Russian Peasant Multiplication: The Ancient Method That Uses Only Doubling and Halving
Russian Peasant Multiplication is an ancient technique that multiplies any two numbers using only doubling and halving. No multiplication tables…
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.
How Your Brain Tricks You With Simple Math (And What It Says About Intelligence)
Most people get this simple addition problem wrong: 1000 + 40 + 1000 + 30 + 1000 + 20 +…
Fox-Rabbit Chase Problem [Solution & Math Proof]
Pursuit problems are some of the most elegant challenges in classical mechanics. A fox chases a rabbit, both moving at…
Everywhere Continuous, Nowhere Differentiable: The Weierstrass Function and Why It Matters
In 1872, Weierstrass presented a function that's continuous everywhere but differentiable nowhere. It shattered the assumption that smooth curves are…
Free Online Calculus Text Books
I've spent years collecting free calculus textbooks. Not scanned copies with missing pages. Real textbooks that professors and universities have…
Dedekind’s Theory of Real Numbers
Most math students use real numbers without ever understanding how they're constructed. Dedekind solved this with his theory of cuts.…
20+ Free Algebra Books for Students & Teachers (PDF Ebooks)
I've compiled 20+ free algebra and topology ebooks. Not sketchy PDFs from torrent sites. Real textbooks that professors and universities…
D’Alembert’s Ratio Test for Convergence of Series
The D'Alembert Ratio Test is one of the most reliable tools for determining whether an infinite series converges or diverges.…
How to Solve Math Problems: Polya’s Method and Beyond
George Polya's four-step method has guided mathematicians since 1945. Understand the problem, devise a plan, carry it out, look back.…
Bhaskara II’s Lilavati: Complete Reference Guide (2026 Edition + PDF)
Lilavati is a 12th-century mathematics treatise that reads like poetry — arithmetic, algebra, and geometry wrapped in riddles about bees,…
The Collatz Conjecture: The Simplest Problem Nobody Can Solve
Pick any positive integer. If it's even, halve it. If it's odd, triple it and add one. Repeat. You always…
Dirichlet’s Theorem and Liouville’s Extension of Dirichlet’s Theorem
The Dirichlet theorem connects the Gamma and Beta functions to evaluate complex multiple integrals. Liouville extended it further, making it…