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Posts Tagged "prime numbers"

Roots of Unity

Extrapolation Gone Wrong: the Case of the Fermat Primes

Sorry, Pierre, but not all Fermat numbers are primes. Image: Public domain, via Wikimedia Commons.

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 [...]

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Roots of Unity

In Praise of Proofs by Contradiction that Aren’t

Opposing arrows, a common conclusion to a proof by contradiction.

If you don’t know what to do, do something. That’s one of my mottos when I teach math (and it’s probably good life advice too). Last year, I taught introductory analysis (basically calculus with the juicy bits left in), one of the first proof-oriented classes students take. Writing proofs is hard, and sometimes the hardest [...]

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Roots of Unity

A Different Pi for Pi Day

Nope, not this kind of pi(e). Image: flickr/djwtwo

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 [...]

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Roots of Unity

Carnival of Mathematics #103

Image: David Simmonds, via flickr.

Welcome to the 103rd Carnival of Mathematics! The number 103 is prime, and it’s the “older” twin of a pair of twin primes as well—or is it the “younger” twin because it comes later? Regardless, 101 and 103 are twin primes. According to Tanya Khovanova’s site Number Gossip, 103 is not only prime and happy [...]

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Roots of Unity

What Is the Funniest Number?

A triangle, heptagon, and 42-sided polygon meet at a vertex. Image: Dllu, via Wikimedia Commons

“There was only one catch and that was Catch-22, which specified that a concern for one’s own safety in the face of dangers that were real and immediate was the process of a rational mind. Orr was crazy and could be grounded. All he had to do was ask; and as soon as he did, [...]

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Roots of Unity

Introducing the Blog on Math Blogs

twin_primes_ulam_spiral1

I’m pleased to introduce a new American Mathematical Society blog: the Blog on Math Blogs! Over there, my co-editor Brie Finegold and I are featuring posts from around the math blogosphere to help you keep up with math news and find new math blogs to follow. We’ve been around for about two months now, and [...]

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Roots of Unity

Goldbach Variations

A letter from Christian Goldbach to Leonhard Euler

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 [...]

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