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Results tagged with soft-question
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user 3106
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
2
votes
Obscure Names in Mathematics
Tropical geometry
Margulis napkin problem
Traveling salesman problem
Canadian traveller problem
10
votes
Accepted
Applications of really large numbers
For the conceptual picture that you seem to be looking for, you probably want to think in terms of fast-growing functions as the primary object of interest, and very large numbers as evaluations of th …
25
votes
New grand projects in contemporary math
Graph minor theory. The first success of this theory was the proof of Wagner's conjecture that in every infinite set of finite graphs, one is a minor of the other. However, the theory developed over …
1
vote
Betting markets for unsolved problems?
I distinctly remember that during the early 1990's, there was some kind of prediction market where one of the items was whether Fermat's Last Theorem would be proved before some date (the year 2000 ma …
10
votes
Examples of "miraculous" proofs
I quote from Michael Monastyrsky's book Modern Mathematics in the Light of the Fields Medals.
The most important of Margulis' results is his proof of Selberg's conjecture that a certain class of d …
5
votes
Is physical stamina important for doing mathematics?
Mathematics is not the same as chess, but here is an anecdote from the Preface of Jan Timman's book The Art of Chess Analysis that you may find interesting.
In his Foreword [to One Hundred Selected G …
29
votes
Discovered Phd topic has already been worked on
Every mathematician has had the experience of being "scooped," and it's never a pleasant feeling. As you can see from the many upvotes, we all sympathize with your situation.
Objectively, though, the …
9
votes
How has "what every mathematician should know" changed?
I believe that one shift is that "what every mathematician should know" is nowadays much less a specific body of mathematical facts and much more a facility with navigating the ocean of mathematical k …
32
votes
How do pure mathematicians assess whether their research ambitions can be realistically achi...
The unfortunate fact of life, from your perspective, is that most mathematical questions are either intractable or known (or follow easily from known results). This is not to say that there aren't als …
13
votes
The unreasonable effectiveness of Logic in Mathematics. Why?
I will not dwell on "unreasonableness" because in my opinion, the word is being used in an emotional way to express appreciation and wonder, not to assert a factual claim that the precise amount of ef …
38
votes
Getting nervous refereeing a paper
Others have already answered your question well, but I want to add something about #4, the mathematically more serious mistake. Since by your own admission you are inexperienced, I can see why you sp …
66
votes
Accepted
When is one 'ready' to make original contributions to mathematics?
It is something of a myth that everything has already been studied and that you have to master thousands of pages of prior work before you can contribute something new.
To be sure, there are some sub …
47
votes
How to read an article and make it actually useful?
Before you decide how to read a particular paper, you have to decide why you're reading that particular paper.
You said you're doing your Ph.D. You might want to take a look at a couple of other MO qu …
18
votes
The relevance of knowing "just facts"
I would suggest the following perspective: Your goal in research is to prove something new. Learning what other people have done is just a means toward that end. In particular:
Obviously, a result is …
- 82.7k
6
votes
Accepted
Arrangement of the introduction of a paper
To some extent this depends on the nature of your result, but the principle I generally follow is this:
State your result as soon as possible, subject to the constraint that when readers arrive at …