Ask me anything. I will be happy to answer some of your questions, and will try to reply to a portion of your questions below in the coming days.

Mathematics for Aliens.

Dream with me. Our place in the observable universe. Laniakea is the large-scale structure centered around the Great Attractor that is home to the Milky Way and approximately 100,000 other nearby galaxies. Source: Andrew Z. Colvin, tinyurl.com/2n4mx34p

How do I prove to people in 2026 that I'm a time traveler from 3026?

Mathematics. Parallel lines.

Universes. Wormholes. Einstein. Beyond. Here's a page from the seemingly infinite notebook of Yuri Kovalenok, @jurijkovalenok1 -- a physics teacher who, through the years, produced sketches for us to ponder. I wonder what ways humans will discover to rapidly traverse great distances, and make all of spacetime their home. Art used with permission.

FREE Math Book. "Counting Rocks! An Intro to Combinatorics" by Adams et al. Combinatorics is the mathematics of counting, arranging, and combining. It's the invisible engine powering our digital world, driving everything from cryptographic security to DNA sequencing. Studying it is FASCINATING because it allows us to solve massive, seemingly impossible puzzle problems using elegant, logical patterns. Machine learning models and neural networks rely on advanced combinatorial graph theory to map relationships and process complex data. “Combinatorics is the mathematical study of discrete mathematical objects and their combinations and arrangements. Other kinds of mathematics (like calculus and analysis) use continuous mathematical objects, which involve infinitesimally small increments. By contrast, discrete mathematics is the study of objects that come in larger chunks, such as whole numbers, polygons, and networks. If you have ever asked 'I wonder how many different ways I could... ?', then you have thought about combinatorics. The history of combinatorics began in ancient times, in places such as Egypt, India, China, and Iran. The computer revolution greatly amplified the importance of combinatorics and graph theory. There are also applications of this class and book to other fields, like linguistics, physics, chemistry, and biology. In general, from this class, you will gain experience solving problems about combinatorial structures and algorithms; we hope you will continue to use the experience and ideas you gain from this class for the benefit of many other people.” Contents What is Combinatorics? Counting Principles Counting Combinations Pascal’s Triangle and the Binomial Theorem Proof Techniques in Combinatorics Recurrence Relations Generating Functions Graph Theory Basics Trees Graph Optimization Planar Graphs Graph Coloring Link: mathematicalgemstones.com/ma…

Mathematics. As if you drift off to sleep tonight, remember that what feels like chaotic randomness in the prime numbers is, in the limit, governed by a simple, elegant law. We are one.

Mathematics. “It’s like asking why Beethoven's Ninth Symphony is beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren't beautiful, nothing is." — Paul Erdös, quoted in “The Man Who Loves Only Numbers,” 1987

Mathematics. Please enjoy this is marvelous 10,000-digit Prime Number for which all digits are even, except for the last digit. It was sent to me from researcher and mathematician Michel Yamagishi, @ymichel.

Here's a chronological map of my books: a decades-long expedition through the strange attractors of science and imagination: computers dreaming, mathematics mutating into art, alien minds, parallel universes, Einsteinian spacetime, time travel, religion, DMT elves, physics, medicine, mortality, the afterlife, and the architecture of human genius. Across these titles, I’ve tried to turn the cosmos inside out and ask: What happens when curiosity becomes a time machine? I’ve also recently published new editions of The Math Book, The Physics Book, and Artificial Intelligence.

Will humans ever know if God exists?

If a single iron atom was shot into your hand at a speed equal to Elon Musk's fastest rocket, would you experience pain and be horribly damaged?

Mathematics. Share with others, if you're able to find one solution that you can justify for this.

Wake up for mathematicians!

FREE Math Book. "Applied Combinatorics," by Keller & Trotter. "We show students the beauty of combinatorics and how combinatorial problems naturally arise in many settings.... Combinatorial mathematics is one of the most fascinating and captivating subjects on the planet. Combinatorics is very concrete and has a wide range of applications, but it also has an intellectually appealing theoretical side. Our goal is to give you a taste of both." Contents: An Introduction to Combinatorics Strings, Sets, and Binomial Coefficients Induction Combinatorial Basics Graph Theory Partially Ordered Sets Inclusion-Exclusion Generating Functions Recurrence Equations Probability Applying Probability to Combinatorics Graph Algorithms Network Flows Combinatorial Applications of Network Flows Pólya’s Enumeration Theorem The Many Faces of Combinatorics Link: appliedcombinatorics.org/app…

Mathematics, physics. Creating "teardrops" using mechanical linkages (an assembly of systems connected to manage forces and movement; the link is considered to be rigid). By上木 敬士郎 / Keishiro Ueki, @KeishiroUeki, Used with permission.

Mathematics. This is a walkable trefoil knot. © Dr. Robert Fathauer, @RobFathauerArt, Used with permission, sketchfab.com/3d-models/walk…

“One sign of an interesting program is that you cannot readily predict its output.” — Brian Hayes, “On the bathtub algorithm for dot-matrix holograms,” 1986

FREE Math Book. 630 pages. A gateway into the architecture of infinity, proof, and the future of human thought. "An Infinite Descent into Pure Mathematics" by Newstead. Topics: prime numbers, logic, sets, functions, induction, relations and infinity, mathematical proofs, number theory, combinatorics, real analysis, infinite cardinality, and probability theory. Undergraduate-level textbook. "I am grateful to the 1000 students who have already used this book to learn mathematics. The goal of this book is to help the reader make the transition from being a consumer of mathematics to a producer of it." Link: infinitedescent.org/

Mathematics. The Woman, the Finger, and Pi: A Math Puzzle That Will Make You Question Everything "Could the decimal expansion of π become all 1s and 0s after some finite location in the decimal digits of π?"