Everything tagged mathematics, newest first. Tags come from the classifier reading each item's summary; 394 tags used 25 times or more have their own page.
A $1 million prize is offered for the first valid solution to the Navier-Stokes existence and smoothness problem, one of the Clay Mathematics Institute’s Millennium Prize Problems.
AI has rapidly advanced in solving complex mathematical problems, surpassing human achievements and raising concerns about its impact on mathematical research and practices.
The puzzle challenges us to find the expected number of intersection points from 10 or 100 random chords on a circle, considering Bertrand's paradox in choosing random chords.
The complexity of long division is mirrored in computers, where division is significantly slower than other operations, prompting compilers to use clever tricks to optimize calculations, such as simplifying division by using multiplication and rounding techniques.
The puzzle involves tying random string ends together until only loops remain, and asks how many loops result from starting with 50 strings, with solutions available on Patreon.
IPv6's complexity stems from essential mathematical requirements, and despite its challenges, an IPv8 proposal would face significant hurdles and lack the decades-long development of IPv6.
MC Escher's 1956 lithograph "The Print Gallery" presents a paradoxical scene analyzed by mathematicians, revealing a unique logarithmic perspective that challenges spatial perception and centers around a mysterious blank spot.
The video explores the intricate process of animating and understanding M.C. Escher's "Print Gallery," highlighting its mathematical depth and the concept of the Drosta effect, while attempting to visually unpack the analysis by mathematicians De Smit and Lenstra.
The puzzle involving bacterial replication on a grid reveals that it's impossible to clear a 16-point lattice box due to the fixed weighted sum of cells, proving that bacteria cannot escape even smaller boxes like the 3x3 grid.
Machine learning models use linear algebra to translate images, texts, audios, and videos into mathematical objects like scalars, vectors, matrices, and tensors, enabling computers to process and analyze data for tasks such as distinguishing between images of dogs and cats.
The speaker discusses the underappreciated mathematical formula related to probability and geometry, emphasizing understanding its origins and representation through puzzles involving random numbers and geometric shapes.
The puzzle explores the probability of a ladybug ending on a specific number on a clock, revealing that all numbers from 1 to 11 are equally likely to be the last touched due to the nature of random walks and boundary conditions.
Google's new Gemini 3 Deepthink model, a highly advanced AI optimized for complex reasoning tasks, surpasses previous benchmarks and offers groundbreaking capabilities in fields like mathematics and 3D modeling, although access is limited by a costly subscription.
The hairy ball theorem illustrates a mathematical principle where it's impossible to comb a hairy sphere flat without creating at least one tuft, and this concept is applied in contexts like programming 3D models in games to ensure smooth orientation transitions.
A ladybug randomly moves on a clock face, coloring numbers red, with the puzzle challenge being to determine the probability that the last number colored is 6, as part of a monthly math puzzle series by MoMath and Peter Winkler.
This comprehensive AI research course covers foundational mathematics, PyTorch fundamentals, neural networks, and transformers, equipping learners with the essential knowledge to understand and contribute to AI research.
The claim that GPT-5 has solved numerous previously unsolved mathematical problems is false and lacks credible evidence.
The expression \( e^{\pi i} \) can be understood through dynamics as a function whose velocity is a 90° rotation of its position vector, resulting in a circular motion that, after \(\pi\) seconds, equates to -1.
The expression \( e^{\pi i} \) represents a unique function in dynamics where the velocity is a 90° rotation of the position vector, resulting in circular motion, and after \(\pi\) seconds, it equates to -1.
The first video in a trilogy introduces the foundational concepts and mental frameworks necessary for understanding the Laplace transform, focusing on exponential functions and their applications in physics, while exploring the implications of using complex numbers in exponents.
The final guest video on the channel, created by Ben Syverson, explores Euclid's Elements and the ancient Greek approach to geometry, emphasizing the role of diagrams in proofs, contrasting with modern mathematical practices.
The problem of counting distinct incomplete cube configurations, considering rotational symmetry, is explored through group theory and Burnside's Lemma, inspired by Sol LeWitt's 1974 artwork.
Sol LeWitt's "Variations of Incomplete Open Cubes" is a conceptual art piece that explores mathematical ideas of symmetry and rotation through 122 unique cube variations, demonstrating the intersection of art and mathematics.
On August 20th, 2025, GPT5 Pro solved an open problem in convex optimization with a novel approach, inspiring human researchers to further advance their work, showcasing AI's potential for groundbreaking contributions in mathematics.
In January 2024, Google DeepMind's AI model, Alpha Geometry, solved 25 out of 30 International Mathematical Olympiad geometry problems by integrating a 25-year-old logical technique with AI, outperforming a silver medalist and highlighting the potential of combining traditional logic with AI.
A non-mathematical AI model has reportedly achieved human-level speeds in solving proofs, causing a stir within the community due to its early disclosure.
Simulated annealing is an effective algorithmic approach for efficiently solving complex scheduling problems by mimicking the cooling process of metals to find optimal solutions.
This comprehensive course by Lun Tech Academy covers essential linear algebra concepts for machine learning, equipping learners with the mathematical foundations needed to excel in AI and develop advanced intelligent systems.
Terence Tao highlights the ingenious mathematical reasoning behind measuring cosmic distances, emphasizing how humanity deduced Earth's spherical shape and the sizes of celestial bodies through clever observations and mathematical tricks.
In the 10th century, Arab mathematician Aloni accurately measured Earth's radius using trigonometry by observing the horizon's angle from a mountain.
The mathematical space describing unordered pairs of musical notes on a circle is a Möbius strip, achieved by folding and twisting a unit square.
This tutorial teaches essential skills for understanding and implementing deep learning research papers, focusing on reading, mathematical notation, and code navigation through practical examples.
The mathematical space describing every possible musical interval as unordered pairs of points on a loop is represented by a Möbius strip.
Alan Turing's groundbreaking work in breaking the Enigma code during World War II was pivotal in countering Germany's military advantage and laid the foundation for modern computing.
The Mandelbrot set is defined by iterating a sequence of complex numbers, visualized by coloring based on boundedness and divergence behavior.
The puzzle challenges finding the smallest sum of strip widths covering a unit disc, revealing that two is the minimum, despite potential overlap considerations.
Archimedes demonstrated that a sphere's surface area equals the lateral area of an enclosing cylinder, using geometric analysis of light-cast shadows.
Newton's fractal is a visually stunning representation of Newton's method applied to complex numbers, revealing intricate patterns from iterative approximations of polynomial solutions.
A proposed symmetric notation using a triangle simplifies the understanding of exponents, logs, and roots by visually unifying their operations.
The content presents a series of intriguing geometry puzzles, exploring tiling patterns and the Tarski-Planck problem, ultimately connecting them to broader themes about higher dimensions and their implications.
Terence Tao likens ChatGPT's reasoning to a mediocre graduate student, suggesting AI may never surpass human expertise.
Switching to inequalities in continuous probability problems often simplifies calculations, relating maximum probabilities to uniform distributions.
Google's AI advancements, including solving complex scientific and mathematical problems, could lead to significant breakthroughs and potentially superintelligence.
Google DeepMind's AlphaProof and AlphaGeometry2 models achieved a significant breakthrough by solving International Mathematical Olympiad problems at a silver medalist level.
AlphaProof and AlphaGeometry 2 are problem-solving tools that require specific time constraints and human assistance for optimal performance.
