Was the ABC conjecture proven?
Various attempts to prove the abc conjecture have been made, but none are currently accepted by the mainstream mathematical community and as of 2020, the conjecture is still regarded as unproven.
Did Mochizuki prove the abc conjecture?
In 2012, Shinichi Mochizuki at Kyoto University in Japan produced a massive proof claiming to have solved a long-standing problem called the ABC conjecture. Spanning 500 pages across four papers, Mochizuki’s proof was written in an impenetrable style, and number theorists struggled to understand its underlying ideas.
Is number Theory proof based?
Proof of theorem: Let q = ⌊a/b⌋ and r = a − bq… Definition If a and b are natural numbers, the greatest common divisor (GCD) of a and b, denoted gcd(a,b), is the largest number that divides both a and b. Definition Natural numbers a and b are relatively prime if gcd(a,b) = 1.
Is Mochizuki’s proof the abc conjecture?
Scholze and Stix on the Mochizuki Proof Posted onSeptember 20, 2018bywoit As discussed herea couple months ago, Peter Scholze and Jakob Stix believe they have found a serious problem with Mochizuki’s claimed proof of the abc conjecture, and traveled to Kyoto in March to discuss it with him. Their write-up is now available here.
What did Scholze and Stix do for Mochizuki?
Peter Scholze was awarded the Fields Medal earlier this month. Scholze and Stix’s conclusions are based not only on their own study of the papers but also on a weeklong visit they paid to Mochizuki and his colleague Yuichiro Hoshi in March at Kyoto University to discuss the proof.
Is Shinichi Mochizuki’s proof flawed?
Shinichi Mochizuki maintains that his proof is not flawed despite the assertions of Jakob Stix and Peter Scholze that they’ve discovered a “serious, unfixable gap.”
Does Peter Scholze’s judgment have changed?
In the Nature article Peter Scholze states: My judgment has not changed in any way since I wrote that manuscript with Jakob Stix.