Cliff Pickover

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.

This is a math joke. Source: tinyurl.com/yrysb577

Math. This mystery space-filling curve is a variant of Hilbert's curve, built from epicycles. Watch it evolve as more harmonics are added. Source: I created this animation using Hopperpop's Epicycle Drawer, an interactive tool: hopperpop.github.io/EpicDrawer/

Mathematics. Free book PDF: open.umn.edu/opentextbooks/…. "Math in Society" is a college-level course for liberal arts majors. Table of Contents: Fractals Graph Theory Problem Solving Voting Theory Weighted Voting Apportionment Fair Division Scheduling Growth Models Finance Statistics Describing Data Probability Sets Historical Counting Systems Cryptography Logic

This is a math meme, circulating widely on the Web.

Mathematics.

Perception, reality. → The spinning dodecahedron seems to disappear when you pause the video. Interactive version: matthen.github.io/animations/#/n… Code: github.com/matthen/animat… By Matt Henderson, @matthen2, used with permission.

Math. Spinning. Perception. → Ant-like creatures come alive. Credit: youtube.com/watch?v=JlkX0y…. I didn’t upload this video to 𝕏. I’m pointing to a video residing in the 𝕏 stream of “木佐貫洋平 プロカリンバ奏者”, 𝕏 ID “LimbaTrip” (Mar 19, 2026).

Mathematics. Free book PDF. "Introduction to Probability," 2nd edition, by Charles M. Grinstead and J. Laurie Snell. "Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continued to influence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a well-established branch of mathematics that finds applications in every area of scholarly activity from music to physics, and in daily experience from weather prediction to predicting the risks of new medical treatments." Link: open.umn.edu/opentextbooks/…

Physics, number of dimensions, universe, reality. Life explained. Adapted from Wikimedia, Max Tegmark, Class. Quantum Grav. 14 (1997) L69–L75. Link: commons.wikimedia.org/wiki/File:Spac…

Mathematics. Biblically Accurate Angel. (Just kidding, This is a Gumowski-Mira strange attractor arising from a discrete dynamical system.) Visualization byア, @yuruyurau, ｱ_ﾅ/A-na5, a-na5.tumblr.com

Mathematics. Each integer from 1 to a million is represented by one million labeled stones in a bag. Merlin the magician randomly selects a stone and replaces it. How many stones must he select in order for the probability of selecting any particular stone to be at least 1/2?

Mathematics. ❄️ π makes an appearance, and helps us shiver in awe. ❄️ The area under this curve is equal to the square root of π.

Some people perceive the black hole to expand, as they stare at this image. By Akiyoshi KITAOKA, @AkiyoshiKitaoka, ritsumei.ac.jp/~akitaoka/inde…, Used with permission.

Mathematics. A mathematician emerges from a cave, hands you the slip of paper below, and asks "Is the distance from one real number to the next greater than zero?" What is your response?

Mathematics and Mystery. The strangest right triangle you'll ever see. Nicely satisfies the Pythagorean Theorem. Drives humans insane.

Mathematics. Free calculus book, which even begins with "a brief review of selected topics from Algebra and Trig that are vital to surviving a Calculus course." The entire 1326-page book may be downloaded as a PDF here: tutorial.math.lamar.edu/Classes/CalcI/…

Virus trading card, by Eleanor Lutz. Source: tinyurl.com/23u2snrx

Strange Universe. Adapted from: tinyurl.com/4krwx65u

Mathematics. Free Game Theory book. "An Open Access Textbook with 165 Solved Exercises." Source: arxiv.org/abs/1512.06808. Book begins: "After teaching game theory (at both the undergraduate and graduate level) at the University of California, Davis for 25 years, I decided to organize all my teaching material in a textbook. ... There are two distinguishing features of this textbook: (1) it is open access and thus free, and (2) it contains an unusually large number of exercises (a total of 165) with complete and detailed answers. I tried to write the book in such a way that it would be accessible to anybody with minimum knowledge of mathematics (high-school level algebra and some elementary notions of probability) and no prior knowledge of game theory."