bio | website | vzn1.wordpress.com |
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location | U.S. | |
age | ||
visits | member for | 2 years, 6 months |
seen | 6 hours ago | |
stats | profile views | 416 |
^{The algorithm designer who does not run experiments risks becoming lost in abstraction. â€”Sedgewick}
Jul 19 |
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Negative impact of wrong or non-rigorous proofs
the question is slightly leading. any erroneous theorem or lemma anywhere leads to "0=1" elsewhere. it can be very timeconsuming for others to discover/find these "defects" (there is some loose analogy to software engineering). so "damage" is an overwrought/dramatic word/adjective in this context. but, ofc, "to err is human..." even by professional mathematicians. agreed that fixing errors can lead to highly constructive new math/research etc. |
Jun 9 |
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Understanding the nature and structure of proofs; Reverse Mathematics and Proof Theory. Prerequisites? Good introductory texts?
did anyone cite the wikipedia article? |
Jun 6 |
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Mistakes in mathematics, false illusions about conjectures
nice question but dislike the vagueness of the initial paragraph. why not cite the example? sounds like you could be referring to an important open problem... |
May 30 |
revised |
Is it easy to produce hard-to-color graphs?
added 61 characters in body |
May 30 |
answered | Is it easy to produce hard-to-color graphs? |
May 30 |
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Is it easy to produce hard-to-color graphs?
suggest migrate to Theoretical Computer Science. the questions are closely connected with P=?NP conjecture. |
May 7 |
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Examples of mathematics motivated by technological considerations
noticing many refs from TCS below. so see also eg core algorithms deployed tcs.se |
May 7 |
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Interesting examples of generic behavior of mathematical objects being either unreasonably structured or simply unreasonable
alas interesting idea but probably too broad when undecidable problems are taken into acct (undecidability is quite rampant). also, fractals. also, Collatz conjecture related to integer iterative/dynamic equations. |
May 2 |
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How do I verify the Coq proof of Feit-Thompson?
think this is on topic but admittedly very unusual. (there are some questions on Theoretical Computer Science on auto thm proving systems & even one highvoted one on Gonthier Feit-Thompson although they might not go for this one.) it would appear from your description that the project (basically verging on a software package) has poor documentation. a not-uncommon scenario for software projects & esp an issue with many open source systems. ie does it even have a README? |
Apr 15 |
accepted | notable inductive proofs relating to fractals |
Apr 15 |
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notable inductive proofs relating to fractals
ok thx... but what did it prove? are you saying the goal was to derive the spectrum of the limit Laplacian of the Sierpinski gasket? |
Apr 15 |
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notable inductive proofs relating to fractals
sounds highly relevant, but not sure what you mean by "induction vs iteration divide". re the ref can you cite it beside the url, & anyway that url is apparently a search url, another one would be better |
Apr 15 |
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Fractal-like structures arising from the action of a group on $\mathbb{Z}^2$
this appears to be a case of what are known by some as "collatz like functions". eg sec 1.4 & others of new/recent paper Problems in number theory from busy beaver competition by Michel. basically these problems are difficult to study & lie at the boundary of decidable and undecidable & are an open/active area of research. |
Apr 15 |
asked | notable inductive proofs relating to fractals |
Apr 2 |
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What areas of pure mathematics research are best for a post-PhD transition to industry?
statistics is a big deal in big data, datamining these days & also has strong ties to machine learning.... |
Mar 29 |
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practical algorithms for np complete problems
examples/refs of recent/notable math/TCS research in the area via SAT |
Mar 16 |
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Analogues of P vs. NP in the history of mathematics
further brainstorming. this answer can be regarded as a template for using hard math problem [x] as the analogy to P vs NP. three others that are close & could be written up similarly also: unsolvability of the quintic with algebraic operations & FLT. yet another, hilberts 10th problem. all have key boundaries. |
Mar 16 |
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Analogues of P vs. NP in the history of mathematics
agreed/thx for that clarification. however note that a lot of the work on the problem was geometric incl probably even some serious/reputable work and it was more later distinctions that made the picture clear about algebraic vs real numbers, ie 2020 hindsight and "modern vision/understanding/defns" superimposed on older theory. eg wonder if Lindemann used that concept at all in his proof? extending this analogy maybe P vs NP could be the tip of some new conceptual/theoretical iceberg; many TCS experts would not rule out that pov. |
Mar 16 |
revised |
Analogues of P vs. NP in the history of mathematics
added 56 characters in body |
Mar 16 |
answered | Analogues of P vs. NP in the history of mathematics |