Read this book.
Or you can just solve one of these math problems.
The distribution of such prime numbers among all natural numbers does not follow any regular pattern, however the German mathematician G.F.B. Riemann (1826 – 1866) observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function
ζ(s) = 1 + 1/2s + 1/3s + 1/4s + …
called the Riemann Zeta function. The Riemann hypothesis asserts that all interesting solutions of the equation
ζ(s) = 0
lie on a certain vertical straight line. This has been checked for the first 1,500,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers.
Or if you saved a penny every hour, it would take you 11415 years to hit a million dollars.
Unfortunately, this is not a blog entry on course 18.
So this week, LSC sponsored a book talk by the authors of Bringing Down the House by Ben Mezrich.
It was the beginning of the book tour for his latest, Busting Vegas, that he wrote with Semyon Dukach about “Dukach’s incredible adventures as the Darling of Vegas – a gambling wunderkind who ransacked the most famous casinos across the globe with his unheard of system.”
10-250 (Home of 3.091) was PACKED.
This is Donald Sadoway. He teaches 3.091 in the fall. He is probably the most stylish professor I’ve had in my life. Not to mention his academic regalia has a three-cornered hat.
Now I’m not a poker player even though given where I’m from, I probably should be.
So anyone who’s daring enough to teach an old dog a new trick, I’m sure I can teach you my favorite card game in exchange.
I somehow remember learning in 18.022 (Intro to Hartley Rogers) that the Riemann Zeta hypothesis was voted the most beautiful mathematical problem of the millenium, or something like that. Just throwing that out there.
But, of course, its beauty is far eclipsed by the pictures of Mitra you have in your previous entry.
I thought the Reimann function came in second, with Euler’s coming in first for expressing so many fundamental mathematical concepts in one equation.
However, if you want beautiful equations, you just have to become a physicist.
*oooh* I just went there. :D
Well, I had a really long comment ready and firefox crashed so this one will be a bit shorter
Is the riemann hypothesis not fascinating? for anyone intrested in a very…on the surface introduction: http://en.wikipedia.org/wiki/Riemann_hypothesis
its one of those things that …is just incredibly beautiful and is what draws me to number theory. As the mathematician Paul Erdos would say “That one is in the book” (The book was something he referred to as a book where god kept the most beautiful of mathematical proofs, while this obviously isnt a proof but a conjecture that has sparked 300 years of searching for a proof…its still equally amazing http://en.wikipedia.org/w/index.php?title=Mathematical_fetishism&redirect=no
*whistle*) however unfourtanetly this is something I have to put on my, shelf until I have more advanced mathematical education/tools list, heh, I have fooled around a bit with a formula I found for even values of s of sigma starting at 1 continuing to infinity….1/n^s (the non complex part of the zeta function) but at this point the mathematics neccesary to prove the Riemann Hypothesis are so far beyond my level of knowledge (Well its of course possible there is a completely intuitive and logical proof, but…eh) I suppose you could tell I want to be a Course 18 major at this point, sorry if I am rambling on here, I get a bit excited when I talk about math. I am trying to find a word for Professor Sadaway, it seems like I have seen that picture before somewhere of course thats fairly unlikely…oh well. Again I apologize for the rambling, and poor sentence structure (Math gets me that way).
Well, eulers formula is definetly an incredibly beautiful formula with a wonderfully simplistic proof (E^(i(x))=cos x + i (sin x) just use the taylor series expansions for a proof…I cant really type it in here, but the basic idea is writing e^x as 1+x+x^2/2!+x^3/3!… and do the equivalent for sin x and cos x [taylor series expansions] so then you write e^ix which would of course be 1+ix+ix^2/2!+ix^3/3!…and if you recall i^0 = 1 i^1=i i^2=-1 i^3=-i etc etc etc you can simplify and you would end up with 1+ix-x^2/2!-ix^3/3!+x^4/4!+ix^5/5!-z^6/6!… so then you just group terms so the odd exponents are together, and the evens are together, then you factor the i out of the odds and substitute sin x and cos x for the taylor series expansions and you are left with e^ix=cos x + i sin x well this is how I like to think of it I suppose you could also do it with calculus [dont worry I wont type it!] but I think when dealing with mathematical proofs the simpler and more elegant the better) and of course a side effect is e^i(pi)=-1 (some people write it as ) e^(i(pi))+1=0 (To link 5 fundamental constants) and it to me is definetly one of the most beautiful things in mathematics, however it is not a problem it was offered by Euler with proof when he discovered it, so I think we can call the Riemann Hypothesis the most beautiful problem, with Eulers Formula being the most beautiful identity, or general mathematical concept. Ugh I know about becoming a physicist! I am really intrested in physics…but im more …mathematics is just…wonderful to me if numbers are not beautiful nothing is. Physics really intrests me though, I am considering maybe a dual major in Mathematics and Physics. Or even if I dont go for a second major in physics I will certainlly take some courses. Mathematics is just more appealing to me now.
Again I am sorry for poor sentence structure, I have difficulty forming “proper” sentences when speaking of things like this my brain is just buzzing.
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