# Linked Questions

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### What are your favorite instructional counterexamples?

Related: question #879, Most interesting mathematics mistake. But the intent of this question is more pedagogical.
In many branches of mathematics, it seems to me that a good counterexample can be ...

**68**

votes

**6**answers

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### Counterexamples in algebraic topology?

In this thread
Books you would like to read (if somebody would just write them...),
I expressed my desire for a book with the title "(Counter)examples in Algebraic Topology".
My reason for doing so ...

**54**

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**39**answers

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### Counterexamples in Algebra?

This is certainly related to "What are your favorite instructional counterexamples?", but I thought I would ask a more focused question. We've all seen Counterexamples in Analysis and Counterexamples ...

**51**

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**24**answers

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### What could be some potentially useful mathematical databases?

This is a soft question but it's not meant as a big-list question. I have recently been asked whether I want to provide feedback at the pre-beta stage on a forthcoming website that will provide a ...

**49**

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**12**answers

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### Counterexamples in PDE

Let us compile a list of counterexamples in PDE, similar in spirit to the books Counterexamples in topology and Counterexamples in analysis. Eventually I plan to type up the examples with their ...

**45**

votes

**20**answers

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### Algebraic geometry examples

What are some surprising or memorable examples in algebraic geometry, suitable for a course I'll be teaching on chapters 1-2 of Hartshorne (varieties, introductory schemes)?
I'd prefer examples that ...

**34**

votes

**26**answers

11k 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 ...

**32**

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**19**answers

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### Canonical examples of algebraic structures

Please list some examples of common examples of algebraic structures. I was thinking answers of the following form.
"When I read about a [insert structure here], I immediately think of [example]."
...

**31**

votes

**25**answers

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### Theorems for nothing (and the proofs for free) [closed]

Some theorems give far more than you feel they ought to: a weak hypothesis is enough to prove a strong result. Of course, there's almost always a lot of machinery hidden below the waterline. Such ...

**28**

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**37**answers

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### What is your favorite “strange” function? [closed]

There are many "strange" functions to choose from and the deeper you get involved with math the more you encounter. I consciously don't mention any for reasons of bias. I am just curious what you ...

**22**

votes

**7**answers

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### What examples of distributions should I keep in mind?

I'm learning a bit about the theory of distributions. What examples of distributions will help me develop good intuition?
Definitions: Let $U$ be an open subset of $\mathbb{R}^n$. Write ...

**19**

votes

**25**answers

9k views

### Most intricate and most beautiful structures in mathematics

In the December 2010 issue of Scientific American, an article "A Geometric Theory of
Everything" by A. G. Lisi and J. O. Weatherall states "... what is arguably the most
intricate structure known to ...

**12**

votes

**17**answers

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### Individual mathematical objects whose study amounts to a (sub)discipline? [closed]

Certain mathematical objects have a theory so rich that their study
alone arguably constitutes a distinct (sub)discipline. My own list
would begin with
1) the absolute Galois group of the rationals;
...