# Why abc is still a conjecture

@inproceedings{Scholze2018WhyAI, title={Why abc is still a conjecture}, author={Peter Scholze}, year={2018} }

In March 2018, the authors spent a week in Kyoto at RIMS of intense and constructive discussions with Prof. Mochizuki and Prof. Hoshi about the suggested proof of the abc conjecture. We thank our hosts for their hospitality and generosity which made this week very special. We, the authors of this note, came to the conclusion that there is no proof. We are going to explain where, in our opinion, the suggested proof has a problem, a problem so severe that in our opinion small modifications will…

## 10 Citations

On the $abc$ Conjecture in Algebraic Number Fields

- Mathematics
- 2021

While currently the abc conjecture and work towards it remains open or is disputed [22], at the same time much work has been done on weaker versions, as well as on its generalisation to number…

The Statement of Mochizuki's Corollary 3.12, Initial Theta Data, and the First Two Indeterminacies

- Mathematics
- 2020

This paper does not give a proof of Mochizuki's Corollary 3.12. It is the first in a series of three papers concerning Mochizuki's Inequalities. The present paper concerns the setup of Corollary 3.12…

COMMENTS ON THE MANUSCRIPT BY SCHOLZE-STIX CONCERNING INTER-UNIVERSAL TEICHMÜLLER THEORY (IUTCH)

- Philosophy
- 2018

(C1) Title, first two paragraphs, and §1: It is interesting to note that here, explicit mention is made of the ABC Conjecture, but not of IUTch. Although very strong assertions are made in the title…

A Replication Crisis in Mathematics?

- MathematicsThe mathematical intelligencer
- 2021

Seeing how mathematics was developing as a science, I understood that the time is approaching when the proof of yet another conjecture will change little. I understood that mathematics is facing a…

Probabilistic Szpiro, Baby Szpiro, and Explicit Szpiro from Mochizuki's Corollary 3.12

- Mathematics
- 2020

In \cite{Dupuy2020a} we gave some explicit formulas for the "indeterminacies" Ind1,Ind2,Ind3 in Mochizuki's Inequality as well as a new presentation of initial theta data. In the present paper we use…

Jury Theorems for Peer Review

- ArtThe British Journal for the Philosophy of Science
- 2022

Peer review is often taken to be the main form of quality control on academic writings. Usually this is carried out by journals. Parts of math and physics appear to have now set up a parallel,…

COMMENTS ON THE MANUSCRIPT (2018-08 VERSION) BY SCHOLZE-STIX CONCERNING INTER-UNIVERSAL TEICHMÜLLER THEORY (IUTCH)

- Psychology
- 2018

In the following, we make various additional Comments concerning the August 2018 version of the manuscript [SS2018-08] by Scholze-Stix (SS), to supplement the comments made in [Cmt2018-05] concerning…

Some Instructive Mathematical Errors

- MathematicsMaple Transactions
- 2021

We describe various errors in the mathematical literature, and consider how some of them might have been avoided, or at least detected at an earlier stage, using tools such as Maple or Sage. Our…

A Proof Of The ABC Conjecture.

- MathematicsSSRN Electronic Journal
- 2020

In this article, its shown that the ABC Conjecture is correct for integers a+b=c, and any real number r>1. This article proposes that the ABC Conjecture is true iff: c>0.

The Arithmetic Partial Derivative

- Mathematics
- 2022

The arithmetic partial derivative (with respect to a prime p) is a function from the set of integers that sends p to 1 and satisfies the Leibniz rule. In this paper, we prove that the p-adic…

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6-8, 60325 Frankfurt am Main, Germany E-mail address: stix@math.uni-frankfurt

Endenicher Allee 60, 53115 Bonn, Germany E-mail address: scholze@math.uni-bonn

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