Number Theory & Mysticism Part 2

So, like, what's your main point?

No point - I just posted it for those with interest such as the guest in part1 and Roger Pink's request (from his Golden Ratio blog) - unless he was kidding.

Hi S,

Since we're talking prime numbers, you may be interested in this excerpt concerning the Riemann Hypothesis:

"The Riemann hypothesis is a highly complex theory about the nature of prime numbers - those numbers divisible only by 1 and themselves - that has stymied mathematicians since 1859. In that year, Bernhard Riemann published a conjecture about how prime numbers were distributed among other numbers. He labored over his own theory until his death in 1866, but was ultimately unable to prove it.

The problem attracted a cult following among mathematicians, but after nearly 150 years no one has ever definitively proven Riemann's theory to be either true or false. Although a definitive solution would not have any immediate industrial application, in 2001 the Clay Mathematics Institute in Cambridge, Mass., offered a $1 million purse to whomever proves it first."

Well now a credible mathematician, proffessor Louis De Branges, says he has solved the Riemann Hypothesis and could very well be in line for the $1M prize. Read more about it here.

-John

Hi JJ,

Interesting. I'm not usually game to solve such things, but for a million $, I may look into it. ca-ching, ca-ching!

$S$

On the contrary, if you had a way of determining whether a number was prime or not, you would either be rich beyond your imagination or dead.

Almost all serious encryption schemes are based on the idea that one cannot tell whether a number is prime without factoring it. If the number selected is really REALLY big, it would take you your entire life to factor it, perhaps, even longer! If you could easily determine whether the number was prime, you'd be able to crack every bank transaction, every government coded message, every encryption scheme in the World! That would make you a very dangerous person!!!

Looks like de Branges may have second thoughts here.

Hi JJ,

No, it looks like he is apologizing for the way he proved it. In your link:

http://www.math.purdue.edu/~branges/apology.pdf

he says in the first paragraph:

"Good writing about mathematics is difficult because the expected reader knows either too much or too little. Those with graduate experience are biased by the choice of a specialty. Those without graduate experience exist in a state of ignorance."

I have only read 3 pages, but after all 39, I will still be too ignorant to understand his proof. The last paragraph starts with:

"The Riemann hypothesis is proved for a Dirichlet zeta function by constructing a Hecke zeta function whose zeros contain the zeros of the Dirichlet zeta function."

This article is an excellent short history of mathematical progress. Thanks for the link.

S

In the above link, on page 3 is says:

"Momentum is introduced as a concept which permeates subsequent treatment of motion. Momentum resembles position since it lies in a space isomorphic to Cartesian space. Momentum is observable by its action on position. The motion of a particle is formulated as a voyage in time through a phase space which is composed of Cartesian space and momentum space."

Can someone tell me what he is saying? What is 'phase space' and what is 'momentum space'?

This might sound like knit-picking but, isn't 2 a prime number?

Hi Troy,

You are right, 2 is a prime, and 1 is not. I must have made a typo. A prime has exactly two distinct natural number divisors: 1 and itself.

Thanks for being picky

S