Daniel Moskovich

Israel

My background is in quantum topology, and I am exploring low dimensional topological formalisms for information and for computation. I blog on mathematics that interests me at Low Dimensional Topology.

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Has philosophy ever clarified mathematics?

ho.history-overview big-list math-philosophy asked Oct 1, 2014 at 5:39

mathoverflow.net

110 votes

Is there a sheaf theoretical characterization of a differentiable manifold?

sheaf-theory differential-topology dg.differential-geometry gn.general-topology asked Feb 10, 2012 at 0:30

mathoverflow.net

81 votes

Intuitive explanation for the Atiyah-Singer index theorem

vector-bundles kt.k-theory-homology differential-operators characteristic-classes index-theory asked May 4, 2010 at 8:41

mathoverflow.net

78 votes

Compelling evidence that two basepoints are better than one

at.algebraic-topology gt.geometric-topology asked Oct 3, 2010 at 18:26

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77 votes

Sophisticated treatments of topics in school mathematics

reference-request big-list mathematics-education gm.general-mathematics asked Dec 7, 2015 at 8:54

mathoverflow.net

70 votes

What are Jacob Lurie's key insights?

higher-category-theory ho.history-overview asked Sep 5, 2010 at 21:11

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68 votes

What is a cumulant really?

pr.probability big-picture cumulants asked Oct 14, 2013 at 3:58

mathoverflow.net

61 votes

What is the high-concept explanation on why real numbers are useful in number theory?

big-picture nt.number-theory lo.logic asked Apr 14, 2011 at 2:40

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52 votes

Mathematically interesting screensavers

soft-question big-list asked Aug 8, 2017 at 8:56

mathoverflow.net

50 votes

Why are smooth manifolds defined to be paracompact?

differential-geometry manifolds big-picture asked Jan 11, 2012 at 8:52

math.stackexchange.com

Top Answers

237

Most interesting mathematics mistake?

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Mathematical "urban legends"

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Theorems that are 'obvious' but hard to prove

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Mathematical "urban legends"

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Which mathematical ideas have done most to change history?

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Demonstrating that rigour is important

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Jokes in the sense of Littlewood: examples?

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A book you would like to write

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What are some examples of ingenious, unexpected constructions?

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Examples of major theorems with very hard proofs that have not dramatically improved over time

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Books you would like to read (if somebody would just write them…)

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Demonstrating that rigour is important

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"Immediate" Applications of Differential Geometry

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What are some examples of colorful language in serious mathematics papers?

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Is it possible to have a research career while checking the proof of every theorem that you cite?

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Examples of common false beliefs in mathematics

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Are there proofs that you feel you did not "understand" for a long time?

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Is Grothendieck a computer?

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Blackbox Theorems

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Examples of theorems misapplied to non-mathematical contexts

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Why are all the interesting constants so small?

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Why algebraic topology is also called combinatorial topology?

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How to motivate and present epsilon-delta proofs to undergraduates?

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

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What would you want to see at the Museum of Mathematics?

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When to start reviewing

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Objects which can't be defined without making choices but which end up independent of the choice

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What are some examples of colorful language in serious mathematics papers?

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Best algebraic geometry textbook? (other than Hartshorne)

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

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