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28 posts tagged with math *and* numbers.

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## The likelihood that there's interesting or important math is pretty high

Shinichi Mochizuki and the impenetrable proof - "Fesenko has studied Mochizuki's work in detail over the past year, visited him at RIMS again in the autumn of 2014 and says that he has now verified the proof. (The other three mathematicians who say they have corroborated it have also spent considerable time working alongside Mochizuki in Japan.) The overarching theme of inter-universal geometry, as Fesenko describes it, is that one must look at whole numbers in a different light — leaving addition aside and seeing the multiplication structure as something malleable and deformable. Standard multiplication would then be just one particular case of a family of structures, just as a circle is a special case of an ellipse." (previously: 1,2; via) [more inside]

## Time with class! Let's Count!

I want to demonstrate how amazing combinatorial explosion is! Please don't stop me. An animation about numbers that get large. It has a happy ending and possibly even a moral. [more inside]

## 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]

## Still Combining Numbers On A Grid To Get Bigger Numbers, But Different

## 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]

## "There's actually no such thing as an uninteresting natural number"

io9 takes a look at why the number 1729 shows up in so many Futurama episodes. It's mathtastic!

## Visualizing Numbers with WebGl

How To Fold a Julia Fractal. A beautiful interactive introduction to complex numbers, fractals and waves. (Requires WebGL). To Infinity And Beyond is a similar introduction to calculus.

## 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)

## Factor Conga

Animation of prime factorization of the integers based on Brent Yorgey's factorization diagrams, described here. [via Data Pointed, previously.]

## 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."

## Big (and small) Numbers

FatFonts creates numerical fonts where the amount of ink/pixels for each number is in direct proportion to its value.

## Number A Day

## 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]

## the idea of a fully operational zero...

"

*Michel de Montaigne, whose essays transformed Western consciousness and literature, was not capable of solving basic arithmetic problems. And most other people would not be able to do so either, if not for the invention of decimal notation by an unknown mathematician in India 1500 years ago.*" The Greatest Mathematical Discovery? (expanded pdf) a paper written for the US Dept. of Energy makes this assertion based in part on the work of Georges Ifrah. [via] [more inside]## Prime numbers are just the beginning.

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

## Beware of Oddity

## 15 bits of crypto should be enough for anybody

On May 13, security advisories published by Debian and Ubuntu revealed that, for over a year, their OpenSSL libraries have had a major flaw in their CSPRNG, which is used by key generation functions in many widely-used applications, which caused the "random" numbers produced to be extremely predictable. [lolcat summary] [more inside]

## 3 is an odd prime, 5 is an odd prime, 7 is an odd prime, 9 is a very odd prime...

The Prime Game is not really much of a game, but it

*is*a neat & little-known fact about the decimal representation of prime numbers.## Operation Kaprekar

Mysterious number 6174. An excellent recreational math article.

## Significant numbers

Significance of numbers. Not to be confused with the concept of "significant figures," this page lists the significance of numbers 0 through 1000.

*See!*"2 is the only even prime."*Hear!*"24 is the largest number divisible by all numbers less than its square root."*Thrill!*"3367 is the smallest number which can be written as the difference of 2 cubes in 3 ways." Whoa!## Number Spirals

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

## Oh, it's nothing...

## LavaRand

LavaRand...harnessing the power of Lava Lite® 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!

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