122

Answers

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4

Measures of entangledness of an open curve

22

objects which can’t be defined without making choices but which end up independent of the choice

9

Is there any proof that you feel you do not “understand”?

4

Great mathematics books by pre-modern authors

4

Are there results from gauge theory known or conjectured to distinguish smooth from PL manifolds?

3

Understanding four manifolds (more details inside)

14

Mathematicians whose works were criticized by contemporaries but became widely accepted later

1

“Philosophical” meaning of the Yoneda Lemma

2

Learning through guided discovery

4

Reference for a proof of the Dehn presentation

9

Fundamental motivation for several complex variables

3

What can be said about a group from its presentation?

6

heegard diagram

7

How much do homological knot invariants improve the classification problem of knots?

1

Koszul duality for modular operads

3

Validity of generalized Reidemeister moves for a virtual knot

11

Motivation and unsolved problems of TQFT

7

Justifying/Explaining math research in a public address

6

Knot theory without planar diagrams?

11

Knot diagrams, sets of moves and equivalence relations

8

What are some interesting problems in the intersection of Algebraic Number Theory and Algebraic Topology?

3

What are some examples of “chimeras” in mathematics?

0

Monodromy in presentations of one group over another

19

Not especially famous, long-open problems which anyone can understand (3)

4

Interesting mathematical documentaries

26

Blackbox Theorems

5

Proofs that require fundamentally new ways of thinking

15

On connection between Knot theory and Operator algebra

8

Rational homology spheres and knots

6

Applications of nonconstructive mathematics