Why Grothendieck would say machine learning is mostly overfitting

Introduction Grothendieck is, by far, the single most influential mathematician of the 20th century. He solved long standing mathematical problems, created whole new fields of human thought, and then spectacularly abandoned it all when his institute refused to accept military funding. The overarching theme of all his research was that when we study mathematical concepts,Continue reading “Why Grothendieck would say machine learning is mostly overfitting”

Sheaf (Čech) Cohomology: A glimpse

This is a blogpost on Sheaf Cohomology. We shall be following this article. If the reader wants to read up on what a sheaf is, he/she can read the very readable wikipedia article on it. From the word cohomology, we can guess that we shall be talking about a complex with abelian groups and boundaryContinue reading “Sheaf (Čech) Cohomology: A glimpse”

Nakayama’s lemma

The Nakayama lemma as a concept is present throughout Commutative Algebra. And truth be told, learning it is not easy. The proof contains a small trick that is deceptively simple, but throws off many people. Also, it is easy to dismiss this lemma as unimportant. But as one would surely find out later, this wouldContinue reading “Nakayama’s lemma”

Algebraic Geometry 4: A short note on Projective Varieties

What is a variety? It is the set of common zeroes for a set of polynomials. For example, for the set of polynomials , the variety is . Now what is a projective variety? Simply put, it is the common set of zeroes of polynomials in which a one-dimensional subspace is effectively considered one point.Continue reading “Algebraic Geometry 4: A short note on Projective Varieties”