Back in 2012, mathematician Shinichi Mochizuki announced he had a proof to the abc conjecture. Six years later, there is still no consensus as to whether Mochizuki's proof is correct or not. The...
Back in 2012, mathematician Shinichi Mochizuki announced he had a proof to the abc conjecture. Six years later, there is still no consensus as to whether Mochizuki's proof is correct or not.
The problem stems from the complexity of the proof: Mochizuki's proof is developed over the course of 500 pages, which itself builds on another 500 or so pages of previous work (a mathematical theory he developed known as Inter-universal Teichmüller theory, which he claims to be an entirely new branch of mathematics). (For those of you who have never had the pleasure of reading a math paper, understand that you can easily spend hours trying to digest a single page when learning something the first time.) Couple this with a particularly dense prose (definitions and theorems go on for pages, only to be justified by saying that the theorems follows from the definitions), and you have a perfectly impenetrable paper. At this point, you might be willing to dismiss the proof outright -- what good is a proof, after all, if nobody can understand it? But Shinichi Mochizuki is an accomplished mathematician; just because we don't understand the proof, doesn't mean that Mochizuki is wrong.
However, it seems several mathematicians may have finally found a snag in the proof -- Corollary 3.12, a result on which the rest of the results lie. Perhaps now mathematicians have a starting point from which they can begin to dismantle (or better understand) the proof.
The reddit discussion is pretty good for this article. Maybe check that out also.
And for funsies, look here (pdf warning) for the controversial corollary. It begins on page 133.
Back in 2012, mathematician Shinichi Mochizuki announced he had a proof to the abc conjecture. Six years later, there is still no consensus as to whether Mochizuki's proof is correct or not.
The problem stems from the complexity of the proof: Mochizuki's proof is developed over the course of 500 pages, which itself builds on another 500 or so pages of previous work (a mathematical theory he developed known as Inter-universal Teichmüller theory, which he claims to be an entirely new branch of mathematics). (For those of you who have never had the pleasure of reading a math paper, understand that you can easily spend hours trying to digest a single page when learning something the first time.) Couple this with a particularly dense prose (definitions and theorems go on for pages, only to be justified by saying that the theorems follows from the definitions), and you have a perfectly impenetrable paper. At this point, you might be willing to dismiss the proof outright -- what good is a proof, after all, if nobody can understand it? But Shinichi Mochizuki is an accomplished mathematician; just because we don't understand the proof, doesn't mean that Mochizuki is wrong.
However, it seems several mathematicians may have finally found a snag in the proof -- Corollary 3.12, a result on which the rest of the results lie. Perhaps now mathematicians have a starting point from which they can begin to dismantle (or better understand) the proof.
The reddit discussion is pretty good for this article. Maybe check that out also.
And for funsies, look here (pdf warning) for the controversial corollary. It begins on page 133.