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What is cutting edge maths? - Mathematics Stack Exchange My maths teacher always keeps telling me about this 'cutting edge maths' that is going on in the world, amazing maths research, etc A lot of the google searches I've done for 'Cutting Edge Mathematics' hasn't returned much useful information, so I've taken to mathematics stack exchange
Minimum Spanning Tree (MST): Cut property direct proof I'm trying to fully understand the cut property in the concept of minimum spanning trees (MST) in graph theory and graph algorithms It seems that all the literature out there proves this theorem via
Why can algebraic geometry be applied into theoretical physics? As I progressed in math graduate school specializing in number theory and algebraic geometry, it was astounding to discover a certain class of researchers who were doing very serious and nontrivial cutting-edge stuff connecting algebraic geometry and mathematical physics
combinatorics - Let G be a connected graph in which every vertex has . . . The edge v v - v1 v 1 (or v v - v2 v 2 or v v - v3 v 3) was a bridge when V V was removed, connecting v1 v 1 to that component Therefore the deletion of v v - v1 v 1 disconnects G G But this is a contradiction since we said G G has no cut-edge Another method is to first see that G G has no loops; if it did, it would contain a cut-edge
general topology - Examples of the difference between Topological . . . 32 There is apparently cutting-edge research by Dustin Clausen Peter Scholze (and probably others) under the name Condensed Mathematics, which is meant to show that the notion of Topological Space is not so well-chosen, and that Condensed Sets lead to better behaved structures What is a simple low-tech example to see the difference?
combinatorics - A visual solution to the cube cutting problem . . . You will find that each tetrahedron is made by piecing together two isosceles right triangles with edge lengths 1 1, 1 1, 2–√ 2, and two right triangles with edge lengths 1 1, 2–√ 2, 3–√ 3 This is something you can actually build by cutting the pieces from card stock and taping them together
Is the Study of Random Numbers part of Number Theory I think the deal is essentially that, once you dig deep, the bodies of theory on which number theory and probability theory are grounded are largely disjoint (abstract algebra and measure theory, resp ) As a result, since one can rarely study more than one subject at a cutting edge level, people tend to be specialized in one or the other, but not both That said, I'm sure that people exist
What is a proper face of a graph? - Mathematics Stack Exchange The paper On the Cutting Edge: Simplified O(n) Planarity by Edge Addition by John Boyer and Wendy Myrvold uses the term quot;proper face quot; I do not know what this term means At a guess, perh
For someone who loves mathematics - Mathematics Stack Exchange Specializing towards communications on the broad sense (network traffic problems, information theory, silicon chip design and logic, filter design, control ) can get pretty cutting edge mathematically How deep you go depends on what a particular department might specialize in as far as research goes
What is the difference between elementary and advanced math? Pell's equation is quite easy to solve, Pythagorean triples were known to the Babylonians, Fermat's Last Marginalium lasted hundreds of years and requires cutting-edge work on general elliptic curves Bisecting an angle is easy with straightedge and compass, trisecting an angle is impossible without neusis The area of a cirle is πr2 π r 2