Shinichi Mochizuki

Shinichi Mochizuki is a math genius. There's no doubt about that. Who is this Shinichi Mochizuki? Well, he claims to have proved the abc conjecture. Now, I say claims because while he turned in four papers for proof, no one can decipher them. 

Why could no one decipher these papers? Mochizuki has been working on the abc conjecture in solitude for so long that he has developed his own mathematical language which only he understands fully. 

Mochizuki posted his papers online one day. A couple of days later, a mathematician found it. The math community was buzzing excitedly. No one can decipher it yet. All we can do is wait, Mochizuki refuses to lecture about his papers to give us a better understanding. He has turned down several offers from great universities. All we can do is wait until a mathematician figures it out. Here are the papers:

Paper 1

Paper 2

Paper 3

Paper 4

I obviously cannot decipher them but if you feel like it, give it a go. 

Ok, the abc conjecture. What is it? 

Well, the abc conjecture starts off fairly simple. a + b = c. Now there are some restrictions. A and B cannot have any common prime factors. 

The abc conjecture also stated that the size of C is bound above by (roughly) the product of the distinct prime numbers dividing A, B, and C. 

For some better explanations:

The Business Insider: ABC Conjecture

As easy as 1, 2, 3, NOT!
If Mochizuki actually proved this conjecture, well, he has advanced his field more than 2 decades!
Figures. Mochizuki graduated high school at 16 and became a professor at age 33, which is unusually young. Here is his website:
The Thoughts of Shinichi Mochizuki

Let us see if any of you can make heads or tails of his writing. 

Next Time: Solitary Numbers and Friendly/Amicable Numbers

Twin Primes (Conjecture)

First, what are twin primes?

Prime numbers are numbers that have only two factors, itself and one.  

Twin primes are two prime numbers that have a gap of two. For example, 3 and 5. The twin primes from   1-100:

As you can see, the gap between twin primes becomes larger and larger. This pattern continues as the numbers get larger. The primes are more infrequent.

The twin prime conjecture states that there are an infinite number a twin primes. Although it seems obvious, like the Goldbach conjecture, it is very hard to prove.
An advancement was made by a Chinese mathematician who was previously unknown. He turned in a paper proving that the distance between primes is not infinity but less than 70 million. Yitang Zhang was what seemed like, a retired mathematician who was far from all the action. He used work from predecessors in advancement of knowledge of primes to help his own work.
Mathematicians are working on narrowing the gap down to two.

Next time: the ABC conjecture.