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.

Mathematics. Strange Realities. Boy's surface is a mind-bending geometrical object. Discovered by Werner Boy in 1901. If you were an ant walking along its single, continuous face, you could traverse the entire surface (apparent "inside" and "outside") without ever crossing a sharp boundary, effectively demonstrating that "inside" and "outside" are one and the same. It stands as one of the most elegant examples of how topologists can visualize abstract, non-orientable mathematical spaces in 3D. By Ulrich Pinkall, imaginary.org/gallery/ulrich…, CC BY-NC-SA-3.0

Geometry. Classic Matchstick Puzzle.

You have the power to set your child’s beauty and intelligence levels before birth by turning these two dials from 0 to 10 (5 is average). Would you choose to use the dials? If so, what numbers do you choose—and why?

If you press this button, the intelligence of every human on Earth will be instantly and noticeably boosted. Would you press the button?

FREE Math Book. "Notes on Combinatorics" by Cameron. Students should study combinatorics to develop structured, creative problem-solving skills necessary for counting, arranging, and optimizing complex systems in fields like computer science, probability, and logistics Preface: What is Combinatorics? 1 Subsets and binomial coefficients 2 Selections and arrangements 3 Power series 4 Recurrence relations 5 Partitions and permutations 6 The Principle of Inclusion and Exclusion 7 Families of sets 8 Systems of distinct representatives 9 Latin squares 10 Steiner triple systems Solutions to odd-numbered exercises Miscellaneous problems These notes accompanied the course MAS219, Combinatorics, at Queen Mary, University of London. Link: cameroncounts.wordpress.com/lecture-notes/

Mathematics. Golden Ratio. Ramanujan. ϕ can be expressed in terms of π and e. Source: math.stackexchange.com/posts/454626/r…

Using ink and white-out to generate hallucinatory vistas, Jake Fried repeatedly modifies and records his images to create mind-bending animations. By Jake Fried, @jakejfried, shor.by/jakefried, Used with permission.

Math, physics, ultimate reality. Don't you wish you could snap your fingers and magically gain a complete and profound understanding of these Heat, Wave and Schrödinger equations? By Daniel Mentrard, @dment37, geogebra.org/m/rrcjsmdv, Used with permission.

When exploring the Mandelbrot Set, it's easy for you to discover a specific pattern or design that no human has ever seen before. Snippet from a long Mandelbrot Fractal zoom by Maths Town at youtube.com/watch?v=8cgp2W…, used with permission.

Mathematics. How many triangles? (Interestingly, people provide many different answers for this.) (There's no "trick" here. Assume that the crude hand-drawing is created with straight lines, and they meet at the top at a point.)

Mathematics, Fractals, Algorithms. A Glimpse of Infinity. "Disc of Nataraja" By @bryceguy72, freymanart.com, Used with permission.

FREE Math Book "THE INFINITE: Discovering the Art of Mathematics" by Fleron et al. Mathematical inquiry in the liberal arts. "Investigates the great mysteries of the infinite that long captivated humankind.... Classical paradoxes of the infinite -- Zeno’s paradoxes, the wheel of Aristotle, and convergence problems -- immerse you in the infinite’s perils. You rebuild a foothold by characterizing infinitely repeated decimals and building an understanding of the convergence of geometric series. Treated with care, you find the initially paradoxical infinite objects like conditionally convergent series and Gabriel’s wedding cake to behave in more predictable ways. By simple matching you investigate cardinalities, seeing that such a simple idea leads to a concrete view of infinity. Following it systematically, you find this view generates infinitely many different sizes of infinity!" Link: artofmathematics.org/books/the-infi…

“Even the mathematician would like to nibble the forbidden fruit, to glimpse what it would be like if he could slip for a moment into a fourth dimension.” —Edward Kasner and James Newman, Mathematics and the Imagination, 1940

Finally, a bucket puzzle that doesn't require a degree in plumbing. Which fills first?

Mathematics. "Infinite Gift" — a challenging problem for the world's deepest minds.

"A fractal is a way of seeing infinity." ~Benoit Mandelbrot

Mathematics. A mathematician emerges from a cave, hands you the slip of paper below, and says "Imagine a sphere A with radius 1. What's the smallest radius of a sphere larger than sphere A?" What is your response?

Physics humor illustrating relationships among volt, amp, and ohm.

Mathematics. When exploring the Mandelbrot Set, it's easy for you to discover a specific pattern that no human has ever seen before. The Mandelbrot Set is the hammer that shatters the ice of our unconscious. Art by @bryceguy72, freymanart.com, Used with permission.

Mathematics. It is conjectured that ALL juggler sequences eventually reach 1. (The juggler sequence starting at a0 = 37 reaches a maximum value of 24906114455136.) More info: tinyurl.com/ydyt4p57