##### A Simple Explanation Of The Legendary Math Problem That Was Just Cracked

Whenever a major leap is made in pure mathematics, the question always leads to “Cool, but what does this mean for *me*?”

Here’s what you want to know.

Shinichiu Mochizuki is a number theorist at Kyoto University.

He went to Philip Exeter Academy, one of the most prestigious High Schools in the country, and graduated in a brief two years. He entered Princeton University at age sixteen and left with a Ph. D at 22. He was a full professor by 33, an absurdly young age for academia. And now, this mathematical rock star may have just cracked one of the most important problems in his field.

In short, the abc conjecture — proposed in 1985 — explores the relationships between prime numbers.

It’s been described as the most important unsolved problem in Diophantine Analysis, a branch of mathematics that — by working with some of the most simple number systems (like ax + by = 1 or x^{n} + y^{n} = z^{n}) explores some of the deepest relationships in math.

So if you’re looking for an instant “real world application,” hit the back button — but if you want to see why one equation can tell us so much about how numbers work, read on.

The abc conjecture is as follows:

*Take three positive integers that have no common factor and where a + b = c. For instance, 5, 8, and 13.*

*Now take the distinct prime factors of these integers—in this case 2, 5, and 13—and multiply them to get a new number, d.*

*In most cases, like this one, d is larger than c. The conjecture states that in rare instances where d is smaller than c, it is usually very close to c. The conjecture also shows that there are a finite number of instances where d is smaller than c. *

Mochizuki claims to have cracked this conjecture in a 500-page proof.

Even if you didn’t catch all of that, solving this would be the necessary missing link for a dozen different, more advanced problems in Diophantine Analysis, including the legendary mathematical problem *Fermat’s Last Theorem*. If Mochizuki did successfully prove it, he may have singlehandedy moved his field forward two decades.

- neonhobbit reblogged this from youmightfindyourself
- run-hide likes this
- stateofbloom likes this
- sleepless-sky reblogged this from youmightfindyourself
- amandabees likes this
- mycherieamour likes this
- thebeautyoflanguage reblogged this from youmightfindyourself
- contentanonymous likes this
- glacierspatience likes this
- pablocomotion likes this
- weihuzuochang likes this
- ridingwithstrangers likes this
- cinema-movie-magic likes this
- loganmsachon likes this
- sakulsky likes this
- dreamschemesupreme likes this
- kalebmarshall likes this
- protops reblogged this from youmightfindyourself
- yumwatch likes this
- geoffnorthcott likes this
- ltwp likes this
- nchepesiuk likes this
- jonnynicknames reblogged this from fubreezy
- jonnynicknames likes this
- hazel likes this
- brainlock likes this
- dorkshdw likes this
- wabox likes this
- traptrippy likes this
- allthethingswelove reblogged this from youmightfindyourself
- soloweirdo likes this
- kayadelaine likes this
- ragasas likes this
- jillsies likes this
- justifiedjennyb likes this
- bonesandroots likes this
- bloopblorp reblogged this from youmightfindyourself
- bloopblorp likes this
- vrtcllychllngd likes this
- creativelybored likes this
- wolfruns likes this
- sitlook likes this
- loveinthehighest reblogged this from youmightfindyourself
- loveinthehighest likes this
- tradandtrue likes this
- monteeee likes this
- verseofivan likes this
- apocalypticrainbows reblogged this from heauton-timorumenos
- tpc472 likes this
- Show more notes