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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
14
votes
16
answers
1k
views
Generalized notions of solutions in various areas of mathematics
In many areas of mathematics (PDE, Algebra, combinatorics, geometry) when we have difficulty in coming with a solution to a problem we consider various notions of "generalized solutions". (There are a …
147
votes
66
answers
39k
views
Important formulas in combinatorics
Motivation:
The poster for the conference celebrating Noga Alon's 60th birthday, fifteen formulas describing some of Alon's work are presented. (See this post, for the poster, and cash prizes offered …
110
votes
89
answers
29k
views
Tweetable Mathematics
Update: Please restrict your answers to "tweets" that give more than just the statement of the result, and give also the essence (or a useful hint) of the argument/novelty.
I am looking for examp …
217
votes
28
answers
52k
views
The most outrageous (or ridiculous) conjectures in mathematics
The purpose of this question is to collect the most outrageous (or ridiculous) conjectures in mathematics.
An outrageous conjecture is qualified ONLY if:
1) It is most likely false
(Being hopeless is …
68
votes
30
answers
37k
views
A book you would like to write
Writing a book from the beginning to the end is (so I heard) a very hard process. Planning a book is easier. This question is dual in a sense to the question "Books you would like to read (if somebody …
172
votes
36
answers
35k
views
Proposals for polymath projects
Background
Polymath projects are a form of open Internet collaboration aimed towards a major mathematical goal, usually to settle a major mathematical problem. This is a concept introduced in 2009 by …
91
votes
24
answers
22k
views
Examples of major theorems with very hard proofs that have not dramatically improved over time
This question complement a previous MO question: Examples of theorems with proofs that have dramatically improved over time.
I am looking for a list of
Major theorems in mathematics whose proofs are v …
75
votes
13
answers
13k
views
What precisely Is "Categorification"?
(And what's it good for.)
Related MO questions (with some very nice answers): examples-of-categorification; can-we-categorify-the-equation $(1-t)(1+t+t^2+\dots)=1$?; categorification-request.
63
votes
19
answers
12k
views
Generalizations of the four-color theorem
The four color theorem asserts that every planar graph can be properly colored by four colors.
The purpose of this question is to collect generalizations, variations, and strengthenings of the four c …
143
votes
12
answers
30k
views
Solutions to the Continuum Hypothesis
Related MO questions: What is the general opinion on the Generalized Continuum Hypothesis? ; Completion of ZFC ; Complete resolutions of GCH How far wrong could the Continuum Hypothesis be? When was t …
36
votes
21
answers
6k
views
Generalizations of Planar Graphs
This is a follow up to Harrison's question: why planar graphs are so exceptional. I would like to ask about (and collect answers to) various notions, in graph theory and beyond graph theory (topology; …
72
votes
13
answers
11k
views
The use of computers leading to major mathematical advances II
I would like to ask about recent examples, mainly after 2015, where experimentation by computers or other use of computers has led to major mathematical advances.
This is a continuation of a question …
156
votes
52
answers
23k
views
Experimental mathematics leading to major advances
I would like to ask about examples where experimentation by computers has led to major mathematical advances.
A new look
Now as the question is five years old and there are certainly more examples of …
220
votes
140
answers
49k
views
Fundamental Examples
It is not unusual that a single example or a very few shape an entire mathematical discipline. Can you give examples for such examples? (One example, or few, per post, please)
I'd love to learn about …