Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free, and hurry—the first 200 people get 20% off an annual premium subscription. 0:00 Multiplying Matrices the standard way 2:05 The Strassen Method for 2x2 Matrices 3:52 Large matrices via induction 7:25 The history and the future 10:19 brilliant.org/TreforBazett In this video we explore how to multiply very large matrices as computationally efficiently as possible. Then standard algorithm from linear algebra results in n^3 multiplications to multiply nxn matrices. But can we do better? The Strassen algorithm improved this to about n^2.8, first in the 2x2 case and then we can prove via induction it works in general. This improvement has seen a range of improvements over the last 50 years inching closer - but still far away - to the theoretically limit of n^2. Further Reading: Going into the details of the laser method (what happened after the Strassen algorithm I showed): https://theoryofcomputing.org/articles/gs005/gs005.pdf The AlphaTensor AI paper: https://www.nature.com/articles/s41586-022-05172-4 A nice summary from Quanta: https://www.quantamagazine.org/mathematicians-inch-closer-to-matrix-multiplication-goal-20210323/ Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://beautifulequations.net/pages/trefor COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...   ► CALCULUS II:    • Calculus II (Integration Methods, Ser...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus ...   ►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line In...   ►DIFFERENTIAL EQUATIONS:    • Ordinary Differential Equations (ODEs)   ►LAPLACE TRANSFORM:    • Laplace Transforms and Solving ODEs   ►GAME THEORY:    • Game Theory   OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0 ►Cool Math Series:    • Cool Math Series   BECOME A MEMBER: ►Join: null MATH BOOKS I LOVE (affilliate link): ► https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography