Cold Reflections

Jean Bourgain and the Fourier Spectrum of Boolean Functions

math

philosophy

compartmentalizing subroutines

efficieny

grokking

Jean Bourgain was a Belgian—Fields Medal winning—mathematician who made significant contributions to various fields of mathematics, including analysis, geometry, and number…

Fourier Entropy Influence Conjecture

boolean functions

analysis

probability

math

\[ \newcommand{\Var}{\mathrm{Var}} \newcommand{\E}{\mathbb{E}} \newcommand{\H}{\mathbb{H}} \newcommand{\Inf}{\operatorname{Inf}} \]

Problems to Think About

math

This will be an updating collection of interesting problems. Please email me if you are interested in working with me on any of these problems.

Ideas on DNA Storage

biology

machine learning

Recently, I have been thinking about the DNA storage problem quite a bit. It’s been something extremely interesting to me. Asking ChatGPT for DNA storage system use-cases…

[DRAFT] Some Important Results in Probability Theory

probability

math

[DRAFT] Language is an Infinitely Incomplete Approximation of Human Concepts

philosophy

cognition

math

I had thought of this idea last year, but never got around to writing it. In this blog, I show how humans are infinitely limited by the mode of language in transmission of…

How to get AGI?

artificial intelligence

artificial general intelligence

philosophy

Here is an excerpt from a brilliant conversation ¹ between Dwarkesh Patel and François Chollet.

Ponderings on OthelloGPT

machine learning

artificial intelligence

interpretability

This is a report of sorts of my playing around with OthelloGPT, a GPT model trained on Othello games to predict all the possible legal moves.

So Far Yet So Close: How Independence is Almost Dependence

probability theory

statistics

math

Imagine two continuous random variables seemingly unrelated and free from any influence from each other. It’s a common assumption in probability theory that independence…

\(k+1\) points uniquely determine a \(k\) degree polynomial: A cool problem

algebra

math

Reading the title: you are probably shouting “Lagrange Interpolation!!!” Yeah, sure, Lagrange is cool. But I will show you something cooler which ensures you don’t have to…

Axiom of Choice, the Zorn’s Lemma, and the Foundations of Mathematics: Set Theory Part I

set theory

math

Mathematics has long been built on the sturdy foundation of intuition. From counting pebbles to solving complex equations, mathematicians have relied on their inner compass…

Shannon’s Card Magic Trick

isi

statistics

math

This was my statistics project at ISI Sem 1. My team had: Myself, Siddhartha, Ayan, Drishti, Aman, Mrittika. Thanks to everyone for their efforts.