Courses

Discover how mathematician and cryptographer Jim Simons applied complex mathematical concepts to revolutionize the world of finance in this 23-minute TED talk. Explore Simons' journey from breaking codes to breaking financial markets, resulting in billions in profits. Learn about his transition to philanthropy, supporting math education and scientific research. Gain insights into topics such as algebraic topology, predictive analytics, and the hedge fund industry. Delve into Simons' perspectives on the effectiveness of mathematics in various fields and his efforts to support the next generation of math teachers and scholars. Understand the impact of his work on Wall Street and his contributions to mathematical and scientific advancements.

Watch an Oxford University mathematician react to and analyze popular math riddles from a viral YouTube video. Explore nine challenging puzzles as Dr. Tom Crawford provides expert insights, explanations, and solutions. Learn problem-solving techniques and mathematical concepts while enjoying the mathematician's engaging commentary on riddles designed to stump even the smartest individuals. Gain a deeper understanding of mathematical thinking and improve your own problem-solving skills through this entertaining and educational video reaction.

Delve into an insightful 27-minute interview with Professor Noga Alon, recipient of the 2022 Shaw Prize in Mathematics, as he discusses his prolific career spanning over 600 publications. Explore the interdisciplinary nature of Alon's work, touching on fields such as Biology, Economics, and Neuroscience. Gain valuable insights into how a renowned mathematician selects research questions and approaches unsolved problems like the Collatz Conjecture, Goldbach's Conjecture, and P vs NP. Discover Alon's contributions to 'necklace splitting' and the Borsuk-Ulam Theorem, and hear a captivating childhood anecdote involving the Eurovision Song Contest that solidified his belief in mathematics' objectivity. Access links to additional interviews with distinguished mathematicians and computer scientists, and explore Alon's full list of publications and Shaw Prize acceptance speech for further learning.

Watch as University of Oxford mathematician Dr. Tom Crawford tackles questions from the Oxford Physics Admissions Test (PAT) in this collaborative video with Zhelyo from @zhelyo_physics. Explore multiple-choice questions and a problem on gravitational force from the 2018 PAT, gaining insight into the exam taken by Oxford undergraduate Physics applicants. Learn about the challenges faced by a mathematician attempting physics problems, and discover links to additional resources, including the full exam paper and a companion video where Zhelyo attempts the Oxford Maths Admissions Test (MAT). Gain valuable exposure to university-level physics concepts and admissions test strategies in this engaging educational content produced by Dr. Crawford, the Public Engagement Lead at Oxford University's Department of Continuing Education.

Watch as a University of Oxford mathematician takes on the AP Calculus BC exam without preparation in this 1-hour 21-minute video. Observe Dr. Tom Crawford tackle the highest level of AP Calculus exams, typically taken by American high school students for college applications. Access the 2022 exam paper and mark scheme for Section II, Part B (non-calculator) through provided links. Learn about various math exams as Dr. Crawford demonstrates his problem-solving skills. Explore additional videos of the mathematician attempting other exams, including A-level Maths, GCSE Maths, SAT Maths, and university admissions tests. Discover more mathematical content on Tom's website and social media channels, and find merchandise options for math enthusiasts.

Watch an Oxford University mathematician tackle the YKS TYT exam, Turkey's standardized high school mathematics test, in this educational video. Follow Dr. Tom Crawford as he works through the challenging problems that Turkish students face, providing insights into different mathematical approaches and problem-solving techniques. Observe how an academic mathematician approaches unfamiliar exam formats and question styles, demonstrating mathematical reasoning and calculation methods in real-time. Learn about the structure and difficulty level of Turkey's university entrance examination system while seeing mathematical concepts explained from a university-level perspective. Gain exposure to international mathematics education standards and compare problem-solving strategies across different educational systems. The video includes access to both the original Turkish exam paper and an English translation, allowing viewers to follow along and attempt the problems themselves.

Watch a collaborative challenge video where University of Oxford mathematician Dr Tom Crawford attempts to solve a complex physics problem from the 2010 International Physics Olympiad (IPHO), guided by physics educator Zhelyo. Explore the intersection of advanced mathematics and physics as an expert mathematician tackles a challenging chimney physics problem involving solar updraft tower systems and convective flows. Discover how mathematical reasoning applies to real-world physics scenarios, including the theoretical foundations behind chimney design and solar energy systems. Learn about the problem-solving approaches used in international olympiad competitions and observe the collaborative process between mathematics and physics experts. Gain insights into the historical context of chimney physics dating back to early 20th century engineering principles and modern applications in solar power generation. Experience the intellectual challenge of cross-disciplinary problem solving and see how mathematical expertise translates to physics applications in this engaging educational collaboration.

Explore the world of pure mathematics in this engaging video lecture. Gain insights into the daily life and work of a pure mathematician, dispelling common misconceptions and delving into the fascinating realm of abstract algebra. Learn about group theory, partitions, and generating functions through practical examples and elegant proofs. Discover the beauty of mathematical logic and problem-solving as the lecturer demonstrates the intricate thought processes involved in tackling complex mathematical concepts. Develop a deeper appreciation for the theoretical aspects of mathematics and how they relate to real-world applications.

Explore the fascinating life and contributions of Thales of Miletus in this 13-minute educational video. Discover how this ancient Greek philosopher, astronomer, and mathematician became known as the father of demonstrative mathematics and one of the seven sages of Greece. Learn about his pioneering use of logical deduction to prove claims of elementary geometry, his clever solution to the olive harvest problem, and his innovative method for measuring the Great Pyramid. The video delves into both the historical accounts and legendary stories surrounding this nearly mythological figure, including famous anecdotes about wells, mules, and philosophical questions. Follow along as mathematical proofs are explained and appreciate how Thales' foundational work in geometry shaped the development of mathematics as we know it today.

Watch as Oxford University mathematician Dr. Tom Crawford takes on the challenge of solving A-level Physics exam questions in this engaging video collaboration with Lewis from @PhysicsOnline. Explore topics including force diagrams, projectile motion, and various multiple-choice questions from the OCR 2020 A Level Physics exam. Access accompanying resources, including a Maple Learn worksheet with practice problems and links to the original exam paper and mark scheme. Gain insights into problem-solving approaches and the intersection of mathematics and physics as an expert mathematician tackles high school-level physics problems.

Explore recent advances in mathematical formalization through a conference talk that presents Gauss, a new AI agent designed to assist working mathematicians with formal proof development. Learn about the successful formalization of the Prime Number Theorem in strong form using Lean, which completed a challenge posed by Alex Kontorovich and Terry Tao in January 2024. Discover how this innovative approach aims to make formal mathematics more accessible to mathematicians who don't typically write formal code themselves, potentially bridging the gap between traditional mathematical practice and computer-verified proofs. Gain insights into the current state of autoformalization technology and its potential impact on mathematical research and verification processes.

Explore the mathematical concept of tensors in this 27-minute video lecture. Gain a deeper understanding of tensors from a mathematician's perspective, learning their definition, properties, and applications in various fields of mathematics and physics. Discover how tensors generalize the notion of scalars, vectors, and matrices, and how they are used to represent multilinear maps between vector spaces. Delve into the abstract algebraic structure of tensors and their importance in differential geometry, relativity theory, and other advanced mathematical topics.

Explore the intersection of deep learning and mathematics in this 52-minute lecture by Geordie Williamson from the University of Sydney. Discover the potential impact of artificial intelligence on mathematical research and problem-solving. Gain insights into how deep learning techniques can be applied to various mathematical domains and learn about the expectations working mathematicians should have regarding this emerging technology. Part of the 2022 Fields Medal Symposium honoring Akshay Venkatesh, this talk provides a thought-provoking examination of the future relationship between deep learning and mathematical practice.

This Friends Talk explores the forgotten legacy of mathematician Hel Braun, a Member (1947–1948) in the School of Mathematics at the Institute for Advanced Study. Join Ellen Eischen, von Neumann Fellow in the School of Mathematics, as she reveals her research on Braun's remarkable contributions and the challenges she faced. Discover how archival documents and correspondence helped piece together Braun's inspiring story and correct misconceptions about her life and work. Learn how non-mathematical factors including immigration, gender, politics, and unrequited love shaped Braun's mathematical legacy, challenging the notion that mathematics exists separately from human concerns. No mathematical expertise is required for this accessible talk that examines how these themes influence knowledge formation even in pure mathematics. The talk will take place on May 8, 2025, at 5:30 p.m. in Meeting Room 5 of the Rubenstein Commons.

Explore the SIR model, one of the simplest disease models used to explain virus spread through populations, in this 25-minute educational video. Learn about the model's origins, underlying assumptions, and equation derivations before delving into three crucial questions: the likelihood of disease spread, maximum simultaneous infections, and total infection count. Examine these concepts in the context of the COVID-19 outbreak, understanding how lowering the 'contact ratio' through social distancing measures can reduce the disease's impact. Gain insights from an Oxford mathematician's explanation, with timestamps provided for key topics. Discover additional resources, including follow-up videos on Travelling Wave solutions and Incubation Time in the SIR model, as well as links to the presenter's website and social media profiles for further mathematical content.

This lecture continues the series on resolution of singularities aimed at non-experts, particularly foliation specialists. In the second talk titled "Resolution of singularities in characteristic 0 - how does it work?", Dan Abramovich builds upon the criterion established in the first lecture, demonstrating how it holds true in characteristic 0. The presentation is part of joint work with André Belotto da Silva, Michael Temkin, and Jaroslaw Wlodarczyk. Explore this mathematical lecture recorded during the thematic meeting "Foliations, birational geometry and applications" held on February 4, 2024, at the Centre International de Rencontres Mathématiques in Marseille, France. Access this video and other talks by mathematicians worldwide through CIRM's Audiovisual Mathematics Library, which offers features like chapter markers, keywords, abstracts, bibliographies, and multi-criteria search capabilities.

This lecture is the first in a series aimed at introducing resolution of singularities to non-experts, particularly foliation specialists. Join Dan Abramovich as he continues his effort to explain why resolution of singularities in characteristic zero works, focusing on a crucial criterion from Wlodarczyk's article that outlines the necessary elements for resolving singularities. The presentation is part of joint work with André Belotto da Silva, Michael Temkin, and Jaroslaw Wlodarczyk, recorded during the thematic meeting "Foliations, birational geometry and applications" on February 3, 2024, at the Centre International de Rencontres Mathématiques in Marseille, France. Access this video and other mathematical talks on CIRM's Audiovisual Mathematics Library, which offers features like chapter markers, keywords, abstracts, bibliographies, and multi-criteria search capabilities.

This lecture, the third in a series, explores resolution of singularities in characteristic 0 with a focus on foliated aspects. Learn about resolution and principalization on foliated manifolds and their implications for resolving foliations. The presentation is part of Dan Abramovich's work with André Belotto da Silva, Michael Temkin, and Jaroslaw Wlodarczyk, designed specifically for non-experts with foliation specialists in mind. Recorded during the thematic meeting "Foliations, birational geometry and applications" on February 6, 2024, at the Centre International de Rencontres Mathématiques in Marseille, France. Access this video and other mathematical talks on CIRM's Audiovisual Mathematics Library, which offers features like chapter markers, keywords, abstracts, bibliographies, and multi-criteria search capabilities.

Explore the inspiring journey of Dr Nira Chamberlain, president of The Institute of Mathematics and its Applications, in this engaging 23-minute video from the Alan Turing Institute. Discover insights on Black History Month, influential mathematicians throughout history, and how mathematics transcends racial, geographical, and cultural boundaries. Gain motivation and perspective on pursuing excellence in mathematics without seeking external validation.

Explore a thought-provoking seminar presentation where Professor Yang-Hui He from the London Institute for Mathematical Sciences delves into the intersection of artificial intelligence and mathematics. Learn how AI approaches mathematics through three key methodologies: theorem-proving, conjecture formulation, and language processing. Drawing from experiments in geometry and string theory, discover practical applications of machine learning algorithms in pattern detection across various mathematical disciplines, including algebraic geometry, representation theory, combinatorics, and number theory. Part of the "Black holes: bridges between number theory and holographic quantum information" event series, this 102-minute talk demonstrates the transformative potential of AI in advancing mathematical research and understanding.