A Possible Proof of Collatz Conjecture
A reader sent me something bold: a claimed proof of the Collatz Conjecture. Eswar Chellappa spent nearly ten years working…
Math
Mathematics Blog by Gaurav Tiwari. This section is dedicated to exploring various mathematical concepts and theories, transcending the boundaries of traditional high school and early college curriculums.
The mathematics topics here encompass various subfields, including algebra, calculus, number theory, geometry, topology, and more.
15 Best Online Communities a Math Major Should Join
Math communities aren't just forums. They're where you sharpen your thinking against other sharp minds. I've curated 15 online communities…
Functional Analysis: Essential Definitions From Normed Spaces to Hilbert Spaces
Functional analysis is where linear algebra meets topology. It's the mathematical backbone of quantum mechanics, signal processing, and machine learning.…
TeXstudio Review: The Most Complete Free LaTeX Editor in 2026
I first installed TeXStudio in 2012. 'Peaceful' was the word I used to describe it, and that hasn't changed through…
How to change Differential Equations into Integral Equations?
Every differential equation can be converted into an integral equation. Just integrate it. Sounds too simple, right? The details matter…
Square Integrable Functions, Norms, and the Trial Method
Part II of the integral equations series. Covers L2 spaces, inner products, norms, Schwarz inequality, and solving integral equations by…
Definitions and Types of Integral Equations
Integral equations look intimidating, but they're built from ideas you already know. I explain what integral equations are, their classification…
Complete Elementary Analysis of Ramanujan’s Nested radicals
I wrote this analysis in 2010 at age 17, obsessed with Ramanujan's nested radicals while studying under the INSPIRE-SHE scholarship.…
Hopalong Orbits Visualizer: The Math Behind the Most Beautiful WebGL Experiment
Barry Martin's Hopalong attractor turns three lines of algebra into galaxy-like structures rendered in real-time 3D. Here's the mathematics behind…
Real Sequences: Definitions, Theorems, and Examples
Real sequences form the backbone of real analysis and advanced calculus. I've taught this topic to dozens of students, and…
Euler’s (Prime to) Prime Generating Equation
Euler discovered a simple formula that generates 40 consecutive prime numbers: n squared plus n plus 41. Plug in 0…
Irrational Numbers and The Proofs of their Irrationality
How do you prove a number is irrational? You can't check infinitely many decimal places. You need a proof. I…