182

Answers

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6

Fundamental Examples

4

What programming languages do mathematicians use?

6

Ways to prove the fundamental theorem of algebra

20

Which mathematical ideas have done most to change history? (2)

9

Which math paper maximizes the ratio (importance)/(length)?

5

Depressed graduate student.

23

The phenomena of eventual counterexamples (3)

7

Text for an introductory Real Analysis course.

2

How do I make the conceptual transition from multivariable calculus to differential forms?

0

What are some correct results discovered with incorrect (or no) proofs? (5)

8

Is there a natural random process that is rigorously known to produce Zipf’s law?

6

nontrivial theorems with trivial proofs

3

Is there an introduction to probability theory from a structuralist/categorical perspective?

21

What is the difference between matrix theory and linear algebra?

23

What are some famous rejections of correct mathematics? (2)

28

What do heat kernels have to do with the Riemann-Roch theorem and the Gauss-Bonnet theorem?

7

Probabilistic Proofs of Analytic Facts

7

Examples of theorems misapplied to non-mathematical contexts

8

“Industry”/Government jobs for mathematicians

8

Has mathoverflow yet led to mathematical breakthroughs?

8

Notable mathematics during World War II

13

Where does a math person go to learn statistical mechanics?

2

Is Fourier analysis a special case of representation theory or an analogue?

14

How has “what every mathematician should know” changed?

6

Books about history of recent mathematics

5

“Homotopy-first” courses in algebraic topology

16

Mathematical explanation of the failure to quantize gravity naively

4

Uniquely generate all permutations of three digits that sum to a particular value?

9

Facts from algebraic geometry that are useful to non-algebraic geometers

1

How do you approach your child’s math education?