22-2005, 03:29 AM

If the sum of twin primes converges, it suggests that they may only be a finite # of them, but obviously not necessarily as many infinite series converge. At the time I studied this (8 years ago), that was the most developed literature on this problem.

In any event, not one intelligent partner at many prestigious law firms had any interest in the answer or the question. Even the one who developed the futility index for measuring the failure of major league sports' teams to win a championship (which has its foundation in probability theory).

David Sklansky · #5 07-22-2005, 03:55 AM

"In any event, not one intelligent partner at many prestigious law firms had any interest in the answer or the question."

And they would have been even less interest in the Riemann conjecture. But they also wouldn't care about Fermat except that it was hyped. I'm simply saying that with Fermat and Four Color gone, this is the one to tell the populace about if you want to get any interest at all.

ihardlyknowher · #6 07-22-2005, 04:04 AM

"And they would have been even less interest in the Riemann conjecture."

You are most certainly correct here.

Why do we want to get the populace interested in these problems anyway?

BruceZ · #7 07-22-2005, 07:32 AM

[ QUOTE ]
If the sum of twin primes converges, it suggests that they may only be a finite # of them, but obviously not necessarily as many infinite series converge.

[/ QUOTE ]

Of course no infinite series of positive integers can converge. If the sum of twin primes were known to converge, then it would be known that there are a finite number of them. What is known to converge is the sum of reciprocals of the twin primes (1/3 + 1/5) + (1/5 + 1/7) + (1/11 + 1/13) + ..., and this suggests a relative "scarcity" of twin primes. The sum of the reciprocals of all primes does not converge.

jason_t · #8 07-22-2005, 08:54 AM

[ QUOTE ]
As far as I'm concerned, an unsolved math problem cannot have widespread appeal unless the general population can understand what is unsolved. Fermat's Theorem and the Four Color problem fit that bill perfectly. Riemann doesn't come close. So (in spite of its importance) I don't know why mathmeticans are building it up as much as they do. I don't think they realize that the question isn't getting much of a following from the masses.

There are hundreds of unsolved number theory problems that everyone can understand. However they don't have history attached to them. An exception is Goldbachs Conjecture. But it has the problem that to an average person, it is self evident, even if there is no proof. Once you get past the first several dozen even numbers it seems inconceivable that you will find one that isn't the sum of two primes.

Thus I am suggesting that the mathematical community shift its focus away from Riemann (when trying to get regular people interested in math by invoking something yet unsolved) and instead start talking about the other well known problem that almost everyone can understand (and wonder why it hasn't been solved.) I am speaking of course about the Twin Prime Conjecture.

[/ QUOTE ]

David,

There is a treemendous amount of romance and history surrounding the Riemann hypothesis and the public seems to be taking it quite well as in the past couple of years there have been two popular books on the subject (one that was very successful) and approximately a half-dozen articles in the NY Times. I seem to recall hearing about a NOVA special on it too.

Jason.

ihardlyknowher · #9 07-22-2005, 02:29 PM

[ QUOTE ]
[ QUOTE ]
If the sum of twin primes converges, it suggests that they may only be a finite # of them, but obviously not necessarily as many infinite series converge.

[/ QUOTE ]

Of course no infinite series of positive integers can converge. If the sum of twin primes were known to converge, then it would be known that there are a finite number of them. What is known to converge is the sum of reciprocals of the twin primes (1/3 + 1/5) + (1/5 + 1/7) + (1/11 + 1/13) + ..., and this suggests a relative "scarcity" of twin primes. The sum of the reciprocals of all primes does not converge.

[/ QUOTE ]

Right, I forgot the reciprocal part. It has been a while.

West · #10 07-22-2005, 03:00 PM

[ QUOTE ]
Are we talking about the same thing? Is there or isn't there an end to twin primes. Like there isn't for single primes. I'm not expecting people to understand the answer. Just the question.

[/ QUOTE ]

Speaking as a member of the general populace - I was going to ask what a twin prime was, but then I decided I'd look it up. Ok, so it's a pair of prime numbers that differ by two, like 5 and 7. So without trying to be a smart ass at all, is there any reason outside of mathematical curiosity that anyone would really care whether there is an end to twin primes?