A Beautiful Identity in Mathematics - Exploring Elegant Mathematical Relationships
Discover an elegant mathematical proof exploring a fascinating identity that connects different mathematical concepts in a clear and intuitive way.
Riemann Hypothesis and the DeBruijn-Newman Constant
Delve into advanced mathematical concepts exploring the Riemann Hypothesis and DeBruijn-Newman constant through expert analysis of their properties, relationships, and significance in number theory.
Class Field Theory Standpoint and Its Three Fundamental Generalisations - Lecture 2
Delve into advanced class field theory concepts, exploring Takagi's existence theory, Mochizuki's IUT theory, and modern perspectives on Langlands program and anabelian geometry.
Curve Counting, Geometric Representation Theory, and Quantum Integrable Systems - Lecture 2
Delve into advanced mathematical concepts exploring curve counting, geometric representation theory, and quantum integrable systems with Professor Andrei Okounkov's expert analysis and insights.
Solving a Math Puzzle - Henry and the 32 Hogs Marriage Problem
Dive into a challenging mathematical puzzle involving couples at a farm auction, using factoring and Diophantine equations to determine spousal relationships.
Stringing Madhava's Pi - A Quantum Field Theory Perspective
Delve into quantum field theory's connection to Madhava's historical calculation of pi, exploring mathematical principles and their modern theoretical physics applications.
Real Numbers
Comprehensive overview of real numbers, covering rational and irrational numbers, integers, and decimals. Includes practice problems and examples for better understanding.
What Is the Riemann Hypothesis?
Explore the Riemann Hypothesis, convergent series, and Euler's solutions in this engaging introduction to complex mathematical concepts and their implications.
The Million Dollar Equations - With Tom Crawford
Explore four of the seven unsolved million-dollar math problems, including the Riemann hypothesis and P vs NP, with Oxford mathematician Tom Crawford in this engaging lecture on complex mathematical concepts.
The Power of Mathematical Visualization - The Power of a Mathematical Picture
Discover the power of visual mathematics with Professor James S. Tanton, exploring innovative problem-solving techniques across various mathematical fields through engaging graphics and practical projects.
Basic Maths for DSA - Sieve - Modular Arithmetics - Euclid’s Algorithm
Learn essential mathematical concepts for DSA: Sieve method for prime numbers, Euclid's algorithm for GCD/LCM, and modular arithmetic with fast exponentiation. Includes code examples and problem-solving techniques.
Secret of Row 10 - A New Visual Key to Ancient Pascalian Puzzles
Explore hidden patterns in Pascal's triangle and snail shells through a visual key, featuring Sierpinski's triangle and modular arithmetic in this fascinating mathematical journey.
The Golden Ratio Spiral - Visual Infinite Descent
Explore number-associated spirals, infinite descent proofs, and continued fractions. Debunk golden ratio myths while gaining insights into number properties through visual representations.
Liouville's Number, the Easiest Transcendental and Its Clones
Explore Liouville's number, its transcendental nature, and a unique proof of its transcendence. Discover how to create paradoxical clones of real numbers using this fascinating mathematical concept.
The Big Mathematics Divide - Between "Exact" and "Approximate" - Sociology and Pure Maths
Explores the divide between exact and approximate theories in pure mathematics, challenging conventional views on arithmetic, algebra, topology, and number theory, including the Riemann Hypothesis.
A Multiset Approach to Arithmetic - Math Foundations
Explore a new framework for arithmetic using multisets, introducing natural numbers, polynumbers, and multinumbers. Learn innovative definitions and operations that offer profound insights into mathematical structures.
Circles and Spheres via Dot Products II - Wild Linear Algebra A
Explore 3D Euclidean dot products, quadrance, linear functionals, and spheres. Learn about projections, Pythagoras' theorem, and perpendicularity in three-dimensional space.
Algebraic Number Theory and Rings I - Math History - NJ Wildberger
Explore algebraic number theory and rings, focusing on extension fields, Gaussian integers, and the development of abstract ring theory in 19th-century mathematics.
Dot Products, Pythagoras' Theorem, and Generalizations - Wild Linear Algebra A - NJ Wildberger
Algebraic approach to metrical geometry using dot products and quadrance. Introduces symmetric bilinear forms for understanding relativistic geometry, with applications to linear algebra and physics.
Hypercomplex Numbers - Math History - NJ Wildberger
Explore hypercomplex numbers, their historical development, and connections to geometry and number theory. Discover quaternions, octonians, and their surprising links to ancient mathematical formulas.
How to Set Up Fractions IV - The Relation Between Fractions and Other Number Systems
Explore number systems, focusing on rational numbers and their relationships. Challenges traditional views on real numbers, emphasizing the distinction between counting and measuring in mathematics.