Is the ABC Conjecture Finally Solved?

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In summary, there has been a recent conference discussing Shirichi Mochizuki's claimed proof of the ABC Conjecture. The press has been eagerly awaiting news on whether a+b=c or not, but it seems that the proof is still in limbo. Mochizuki's proof is already very long and may be difficult for other mathematicians to understand. Additionally, there is concern about the level of detail and the risk of peer review taking many years. Mochizuki's proof, called 'Inter-universal Teichmuller Theory', was last updated in November 2016, while the 'Panoramic Overview of Inter-universal Teichm¨uller Theory' has remained unchanged. Despite the media
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  • #2
Oh, all the great headlines the press could write...
"Mathematicians still unsure if a+b=c"
"Conference on whether a+b=c or not, no solution"

Does Mochizuki write down more details and steps in regions where other mathematicians struggle? It looks like an obvious thing to do.
 
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  • #3
mfb said:
Oh, all the great headlines the press could write...
"Mathematicians still unsure if a+b=c"
"Conference on whether a+b=c or not, no solution"

Does Mochizuki write down more details and steps in regions where other mathematicians struggle? It looks like an obvious thing to do.

Usually the proof is with a consistent level of detail. It is already very long, perhaps a thousand pages. It could be that different mathematicians struggle with different steps, or maybe they are just overwhelmed with the whole thing. That's the trouble with highly original research: peer review could take many man-years, and there is risk that the whole thing will be useless. If Mochizuki didn't have a heavy rep there would be no chance that his proof would be accepted: too risky an investment.
 
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  • #5
I never took number theory, but I've taken lots of combinatorics and I usually stay up on math related "news." But I've heard more about this conjecture in the press than I've heard from anybody I know in the math community. Does anyone really think it's really such an important conjecture?

-Dave K
 

1. What is the ABC Conjecture?

The ABC Conjecture is a mathematical conjecture in number theory that states that if a + b = c, where a, b, and c are positive integers with no common factors, then the product of the distinct prime factors of abc is greater than c.

2. Has the ABC Conjecture been proven?

No, the ABC Conjecture has not yet been proven. It remains one of the most famous unsolved problems in mathematics.

3. What is the latest development in the search for a proof of the ABC Conjecture?

In 2015, mathematician Shinichi Mochizuki released a proposed proof of the ABC Conjecture, but it has not yet been accepted by the mathematical community. Other mathematicians are still working on finding a proof or a counterexample to the conjecture.

4. Why is the ABC Conjecture important?

The ABC Conjecture has important implications in many areas of mathematics, including number theory, algebraic geometry, and cryptography. If proven true, it would also have significant applications in computer science and physics.

5. When do experts predict that the ABC Conjecture will be solved?

There is no way to predict when or if the ABC Conjecture will be solved. It may be solved in the near future, or it may remain an unsolved problem for many years to come.

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