Linked Questions

238 votes
46 answers
90k views

Most interesting mathematics mistake?

Some mistakes in mathematics made by extremely smart and famous people can eventually lead to interesting developments and theorems, e.g. Poincaré's 3d sphere characterization or the search to prove ...
122 votes
41 answers
29k views

What are some very important papers published in non-top journals?

There has already been a question about important papers that were initially rejected. Many of the answers were very interesting. The question is here. My concern in this question is slightly ...
167 votes
9 answers
30k views

Endless controversy about the correctness of significant papers

In principle, a mathematical paper should be complete and correct. New statements should be supported by appropriate proofs. But this is only theory. Because we often cannot enter into the smallest ...
67 votes
19 answers
14k views

Mathematicians whose works were criticized by contemporaries but became widely accepted later

Gauss famously discarded Abel's proof that an algebraic equation of degree five or more cannot have a general solution (Abel himself had rejected divergent series as the work of the devil). Cantor's ...
81 votes
15 answers
9k views

Theorems that impeded progress

It may be that certain theorems, when proved true, counterintuitively retard progress in certain domains. Lloyd Trefethen provides two examples: Faber's Theorem on polynomial interpolation: ...
52 votes
14 answers
9k views

Modern results that are widely known, yet which at the time were ignored, not accepted or criticized

What is your favorite example of a celebrated mathematical fact that had a hard time to become accepted by the community, but after overcoming some initial "resistance" quickly took on? It ...
61 votes
8 answers
9k views

What does it mean to suspect that two conjectures are logically equivalent?

Here's a familiar conversation: Me: Do you think Conjecture A and Conjecture B are equivalent? Friend: Yes, because I think they're both true. Me: [eye roll] You know what I mean... Does there ...
Dustin G. Mixon's user avatar
47 votes
7 answers
8k views

Swimming against the tide in the past century: remarkable achievements that arose in contrast to the general view of mathematicians

I would like to ask a question inspired by the title of a book by Sir Roger Penrose ([1]). The germ of this is to ask about the role, if any, of the fashion in research of pure and applied mathematics....
11 votes
3 answers
3k views

The definition of "proof" throughout the history of mathematics

It is widely believed that mathematicians have a uniform standard of what constitutes a correct proof. However, this standard has, at minimum, changed over time. What are some striking examples where ...
10 votes
1 answer
1k views

Example of a mathematician who had problems with peer review system? [closed]

I am wondering if there is some example of a famous or well-known mathematician who often had trouble with peer review, or who often had to publish in obscure journals because referees didn't 'get' ...