Contributed Articles

A COOPERATION TO BUILD ‘THE FOUNDATIONS OF SYMPLECTIC GEOMETRY’

By Kenji Fukaya Recently there has been a discussion among mathematicians, as well as in press and several blogs, covering the developments in symplectic geometry. Professor Fukaya expressed interest in giving his opinion and we are happy to present it here: The set of the solutions of the equation x2 + y2 – z2 = … Read more

Two And Two Make Four. By Simon Donaldson

By Simon Donaldson If we have four objects—say A, B, C, D—there are just three ways of dividing them into pairs: (AB)(CD) (AC)(BD) (AD)(BC). The salient property is that 3 is less than 4. This simple fact expresses something special about the number 4. For example if we take 6 objects there are 10 ways to divide … Read more