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seen Apr 16 at 4:48

The algorithm designer who does not run experiments risks becoming lost in abstraction. —Sedgewick


Apr
15
accepted notable inductive proofs relating to fractals
Apr
15
comment 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
comment 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
comment 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
comment 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
comment practical algorithms for np complete problems
examples/refs of recent/notable math/TCS research in the area via SAT
Mar
16
comment 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
comment 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
Mar
7
comment Who made the famous error in calculation that 'wasted' the final years of his life?
somewhat similar, have heard there is some lament by math historians that Gauss spent ~2 decades off/on doing a massive manual calculation of the orbit of Ceres asteroid....
Feb
18
comment When would you read a paper claiming to have settled a long open problem like $P$ vs. $NP$?
ok, highly commend/appreciate your declared flexibility/enthusiasm, now what about a proof outline? =)
Feb
18
comment How can an approach to $P$ vs $NP$ based on descriptive complexity avoid being a natural proof in the sense of Raborov-Rudich?
interesting question! fyi it seems one expected major/key way to approach P=?NP question from descriptive complexity theory would be Fagins thm but presumably Deolalikar did not go this route... also this post by aaronson Eight Signs A Claimed P≠NP Proof Is Wrong has a point or two relevant to the use of descriptive complexity in a P vs NP proof & this particular proof attempt/attack.
Feb
16
comment Number of vectors so that no two subset sums are equal
bears some resemblance to the subset sum problem from TCS have you heard of it?
Feb
15
comment Number of vectors so that no two subset sums are equal
why addition over $\mathbb{R}$ and not $\mathbb{N}$ if all the elements are also in $\mathbb{N}$?
Feb
14
comment What is the shortest program for which halting is unknown?
see also smallest TM with unknown halting, Theoretical Computer Science
Feb
14
comment A combinatorial problem concerned with logic circuits
re bounty assigned for proof of NP completeness: huh? the bandwidth problem is already proven NP complete. the proof/ref is surely on the wiki page. oh was the bounty assigned before the 1st answer by suresh? (ok)
Feb
14
comment A problem seeking for algorithm
suggest migrate to Computer Science
Feb
13
comment Fields of mathematics that were dormant for a long time until someone revitalized them
@Andy ok didnt state that fully. the idea is that the great application also led to a burst/surge of interest/research in the theoretical analysis & mathematical development, revitalizing it