0 like 0 dislike
0 like 0 dislike
What makes math efficient ?

3 Answers

0 like 0 dislike
0 like 0 dislike
what
0 like 0 dislike
0 like 0 dislike
Anything after  "A logical theory" sounds not logical to me
0 like 0 dislike
0 like 0 dislike
I mean, math is not necessarily efficient at all. That's why there's a whole sub-field of computer science dedicated to numerical analysis.

For example, all will be in agreement that the Schrodinger equation is math. However, as of today, there's no uniquely most-efficient algorithm to find it's solutions and observables of interest. In fact it's an NP-hard problem, incredibly costly to solve. There are many workarounds, methods and approximations, which work well under certain limits (perturbation theory, markovian approachs, tensor networks and neural networks as a whole, density functional theory, and many many more), but all have their drawbacks. There's no one-trick pony. Just because math is formalized and rigorous, it doesn't mean it's calculations are efficient.

See for example the 3SUM problem, which is an open problem where we'd like to construct an algorithm to find if a given set of n real numbers contains three elements that sum to zero. It's trivial to solve in O(n\^3) time (loop three times in the array and be done with it), a little more difficult to solve in O(n\^2) time by the means of a binary search but absolutely non-trivial to solve in O(n\^(2-\\epsilon)) time.

Related questions

0 like 0 dislike
0 like 0 dislike
79 answers
coL_Punisher asked Jun 21, 2022
Regretting majoring in math
coL_Punisher asked Jun 21, 2022
0 like 0 dislike
0 like 0 dislike
2 answers
a_dalgleish asked Jun 21, 2022
Contributing to the right math area, If all areas are equally curious
a_dalgleish asked Jun 21, 2022
0 like 0 dislike
0 like 0 dislike
47 answers
countykathleen asked Jun 21, 2022
Is it possible to suck at rigor of math but great at intuition?
countykathleen asked Jun 21, 2022
0 like 0 dislike
0 like 0 dislike
6 answers
Aiden_Zhane asked Jun 21, 2022
I need an idea for a gift fot my math teacher!
Aiden_Zhane asked Jun 21, 2022
0 like 0 dislike
0 like 0 dislike
13 answers
angiemartoccio asked Jun 21, 2022
Why does math make no sense to me?
angiemartoccio asked Jun 21, 2022

33.4k questions

135k answers

0 comments

33.7k users

OhhAskMe is a math solving hub where high school and university students ask and answer loads of math questions, discuss the latest in math, and share their knowledge. It’s 100% free!