The heart of the matter is written by Graham Green who was born on 2nd October the year 1904 in England. Graham Green went to a school where his father was the principal. His father being the principal of the school that Graham green attended, it resulted to him being mercilessly teased by his classmates. While in his teenage, Green underwent a mental crisis. So bad was the situation that he tr...

Ever since Higman’s ground-breaking work $1, there have been many rank 3 characterizations of the classical symplectic, unitary and orthogonal groups and geometries. The purpose of this paper is to add another such characterization to that pile. Take a finite symplectic, unitary or orthogonal geometry having a totally singular (projective) plane. Let R be the number of singular points # x ortho...

Recently there has been substantial progress towards computing the mod 2 cohomology of low rank sporadic simple groups. In fact the mod 2 cohomology of every sporadic simple group not containing (Z/2) has been computed, with the notable exceptions of HS (the Higman–Sims group) and Co3 (one of the Conway groups). The reason for these exceptions is that these two groups have large and complicated...

A particular case of a conjecture of Erdös and Graham, which concerns the number of integer points on a family of quartic curves, is investigated. An absolute bound for the number of such integer points is obtained.