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Mohammed S. Al Sahaf
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Mohammed S. Al Sahaf

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In today's unfortunate news we have...

#mathematics #gametheory #economics
Nash was in Norway on Tuesday to receive the Abel Prize for mathematics from King Harald V for his work, along with longtime colleague Louis Nirenberg, on nonlinear partial differential equations.
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Sad news indeed
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I caught that last 20 minutes of the movie on TV and I liked it, so I googled him and found this article that gives a nice summary and perspective.

#politics #history
The story of the stuttering sovereign: the epic events that inspired the Oscar-tipped film, 'The King’s Speech’.
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Drink and Feel Not Guilty

#sciencesunday #coffee
A review of studies shows that coffee’s reputation as being unhealthy is undeserved, with the potential health benefits surprisingly large.
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"Teaching people how to fish, giving them fishing nets, and giving them the fish too."

#poverty #aid  
A new study finds that aid and training do the trick.
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+Mohammed S. Al Sahaf Hey! Glad you're doing well. Just thought I'd check in to talk to you since you have me in your circles for some reason. I'm doing okay, but I've been getting a little worked up because of people's responses to my beliefs about cats. What do you think about cats?
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Summary:OPINION: A new report by RAND commissioned by Juniper Networks has some eyebrow-raising conclusions about the black market for hacks, cracks, data theft, botnets, and zero days.
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Stephen Fry Uncovering the Hidden Secrets of the City of London

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"The Islamic State (IS) group says it was behind a suicide bombing on a Shia mosque in Saudi Arabia that killed at least 21 people.
The attack in Saudi Arabia's Eastern Province is the first to be claimed by the Saudi branch of IS, which was formally established last November."
The Islamic State group says it was behind a deadly suicide bombing on a Shia mosque in Saudi Arabia, apparently its first attack in the kingdom.
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The Story of John Nash
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"We found measles predisposes children to all other infectious diseases for up to a few years," Mina says.

When the U.S. introduced the measles vaccine, childhood deaths from all infections plummeted. Scientists think they might know why: Benefits of the measles vaccine go way beyond the measles.
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Why is this true?

The spooky-smart mathematician Srinivasa Ramanujan came up with this formula around 1913.  Why is it true?

I don't know, let's see...

In 1735, a young fellow named Euler stunned the world by cracking a famous puzzle that had been unsolved for almost a century: the Basel problem.  The problem was to sum the reciprocals of perfect squares:

1/1² + 1/2² + 1/3² + 1/4² + 1/5² ... = ???

Euler showed that the answer was π²/6:

1/1² + 1/2² + 1/3² + 1/4² + 1/5² ... = π²/6

He also showed you could rewrite this sum as a product over primes:

1/1² + 1/2² + 1/3² + 1/4² + 1/5² ... =

(2²/(2² - 1)) (3²/(3² - 1)) (5²/(5² - 1)) (7²/(7² - 1)) ...

That's actually the easy part: it's a cute trick called the Euler product formula.

So we know

(2²/(2² - 1)) (3²/(3² - 1)) (5²/(5² - 1)) (7²/(7² - 1)) ... = π²/6

If you think about it, Ramanujan's formula is saying that

(2²/(2² + 1)) (3²/(3² + 1)) (5²/(5² + 1)) (7²/(7² + 1)) ...

is 2/5 as big.  So, proving it is the same as showing

(2²/(2² + 1)) (3²/(3² + 1)) (5²/(5² + 1)) (7²/(7² + 1)) ... = π²/15

Maybe the next step is to use the same idea as the Euler product formula.  I think this gives

(2²/(2² + 1)) (3²/(3² + 1)) (5²/(5² + 1)) (7²/(7² + 1)) ... =
1/1² - 1/2² - 1/3² + 1/4² + 1/5² - 1/6² + 1/7² + ...

where the signs at right follow a fancy pattern: we get 1/n² whenever n is the product of an even number of primes, and -1/n² when n is the product of an odd number of primes.  For example, 4 = 2 x 2 is the product of an even number of primes, so we get 1/4².

So I'm left wanting to know why this strange sum

1/1² - 1/2² - 1/3² + 1/4² + 1/5² - 1/6² + 1/7² + ...

equals π²/15.  Ramanujan, dead since 1920, is still messing with my mind! 

The formula is supposed to be in here:

• Srinivasa Ramanujan, Modular equations and approximations to π, Quart. J. Pure. Appl. Math. 45 (1913-1914), 350-372.  Also available at ://

But I don't see it!

Here you can see how Euler solved the Basel problem:

It's a great example of his brilliant tactics, many of which were far from rigorous by today's standards... but can be made rigorous.

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Honey Bunches of Lies

They stagger into Andrew Murphy’s office itchy, sneezing, and watery-eyed. This, in itself, is unremarkable. As an allergist in Pennsylvania, Murphy regularly treats patients suffering from seasonal allergies. But when Murphy starts to explain to these patients the standard options for treatment—oral anti-histamines, nasal steroids, or immunotherapy—they want none of...
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The Machine That Made Us is a documentary in which Stephen Fry examines the story behind the first media entrepreneur, printing press inventor Johann Gutenberg, to find out why he did it and how, a story which involves both historical inquiry and hands-on craft and technology.
Fry travels across Europe to find out how Gutenberg kept his development work secret, about the role of avaricious investors and unscrupulous competitors and why Gutenberg's approach started a cultural revolution. He then sets about building a copy of Gutenberg's press.

#fryday   #Gutenberg  
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