# Is the ABC Conjecture Solved? New Proof Claims Deep Connection to Prime Numbers

• Dragonfall
In summary, Mochizuki has been working on a new abstraction that is difficult for others to understand. Despite this, he has produced important results and has now announced a solution to a significant problem. However, his colleagues must not only read his 500-page paper, but also familiarize themselves with his unconventional math that he has been developing for the past decade. This poses a challenge for the rest of the number theorists.

#### Dragonfall

phospho said:

That's a great MO thread. It's amazing what the pros do.

What tiny little I gather is that Mochizuki has been working for years on some kind of new "next level up" kind of abstraction that nobody understands. And people know he's not a crank because he has been producing important results as he goes. But now that he's announced a solution to this really important problem, the rest of the number theorists have to not only read his 500 page paper; but they also have to come up to speed on the strange and revolutionary math he's been creating over the past decade.

That sounds really wild to me.

## 1. What is the ABC conjecture?

The ABC conjecture is a mathematical conjecture that states that for any given positive integer n, there exists only a finite number of triples of relatively prime positive integers a, b, and c such that a + b = c and a, b, and c have no prime factors in common.

## 2. Has the ABC conjecture been solved?

As of now, the ABC conjecture remains unsolved. However, there have been several attempts and claims of a proof, but none have been accepted and proven to be correct by the mathematical community.

## 3. Who solved the ABC conjecture?

The ABC conjecture has not been officially solved by any mathematician. There have been several claims of a proof, but none have been accepted and proven to be correct by the mathematical community.

## 4. What would be the significance of solving the ABC conjecture?

If the ABC conjecture were to be solved, it would have far-reaching implications in number theory and other areas of mathematics. It would also provide a better understanding of the relationships between prime numbers and their distribution.

## 5. How would the solution of the ABC conjecture impact the mathematical community?

The solution of the ABC conjecture would have a significant impact on the mathematical community, as it would open up new avenues for research and potentially lead to the development of new mathematical techniques and theories. It would also be considered a major achievement in the field of mathematics.