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In maths you learn to solve problem by expanding the abstractions by adding new elements. There is a crucial difference between problems easy to solve by repeti

In maths you learn to solve problem by expanding the abstractions by adding new elements. There is a crucial difference between problems easy to solve by repetition and problems that require some insight.

lokiboi 10y ago
Exactly, otherwise all those IOI and IMO contestants would be pure geniuses, probably they are, but they practiced a lot to be good at a single task - problem solving in programming or mathematics for competitions. That's a good foundation built on insane amounts of repetition and memorization, but still, not many turn out to be Terence Tao or Peter Shor. Although https://en.wikipedia.org/wiki/List_of_International_Mathematical_Olympiad_participants#Notable_participants https://en.wikipedia.org/wiki/List_of_International_Mathemat... seems many did "pivot" from competitive memorization and repetition to some lovely mathmakers.
- tamana 10y ago
  You don't get to the IMO by mere memorization.
  - lokiboi 10y ago
    Pattern matching is huge contributor to solving problems fast or even having the problems reachable. Just checkout these results https://icpc.baylor.edu/scoreboard/ https://icpc.baylor.edu/scoreboard/ They practically solve a very hard problem (it might take days for me to solve it) in 5 minutes. If that is not some supreme pattern matching then I don't know what it is. Bunch of proof strategies used in math competitions are the same. You have to have a giant knowledge of algorithms: fast fourier transform, bfs, dfs, iterative deepening, dijkstra, a*, sweep line algs, practically have to master dynamic programming (there's DP on trees, hidden markov model like DPs etc.), flood fill, topological sort, bipartite graph checks, kruskal, prim, edmonds karp, bunch of combinatorics, geometry algorithms. data structures like segment trees, fenwick tree, suffix trees, etc. you see where I'm going, there's a lot of memorization, and a lot of repetition (which improves memorization). same thing goes for IMO, you have to do a lot of proofs, have to memorize and repeat a bunch of proof strategies in a huge number of mathematical areas. memorization and repetition!

lokiboi 10y ago

Exactly, otherwise all those IOI and IMO contestants would be pure geniuses, probably they are, but they practiced a lot to be good at a single task - problem solving in programming or mathematics for competitions. That's a good foundation built on insane amounts of repetition and memorization, but still, not many turn out to be Terence Tao or Peter Shor. Although https://en.wikipedia.org/wiki/List_of_International_Mathematical_Olympiad_participants#Notable_participants https://en.wikipedia.org/wiki/List_of_International_Mathemat... seems many did "pivot" from competitive memorization and repetition to some lovely mathmakers.

tamana 10y ago
You don't get to the IMO by mere memorization.
- lokiboi 10y ago
  Pattern matching is huge contributor to solving problems fast or even having the problems reachable. Just checkout these results https://icpc.baylor.edu/scoreboard/ https://icpc.baylor.edu/scoreboard/ They practically solve a very hard problem (it might take days for me to solve it) in 5 minutes. If that is not some supreme pattern matching then I don't know what it is. Bunch of proof strategies used in math competitions are the same. You have to have a giant knowledge of algorithms: fast fourier transform, bfs, dfs, iterative deepening, dijkstra, a*, sweep line algs, practically have to master dynamic programming (there's DP on trees, hidden markov model like DPs etc.), flood fill, topological sort, bipartite graph checks, kruskal, prim, edmonds karp, bunch of combinatorics, geometry algorithms. data structures like segment trees, fenwick tree, suffix trees, etc. you see where I'm going, there's a lot of memorization, and a lot of repetition (which improves memorization). same thing goes for IMO, you have to do a lot of proofs, have to memorize and repeat a bunch of proof strategies in a huge number of mathematical areas. memorization and repetition!