Riemann Hypothesis Day

[MW1990]

Argh, I know I am late, but, I would like to make it known that yesterday was Riemann Hypothesis day! :-D Yesterday was the 150th anniversary (technically he submitted his findings on October 19, 1859, but was celebrated worldwide on November 18) of one of the biggest and most important problems in number theory being posed by the great Bernhard Riemann. Just a little background, the conjecture basically deals with the distribution of the zeros of the Riemann-zeta function along it's critical line, which offers some implications on the distribution of prime numbers.

Also, Dr. Terence Tao has some great lectures on youtube on "The Structure and Randomness in the Prime Numbers," "Nilsequences and the Primes," and "Compressed Sensing."

Many a mathematician have tried to prove this conjecture (Hardy amongst them), but to no avail yet. In difficulty, it is somewhere in the general area of three times more difficult than Fermat's Last Theorem, and the same magnitude of difficulty or so with the 4 color problem. It is of such importance and difficulty, it has been listed as one of the seven problems posted by the Clay Mathematics Institute, in which each correct solution offeres a reward of $1,000,000 (and possibly a fields medal, which, the man who proved the Poincare conjecture turned it and the money down).

The seven Millenium Problems:
-Riemann Hypothesis
-Birch and Swinnerton-Dyer Conjecture
-Hodge Conjecture
-Navier-Stokes Equation
-P vs NP
-Poincaré Conjecture(proven)
-Yang-Mills Theory

anyway...I just wanted to share some mathematic news with everyone, so... enjoy!!

-Aric

 

[qqwref]

Interesting holiday. I know the Riemann Hypothesis is a pretty important thing, although it seems pretty abstract to me so I'm not sure how it would actually be applied to any other proof(s). (But hey, I'm not a mathematician, just a math enthusiast )

In difficulty, it is somewhere in the general area of three times more difficult than Fermat's Last Theorem, and the same magnitude of difficulty or so with the 4 color problem.

Wait, what? I'm not sure difficulty of proof is an easily measurable quantity.

It is of such importance and difficulty, it has been listed as one of the seven problems posted by the Clay Mathematics Institute, in which each correct solution offeres a reward of $1,000,000

Yes, but I think this is a matter of importance more of difficulty. Prizes wouldn't be offered at all if the problems weren't difficult (since they'd be already solved if they were easy, right?) but I think the reason they were chosen is because each of the problems given has a lot of importance in some field(s). Knowing for sure whether the Riemann Hypothesis was true or not would mean that quite a few interesting results are immediately verified.

 

[MW1990]

That difficulty thing I mentioned, was in a series of lectures: http://www.math.auckland.ac.nz/wiki/RHD I used difficulty and complexity as being the same thing (which is not generally true), my apologies

-For the importance thing: the implication was that they are of such importance in the field of number theory, general mathematics, and some applied mathematics, they were given that amount of precedence over many other problems in mathematics.

Also,the first 1,500,000,000 values have been checked, but, as in almost everything in mathematics, it must hold true for (at least, in this case) all values

 

[gylve]

I used to study a lot about RH, since its the millenium problem that has the most accessible mathematics.

Well about check values is really a waste since already has been proved that the critical line contains an infinite number of zeros.

Also i think someone proved that at least 40% of the zeros lies in the critical line.

 

[Ron]

Why is RH so important?
I read the wikipedia page and it sounds pretty boring.

 

[Swoncen]

I used to work on P != NP but it is very time consuming and after some time you see why it is not solved yet. Very difficult!

 

[qqwref]

Why is RH so important?
I read the wikipedia page and it sounds pretty boring.

It has many more applications than it appears at first! I have heard of many cases where smaller theorems have been proved by essentially assuming RH is true at the start :rolleyes: Of course, they don't know it's true yet, but the point is that if it is ever proved a lot of results will immediately follow. It's kind of like finding tons of algorithms for a step before anyone has thought of a method that uses it, but that's the way mathematics operates sometimes