If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is “simply connected,” but that the surface of the doughnut is not. Poincaré, almost…

As a pure mathematician Newton reached his climax in the invention of the calculus, an invention also made independently by Leibniz. But do you know that, Fermat conceived and applied the leading idea of the differential calculus thirteen years before Newton was born and seventeen before Leibniz was born. Today we are going delve into Fermat’s last work, whose proof took three and a half centuries to hail again after Fermat. Its nothing but Fermat’s Last Theorem. We will start to take our steps towards the brilliance of this theorem by learning a bit about the Pythagorean Triples.Pythagorean triples have…