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In a 2026 breakthrough, Terence Tao uses Aristotle AI and Lean 4 to solve the Erdős-Herzog-Piranian lemniscate conjecture. Explore the technical details of this AI-math collaboration.
Explore Masaki Kashiwara’s groundbreaking 2026 paper on the Riemann-Hilbert correspondence, D-modules, and its impact on quantum technology and mathematical physics.
Explore the surging betting markets and expert predictions for the 2026 Fields Medal ahead of ICM Philadelphia. Analysis of Hong Wang, Yu Deng, and more.
A technical guide to evaluating complex expressions. Learn how to compute ##z^3 + 8 \text{ for } z = 1 + i\sqrt{3}## using De Moivre’s Theorem and binomial expansion.
Discover which functions have compositional square roots! Learn about bijections, cycle decomposition, and how to find these roots.
Explore the function codomain, its definition, and why it’s crucial in math. Understand its role in function composition and surjectivity.
Explore the density of smooth functions in L1 and L2 spaces. Learn how smooth functions approximate complex functions effectively.
Explore the Mandelbrot set main cardioid, its fixed points, and multipliers. Understand its role in complex dynamics and the Mandelbrot set.