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Roots of Unity

## Extrapolation Gone Wrong: the Case of the Fermat Primes

Samuel Arbesman recently wrote about incorrect mathematical conjectures. I wanted to add one of my favorites, which came up in my math history class a couple weeks ago. Unlike the disproven conjectures Arbesman wrote about, which fail only for very large numbers, this one fails at 5. Pierre de Fermat was an amateur number theorist [...]

Roots of Unity

## Really Big Numbers (Book Review)

“Now and then we pluck numbers from the blur…numbers which have no names except the ones we might now give them…souvenirs from alien, unknowable worlds.” -Really Big Numbers by Richard Evan Schwartz Really Big Numbers by Richard Schwartz, a mathematician at Brown University, is the first children’s book published by the American Mathematical Society. (Disclosure: [...]

Roots of Unity

## Graham’s Number Is Too Big for Me to Tell You How Big It Is

I was going to write an April Fool’s Day post with the title “Mathematicians Declare Graham’s Number Equal to Infinity.” Graham’s number is really big, but of course, it’s precisely 0% as big as infinity. On the other hand, everything we touch is finite, so in some sense, Graham’s number is probably “close enough” to [...]

Roots of Unity

## We Only Need to Fill Out 425 Brackets Each to Win Buffett’s Billion

Warren Buffett’s Bracket Challenge* has put even more of a spotlight than usual on March Madness, the annual NCAA basketball tournament. Buffett has offered a billion dollars to anyone who correctly predicts the outcome of all 63 games in the tournament. There are 2 possible outcomes of every game and therefore 263— 9,223,372,036,854,775,808, or about [...]

Roots of Unity

## A Different Pi for Pi Day

The symbol π is overloaded in math: depending on context and capitalization, π could be the constant we all know and love (or hate), a projection, a product, or a function. There’s plenty of stuff to read about the circle constant, so today I’m writing about one of those other π’s. Today’s π is the [...]

Roots of Unity

## Has Anyone Ever Flipped Heads 76 Times in a Row?

Tom Stoppard’s absurdist play Rosencrantz and Guildenstern Are Dead begins with one of them, Guildenstern (or is it Rosencrantz?), flipping coins. “Heads,” Rosencrantz says, and takes the coin. Guildenstern flips again. “Heads,” Rosencrantz says, and takes the coin. Another flip. “Heads.” Again, “Heads.” Soon we find out that Guildenstern has flipped 76 coins, and all [...]

Roots of Unity

## Goldbach Variations

On Monday, Harald Helfgott of the École Normale Supériure in Paris posted a proof of one of the oldest open problems in number theory to the preprint repository arxiv. The ternary Goldbach conjecture, like so many questions in number theory, is easy to state but hard to prove. Every odd number greater than 5 can [...]

Roots of Unity

## Big Numbers Are Big

Today I have a piece in Slate about that pi meme that’s been going around. According to the meme, your life story is encoded in pi somewhere. My life story would probably include the word “Evelyn” at some point. (I’m going out on a limb, but stay with me.) In a code that assigns the [...]

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