Mathematical Proofs Courses and Certifications

Explosive Proofs of Mathematical Truths

Explore how mathematical proofs achieve certainty through network structure, enabling explosive emergence of belief even under skepticism. Data science analysis reveals insights into proof validity and mathematical reasoning.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

The Royal Institution

Why Does Maths Give Humans the Edge Over Machines? - With Junaid Mubeen

Exploring human mathematical intelligence and its advantages over machines, highlighting reasoning, imagination, and questioning as key principles that give humans an edge in problem-solving.

• YouTube
• 58 minutes
• On-Demand
• Free Video

IMSA

A More Comprehensible Proof of the Reductive Shafarevich Conjecture

Explore a new, more comprehensible proof of the reductive Shafarevich conjecture in complex geometry, connecting non-abelian Hodge theories and presenting recent work on Shafarevich morphisms construction.

• YouTube
• 58 minutes
• On-Demand
• Free Video

The Royal Institution

The Story of Mathematical Proof - From Ancient Greece to Modern Logic

Explore the evolution of mathematical proof across number theory, geometry, topology, and logic, delving into the fascinating gap between natural and real numbers.

• YouTube
• 44 minutes
• On-Demand
• Free Video

Fields Institute

Generators of C0-Semigroups of Weighted Composition Operators

Explore generators of C0-semigroups and weighted composition operators in analytic function spaces, examining key assumptions, proofs, and recent developments in the field.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Michael Penn

A Cornucopia of Proofs

Learn various proof-writing techniques with Michael Penn in less than an hour. Randolph College Math and Science.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

Algorithm and Abstraction in Formal Mathematics - IPAM at UCLA

Explore the paradox of formalized proofs, blending abstraction and computation in mathematics. Discover a new aesthetic that embraces algorithms and cross-referencing in formal mathematical discourse.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Institute for Pure & Applied Mathematics (IPAM)

How to Prove a Calculation Correct? - IPAM at UCLA

Explore alternative methods for proving calculation correctness, focusing on real algebraic geometry and using intermediate information as hints for proof engines.

• YouTube
• 52 minutes
• On-Demand
• Free Video

International Mathematical Union

Lower Bounds on the Top Lyapunov Exponent of Stochastic Systems

Explore lower bounds on top Lyapunov exponents in stochastic systems, examining mathematical techniques and implications for understanding system behavior and stability.

• YouTube
• 49 minutes
• On-Demand
• Free Video

International Mathematical Union

Oded Regev: The Reverse Minkowski Theorem

Explore the Reverse Minkowski Theorem, its applications, and open questions in lattice theory with mathematician Oded Regev in this insightful mathematical lecture.

• YouTube
• 44 minutes
• On-Demand
• Free Video

International Mathematical Union

Composing and Decomposing Surfaces in R^n

Explore surface decomposition in R^n, Lipschitz functions, nonorientability, and their applications in mathematics, with insights on the Heisenberg group.

• YouTube
• 44 minutes
• On-Demand
• Free Video

International Mathematical Union

Georges Gonthier - Computer Proofs - Teaching Computers Mathematics, and Conversely

Explore computer-assisted mathematical proofs, from the four-color puzzle to homotopy type theory. Learn how computer science methods enhance mathematical language, leading to new insights and advancements in formal proofs.

• YouTube
• 47 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Viscosity Solutions Approach to Variational Problems - Daniela De Silva

Explore viscosity solutions for variational problems with Daniela De Silva. Learn about Laplace's equation, Harnack inequality, and discrete equations in this advanced mathematics lecture.

• YouTube
• 55 minutes
• On-Demand
• Free Video

Michael Penn

A Great Proof of the Euler-Mascheroni Constant Identity

Explore a captivating proof of a fascinating mathematical identity, delving into elegant reasoning and surprising connections that illuminate the beauty of number theory.

• YouTube
• 19 minutes
• On-Demand
• Free Video

Fields Institute

The Value of Errors in Proofs

Explore the significance of errors in mathematical proofs with Avi Wigderson. Gain insights into how mistakes contribute to advancing mathematical understanding and problem-solving techniques.

• YouTube
• 43 minutes
• On-Demand
• Free Video