Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [soft-question]

For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still relevant to this site. Please be specific about what you are after.

For questions whose answers cannot be objectively evaluated as correct or incorrect, but which are still relevant to this site.

11201 questions
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What do modern-day analysts actually do?

In an abstract algebra class, one learns about groups, rings, and fields, and (perhaps naively) conceives of a modern-day algebraist as someone who studies these sorts of structures. One learns about the classification of finite simple groups, and…
Jesse Madnick
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10 answers

How do I sell out with abstract algebra?

My plan as an undergraduate was unequivocally to be a pure mathematician, working as an algebraist as a bigshot professor at a bigshot university. I'm graduating this month, and I didn't get into where I expected to get into. My letters were great…
Samuel Handwich
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13 answers

Is computer science a branch of mathematics?

I have been wondering, is computer science a branch of mathematics? No one has ever adequately described it to me. It all seems very math-like to me. My second question is, are there any books about computer science/programming that are very…
user107952
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13 answers

Why is compactness so important?

I've read many times that 'compactness' is such an extremely important and useful concept, though it's still not very apparent why. The only theorems I've seen concerning it are the Heine-Borel theorem, and a proof continuous functions on R from…
FireGarden
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200
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34 answers

List of interesting math videos / documentaries

This is an offshoot of the question on Fun math outreach/social activities. I have listed a few videos/documentaries I have seen. I would appreciate if people could add on to this list. $1.$ Story of maths Part1 Part2 Part3 Part4 $2.$ Dangerous…
user17762
199
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32 answers

Books on Number Theory for Layman

Books on Number Theory for anyone who loves Mathematics? (Beginner to Advanced & just for someone who has a basic grasp of math)
Prasoon Saurav
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192
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22 answers

List of Interesting Math Blogs

I have the one or other interesting Math blog in my feedreader that I follow. It would be interesting to compile a list of Math blogs that are interesting to read, and do not require research-level math skills. I'll start with my entries: Division…
Giuseppe Accaputo
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192
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31 answers

Counterintuitive examples in probability

I want to teach a short course in probability and I am looking for some counter-intuitive examples in Probability. The results seem to be obviously false but they true or vice versa. I already found some things. For example these two…
MR_BD
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190
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8 answers

How do we prove that something is unprovable?

I have read somewhere there are some theorems that are shown to be "unprovable". It was a while ago and I don't remember the details, and I suspect that this question might be the result of a total misunderstanding. By the way, I assume that…
polfosol
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8 answers

Are there any series whose convergence is unknown?

Are there any infinite series about which we don't know whether it converges or not? Or are the convergence tests exhaustive, so that in the hands of a competent mathematician any series will eventually be shown to converge or diverge? EDIT: People…
pseudosudo
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185
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4 answers

Some users are mind bogglingly skilled at integration. How did they get there?

Looking through old problems, it is not difficult to see that some users are beyond incredible at computing integrals. It only took a couple seconds to dig up an example like this. Especially in a world where most scientists compute their integrals…
JessicaK
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185
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9 answers

"Advice to young mathematicians"

I have been suggested to read the Advice to a Young Mathematician section of the Princeton Companion to Mathematics, the short paper Ten Lessons I wish I had been Taught by Gian-Carlo Rota, and the Career Advice section of Terence Tao's blog, and I…
Dal
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6 answers

What were some major mathematical breakthroughs in 2016?

As the year is slowly coming to an end, I was wondering which great advances have there been in mathematics in the past 12 months. As researchers usually work in only a limited number of fields in mathematics, one often does not hear a lot of news…
YukiJ
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14 answers

How do you revise material that you already half-know, without getting bored and demotivated?

Mathematics inevitably involves a lot of self-teaching; if you're just planning to sit there and wait for the lecturer to introduce you to important ideas, you probably need to find yourself another career. So, like a lot people here, I try to…
goblin GONE
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Mathematical ideas that took long to define rigorously

It often happens in mathematics that the answer to a problem is "known" long before anybody knows how to prove it. (Some examples of contemporary interest are among the Millennium Prize problems: E.g. Yang-Mills existence is widely believed to be…
Yly
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