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Results tagged with soft-question
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user 1131
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.
89
votes
What's a nice argument that shows the volume of the unit ball in $\mathbb R^n$ approaches 0?
The ultimate reason is, of course, that the typical coordinate of a point in the unit ball is of size $\frac{1}{\sqrt{n}}\ll 1$. This can be turned into a simple geometric argument (as suggested by fe …
88
votes
How to present mathematics to non-mathematicians?
Here is one example of what is mathematics as opposed to "layman reasoning" that I was told about by Yuval Peres. During WWII, the British airplanes were often shot down by Germans because the armor w …
78
votes
Why should one still teach Riemann integration?
I often introduce the Lebesgue integral (say, for positive functions) as a direct generalization of the Riemann/Riemann-Darboux one just saying that the only differences are that we now use measurable …
72
votes
How do you not forget old math?
You do forget things you are not working on. Nothing can be done about it. I could read German easily by the end of 8th grade and now I can hardly spell "Entshuldigen Sie mir bitte". There are several …
70
votes
What are some deep theorems, and why are they considered deep?
There are many possible meanings of word "deep" one can detect in the common speech. I'll list three good and three bad but I do not pretend the list is anywhere near complete.
1) Very difficult (Fer …
66
votes
Thinking and Explaining
Just to talk about something fresh for which I still have a good memory of what I actually thought and what I wrote, let's take this example
Thoughts:
1) Ivan Fesenko teased me with the puzzle with …
60
votes
Should one attack hard problems?
Actually, I think trying a "hard problem" may be a good idea IF
1) You have a fair evidence that you are strong enough to tackle things other clever people gave up on. The evidence should be tangible …
48
votes
A book you would like to write
I would love to write something titled "Higher mathematics from engineer's perspective", which would consist of a few chapters each of which should be devoted to a single simple to state real engineer …
46
votes
Accepted
Papers better than books?
Very recently I and Misha Sodin had a strong incentive to learn the Ito-Nisio lemma (which, roughly speaking, says that weak convergence in probability of a series of symmetric independent random vari …
40
votes
Lost soul: loneliness in pursing math. Advice needed.
I look at my professors, they are almost always there to do research, day and night, weekday and weekends, even the ones with family. The more leisurely ones are the ones who either got their profe …
36
votes
Can breadth hurt a job candidate?
For all I can tell (and I've been on a hiring committee for the last 2 years), to have extra areas of expertise is always a plus, and to have areas of expertise that can connect you to other departmen …
36
votes
The Unreasonable Effectiveness of Physics in Mathematics. Why ? What/how to catch?
My opinion is that physicists transferred from study of "individual objects" to that of "large systems" where the order arises from limit probability laws rather than from simple deterministic formula …
35
votes
Jokes in the sense of Littlewood: examples?
The classical Stokes formula $\int_{\partial\Omega}\omega=\int_\Omega d\omega$ is certainly a Littlewood type joke. That is especially true if you learn it after you've spent a few months covering vec …
34
votes
Submission of a paper with a serious error to a good journal
1) Has this happened to anyone else? Is this a relatively common occurrence, or am I just sloppy?
It is not very common (the usual preventive techniques include showing the draft to a few experts/fri …
34
votes
What is the oldest open math problem outside of number theory?
I don't have a 200 year old candidate but I can offer a 150 year old one (from Maxwell's "Treatise on Electricity and Magnetism" written in 1873).
You are allowed to put $n$ electric point charges in …
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