The language of forms (A journey from the Mobius strip to affine Kac-Moody and superconformal algebras)

One of the most recurrent themes in Geometry, is the study of objects that locally look the same. I will explain, mainly via examples and in non-technical terms, how the concept of 'locally look the same' has evolved through time (mostly through some beautiful ideas of Serre and of Grothendieck).