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23 posts tagged with numbers *and* mathematics.

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## HoTT Coq

Univalent Foundations Redefines Mathematics - "When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the century-old rules underlying all of mathematics." (previously) [more inside]

## 3Blue1Brown: Reminding the world that math makes sense

Understanding e to the pi i - "An intuitive explanation as to why e to the pi i equals -1 without a hint of calculus. This is not your usual Taylor series nonsense." (via via; reddit; previously) [more inside]

## binding the andat

Closing in on the twin prime conjecture (Quanta) - "Just months after Zhang announced his result, Maynard has presented an independent proof that pushes the gap down to 600. A new Polymath project is in the planning stages, to try to combine the collaboration's techniques with Maynard's approach to push this bound even lower." [more inside]

## Proof and Community Standards

In August of last year, mathematician Shinichi Mochizuki reported that he had solved one of the great puzzles of number theory: the ABC conjecture (previously on Metafilter). Almost a year later, no one else knows whether he has succeeded. No one can understand his proof.

## Computerized Math, Formal Proofs and Alternative Logic

Using computer systems for doing mathematical proofs - "With the proliferation of computer-assisted proofs that are all but impossible to check by hand, Hales thinks computers must become the judge." [more inside]

## the power and beauty of mathematics

## Numberphile: videos about numbers and stuff

Numberphile is a website containing short videos (approx. 5-10 min.) about numbers and stuff. Mathematicians and physicists play around with the tools of their trade and explain things in simple, clear language. Learn things you didn't know you were interested in! Find out why 493-7775 is a pretty cool phone number! What's the significance of 42, anyway? What the heck is a vampire number? Why does Pac-Man have only 255 screens?
Suitable for viewing by everyone from intelligent and curious middle-schoolers to math-impaired adults. Browse their YouTube channel here. (Via)

## What is the smallest prime?

What is the smallest prime? "It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first prime, we must also know what the first positive integer is. Surprisingly, with the definitions used at various times throughout history, one was often not the first positive integer (some started with two, and a few with three). In this article, we survey the history of the primality of one, from the ancient Greeks to modern times. We will discuss some of the reasons definitions changed, and provide several examples. We will also discuss the last significant mathematicians to list the number one as prime."

## Finite formula found for partition numbers

New math theories reveal the nature of numbers [1,2] - "We prove that partition numbers are 'fractal' for every prime. These numbers, in a way we make precise, are self-similar in a shocking way. Our 'zooming' procedure resolves several open conjectures, and it will change how mathematicians study partitions." (/.|via) [more inside]

## Prime numbers are just the beginning.

Every number from 1 to 9,999 has a special meaning. (much mathematical terminology, scrolling)

## Very large numbers

The Shannon number? Skewes' number? Graham's number? Please. When you're ready to get serious, here are some truly large numbers. (previously, but with dead links)

## 3D Mapping

Durango Bill's Home Page. With topics that include: 3D end-to-end tour of the Grand Canyon, the origin and formation of the Colorado River, and examples of river systems that cut through mountain ranges instead of taking easier routes around them in Ancestral Rivers of the World. [more inside]

## The H&FJ Institute for Unapplied Mathematics

Joe Palca, a science correspondent for NPR's Morning Edition, was meditating on the best way to convey the magnitude of the world's largest known prime number, 2

^{43112609}-1. He contacted H&FJ at Typography.com to discuss the implications of typesetting a number with more than twelve million digits. Crunching of numbers and fonts ensued.## Operation Kaprekar

Mysterious number 6174. An excellent recreational math article.

## It's all a numbers game...

## Lost and Found

Not Lost After All Given recent posts proving and disproving various meanings of the ongoing numbers references on the television program Lost, I figured that some of you would be interested that a person over on Flickr seems to have a much better explanation: they're simply geographic coordinates.

## Number Spirals

Number Spirals: Coincidences of order. "In mathematics you don't understand things. You just get used to them."

## Can you stump the Encyclopedia of Integer Sequences?

Can you stump the Encyclopedia of Integer Sequences? Every identifiable sequence known to man, including:

If your sequence does not appear there, you might want to try the Super Seeker.

*Name: Busy Beaver problem: maximal number of steps that an n-state Turing machine can make on an initially blank tape before eventually halting.*

Comment: The sequence grows faster than any computable function of n, and so is non-computable.

Keywords: hard,huge,nice,nonn,brefComment: The sequence grows faster than any computable function of n, and so is non-computable.

Keywords: hard,huge,nice,nonn,bref

If your sequence does not appear there, you might want to try the Super Seeker.

## Never be stuck without numbers

Never be stuck without numbers ane twa thrie fower fyve sax seiven aicht nyne ten < Count to ten in scottish and over 4000 other languages.

## LavaRand

LavaRand...harnessing the power of Lava LiteĀ® lamps to generate truly random numbers....

That's a bold statement, but who am I to doubt the power of the lava lamp. The mathematical purist may disagree with the "truely random" part, but this geek speak convinced me that LavaRand can handle all my random number needs.

That's a bold statement, but who am I to doubt the power of the lava lamp. The mathematical purist may disagree with the "truely random" part, but this geek speak convinced me that LavaRand can handle all my random number needs.

## Mathematician Bums Out Entire Scientific Community

Mathematician Bums Out Entire Scientific Community His "Omega" number--infinite and incalculable--guts hopes for pure mathematics, physicists' hopes for a Theory of Everything, and is just in general kind of bafflingly cool. Builds on the whole Godel/Turing foundation of hopelessness!

## Prime Time.

Prime Time. A prime is a whole number divisible only by itself and 1. In Aesthetics of the prime sequence one can hear primes, view primes (here also) and test for primes. Quite interesting and not just for math geeks...

## Call me Ishmael.

Call me Ishmael. Now all I need is a group of blind followers.

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