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Questions tagged [soft-question]

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.

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.

More elementary questions in mathematics are better asked on https://math.stackexchange.com/, and questions about teaching mathematics are welcome on https://matheducators.stackexchange.com/.

2233 questions
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20 answers

How can a mathematician handle the pressure to discover something new?

Suppose I'm an aspiring mathematician-to-be, who started doing research. Although this is really what I love doing, I found that one disturbing point is that there's always the pressure of discovering something new. When I'm doing mathematical…
user103598
114
votes
30 answers

New grand projects in contemporary math

When I was a graduate student in math (mid-late eighties and early nineties) the arena was dominated by a few grand projects: for instance, Misha Gromov's hyperbolic groups, which spread into many seemingly heterogeneous domains (such as…
Mirco A. Mannucci
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108
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11 answers

Examples of notably long or difficult proofs that only improve upon existing results by a small amount

I was recently reading Bui, Conrey and Young's 2011 paper "More than 41% of the zeros of the zeta function are on the critical line", in which they improve the lower bound on the proportion of zeros on the critical line of the Riemann…
Klangen
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103
votes
23 answers

eBook readers for mathematics

For a while I have been eying stand-alone eBook readers that use "electronic ink" displays, the most popular ones seem to be the Amazon Kindle readers. My criteria are as follows: It should be able to display pdf's and math formulas in them just…
Lars
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102
votes
61 answers

Which mathematicians have influenced you the most?

There are mathematicians whose creativity, insight and taste have the power of driving anyone into a world of beautiful ideas, which can inspire the desire, even the need for doing mathematics, or can make one to confront some kind of problems,…
Jose Brox
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101
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34 answers

What is the most useful non-existing object of your field?

When many proofs by contradiction end with "we have built an object with such, such and such properties, which does not exist", it seems relevant to give this object a name, even though (in fact because) it does not exist. The most striking example…
user56097
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97
votes
11 answers

How has "what every mathematician should know" changed?

So I was wondering: are there any general differences in the nature of "what every mathematician should know" over the last 50-60 years? I'm not just talking of small changes where new results are added on to old ones, but fundamental shifts in the…
Vipul Naik
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94
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37 answers

What's a great christmas present for someone with a PhD in Mathematics?

Christmas is just around the corner and I haven't bought all the gifts for my family yet ( yeah, ) My Dad has a PhD in Mathematics, he works in Graph theory and his thesis was about Quasiperiodic tilings. What do you think would make a good gift for…
Antenor Briareo
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85
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7 answers

How many mathematicians are there?

Although we are not so numerous as other respected professionals, like for example lawyers, I wonder if we could come up with a reasonable estimate of our population. Needless to say, the question more or less amounts to the definition…
Georges Elencwajg
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68
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7 answers

When is one 'ready' to make original contributions to mathematics?

This is quite a philosophical, soft question which can be moved if necessary. So, basically I started my PhD 9 months ago and have thrown myself into learning more mathematics and found this an enjoyable and rewarding experience. However, I have…
Hollis Williams
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65
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2 answers

How do pure mathematicians assess whether their research ambitions can be realistically achieved?

I am an enthusiastic but ever-so-slightly naive PhD student and have been 'following my nose' a lot recently, seeing whether topics that I have studied can be generalised or translated in various ways into unfamiliar settings; exploring where the…
Very Forgetful Functor
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63
votes
11 answers

Has mathoverflow yet led to mathematical breakthroughs?

Some people ask questions here out of simple curiosity. But some ask them because they are working on a research project, come up with a question they need to know the answer to, and think that the answer is probably known. In the past, one had to…
gowers
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61
votes
6 answers

Discovered Phd topic has already been worked on

I am a second-year French Ph.D. student and two days ago I found out the topic I had been working on has already been studied, and the result I wanted to prove is basically already known. Unfortunately, neither I nor the supervisor were aware of…
M.S.L.
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58
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22 answers

How to respond to "I was never much good at maths at school."

We've all heard it. I even got it in Norwegian recently. It's number 1 on the list of responses to the statement "I'm a mathematician.". Does anyone have any good comebacks? What other responses have you heard? Standard community wiki rules (not…
Andrew Stacey
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55
votes
10 answers

How often do people read the work that they cite?

I have the following question: How likely it is that an author carefully read through a paper cited by him? Not everyone reads through everything that they have cited. Sometimes, if one wants to use a theorem that is not in a standard textbook,…
Vidit Nanda
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