Combinatorics made easy!

Combinatorics as a discipline differs from many other (not all) mathematical disciplines in that it is progressed mostly by problem-solving rather than theory-building. This occurs to such an extent that Sir Timothy Gowers, 1998 Fields medalist and blogger extraordinaire, used “combinatorics“ as a representative of all problem-solving and first-principles fields in his famous work The Two Cultures of Mathematics. The reason why combinatorics relies on problem-solving so much is that there are relatively few over-arching, useful techniques. This has the advantage of making many combinatorial papers fundamentally first-principled, and therefore more or less self-contained. If we compare this to any of the algebraic or analytic fields, so heavily established and coupled with theory and shoulder-standing, we might find combinatorics both refreshingly easy to approach and frustratingly lacking in direction. #Combinatorics #combinations #Permutations #problemSolving #statistics #logicalThinking #Genetics #math