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Cliff Pickover

@pickover • 229,692 subscribers

Increase your sense of wonder. (Author of 50 books & 800 patents. Yale Ph.D.) "Pickover contemplates realms beyond our known reality." ~NY Times

Shorts

Mathematics, computer programming, engineering, motion, creativity. This is a linkage-mechanism for converting Binary Numbers to Decimal Numbers. Created by 上木敬士郎/Keishiro Ueki, 上木敬士郎 / Keishiro Ueki, Used with permission.

Mathematics, computer programming, engineering, motion, creativity. This is a linkage-mechanism for converting Binary Numbers to Decimal Numbers. Created by 上木敬士郎/Keishiro Ueki, 上木敬士郎 / Keishiro Ueki, Used with permission.

65,118 次观看

Engineering, mathematics. Unconventional gears. The center of a logarithmic spiral traces a straight line as it is rolled. By Matt Henderson, Matt Henderson, used with permission.

Engineering, mathematics. Unconventional gears. The center of a logarithmic spiral traces a straight line as it is rolled. By Matt Henderson, Matt Henderson, used with permission.

1,467,413 次观看

Life on the Edge. Creatures from mathematics. We are Not Alone. Experimenting with simulated ecosystems. By SPACEFILLER, Used with permission.

Life on the Edge. Creatures from mathematics. We are Not Alone. Experimenting with simulated ecosystems. By SPACEFILLER, Used with permission.

17,566 次观看

Math. A rare peek from within a "Gyroid," a fascinating minimal surface in geometry that separates space into two oppositely congruent labyrinths of passages. By Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission. This infinitely extending "labyrinth" surface divides all of space into two identical, intertwined, mirror-image passages: without ever intersecting itself. Discovered by mathematician Alan Schoen in 1970, it's a triply periodic minimal surface (zero mean curvature everywhere, like a soap film), with no straight lines or mirror symmetry. It can be approximated by the surprisingly simple equation: sin(x)cos(y) + sin(y)cos(z) + sin(z)cos(x) = 0. Nature loves it too: gyroid nanostructures in butterfly wing scales create iridescent colors through light interference, and similar forms appear in cell membranes, polymers, and even ketchup-like fluids. It's a superstar in materials science for lightweight, strong 3D-printed structures and photonic crystals.

Math. A rare peek from within a "Gyroid," a fascinating minimal surface in geometry that separates space into two oppositely congruent labyrinths of passages. By Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission. This infinitely extending "labyrinth" surface divides all of space into two identical, intertwined, mirror-image passages: without ever intersecting itself. Discovered by mathematician Alan Schoen in 1970, it's a triply periodic minimal surface (zero mean curvature everywhere, like a soap film), with no straight lines or mirror symmetry. It can be approximated by the surprisingly simple equation: sin(x)cos(y) + sin(y)cos(z) + sin(z)cos(x) = 0. Nature loves it too: gyroid nanostructures in butterfly wing scales create iridescent colors through light interference, and similar forms appear in cell membranes, polymers, and even ketchup-like fluids. It's a superstar in materials science for lightweight, strong 3D-printed structures and photonic crystals.

40,847 次观看

Visualization by Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission. Physicist Roger Penrose wrote: "Everything in the physical Universe is indeed governed in completely precise detail by mathematical principles — perhaps by equations... or perhaps by some future mathematical notions fundamentally different from those which we would today label by the term ‘equations’.... Even our own physical actions would be entirely subject to such ultimate mathematical control, where ‘control’ might still allow for some random behaviour governed by strict probabilistic principles." ~ The Road to Reality Belloni visualization employs 256K particles.

Visualization by Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission. Physicist Roger Penrose wrote: "Everything in the physical Universe is indeed governed in completely precise detail by mathematical principles — perhaps by equations... or perhaps by some future mathematical notions fundamentally different from those which we would today label by the term ‘equations’.... Even our own physical actions would be entirely subject to such ultimate mathematical control, where ‘control’ might still allow for some random behaviour governed by strict probabilistic principles." ~ The Road to Reality Belloni visualization employs 256K particles.

27,964 次观看

Mathematics and mystery. "Two Ellipses." By Idan Tal, Idan Tal, Used with permission

Mathematics and mystery. "Two Ellipses." By Idan Tal, Idan Tal, Used with permission

53,397 次观看

Math and the Mind. Dodecahedron. By Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission. In your personal opinion, do dodecahedrons exist, or are they abstract ideal geometries, Platonic solids that exist in some non-human realm? Perhaps they exist in both ways: as precise, abstract mathematical ideals and as real physical objects you can hold, study, or even find in ancient ruins and nature. The abstract, ideal version a convex polyhedron with 12 identical regular pentagonal faces, 20 vertices, and 30 edges, where the same number of faces meet at each vertex (all faces congruent, all angles equal, etc.). Platonists argue these forms inhabit an abstract realm independent of human minds or the physical universe. Others see them as human inventions or patterns inherent to logic and reality itself. [Humans have been building dodecahedrons for millennia, and close approximations appear, such as pyritohedrons in pyrite (fool's gold) crystals.]

Math and the Mind. Dodecahedron. By Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission. In your personal opinion, do dodecahedrons exist, or are they abstract ideal geometries, Platonic solids that exist in some non-human realm? Perhaps they exist in both ways: as precise, abstract mathematical ideals and as real physical objects you can hold, study, or even find in ancient ruins and nature. The abstract, ideal version a convex polyhedron with 12 identical regular pentagonal faces, 20 vertices, and 30 edges, where the same number of faces meet at each vertex (all faces congruent, all angles equal, etc.). Platonists argue these forms inhabit an abstract realm independent of human minds or the physical universe. Others see them as human inventions or patterns inherent to logic and reality itself. [Humans have been building dodecahedrons for millennia, and close approximations appear, such as pyritohedrons in pyrite (fool's gold) crystals.]

17,327 次观看

World map shows global population distribution by latitude and longitude. (Will this be very different in 50 years?) By Engaging Data, Used with permission.

World map shows global population distribution by latitude and longitude. (Will this be very different in 50 years?) By Engaging Data, Used with permission.

85,149 次观看

Mathematics, algorithms, spirals, geometry, programming. "The Hidden Music of Concentric Souls." Rotational Moiré Interference from Phase-Shifted Polar Sources. Animation by A. L. Crego, Used with permission

Mathematics, algorithms, spirals, geometry, programming. "The Hidden Music of Concentric Souls." Rotational Moiré Interference from Phase-Shifted Polar Sources. Animation by A. L. Crego, Used with permission

72,333 次观看

Mathematics. By Daniel Mentrard, Daniel Mentrard, Source: Used with permission.

Mathematics. By Daniel Mentrard, Daniel Mentrard, Source: Used with permission.

52,351 次观看

Mathematics, motion, polygons, alignment, harmony. The journey begins. By dave, Used with permission.

Mathematics, motion, polygons, alignment, harmony. The journey begins. By dave, Used with permission.

136,334 次观看

Mathematics. Procedural animation. Harmonic tango. By Etienne Jacob, Etienne Jacob, Source: Used with permission.

Mathematics. Procedural animation. Harmonic tango. By Etienne Jacob, Etienne Jacob, Source: Used with permission.

35,796 次观看

Mathematics and beauty. "It's called the Lorenz 𝘢𝘵𝘵𝘳𝘢𝘤𝘵𝘰𝘳 because all nearby points are 𝘢𝘵𝘵𝘳𝘢𝘤𝘵𝘦𝘥 into the set of chaotic orbits, regardless of initial conditions." By Ben Bartlett, Ben Bartlett, Source: Used with permission.

Mathematics and beauty. "It's called the Lorenz 𝘢𝘵𝘵𝘳𝘢𝘤𝘵𝘰𝘳 because all nearby points are 𝘢𝘵𝘵𝘳𝘢𝘤𝘵𝘦𝘥 into the set of chaotic orbits, regardless of initial conditions." By Ben Bartlett, Ben Bartlett, Source: Used with permission.

119,183 次观看

Mathematics. Fractals. → Sierpiński pyramid. Infinity in your hand. Credit: I didn’t upload this video to 𝕏. I’m pointing to a video residing in the 𝕏 stream of “creapills” (Jul 18, 2020). [math, maths]

Mathematics. Fractals. → Sierpiński pyramid. Infinity in your hand. Credit: I didn’t upload this video to 𝕏. I’m pointing to a video residing in the 𝕏 stream of “creapills” (Jul 18, 2020). [math, maths]

31,564 次观看

This is a mathematics joke. Source:

This is a mathematics joke. Source:

75,473 次观看

Mathematics. Fractals. Mandelbrot. Infinity. Created by iterating simple formulas, revealing the mystery of math. How chaos theory and iteration can birth entire universes that look alive. By Trips, Used with permission.

Mathematics. Fractals. Mandelbrot. Infinity. Created by iterating simple formulas, revealing the mystery of math. How chaos theory and iteration can birth entire universes that look alive. By Trips, Used with permission.

14,271 次观看

Math, "3.14 means we'll meet again." 𝑍(𝜃)=𝑒^(𝑖𝜃) + 𝑒^(𝑖3.14𝜃) →Credit: I didn’t upload this video to 𝕏. I’m pointing to a video residing in the 𝕏 stream of “Viral Vibes”, 𝕏 ID “x_viral_vibes” (Dec 29, 2025)

Math, "3.14 means we'll meet again." 𝑍(𝜃)=𝑒^(𝑖𝜃) + 𝑒^(𝑖3.14𝜃) →Credit: I didn’t upload this video to 𝕏. I’m pointing to a video residing in the 𝕏 stream of “Viral Vibes”, 𝕏 ID “x_viral_vibes” (Dec 29, 2025)

14,358 次观看

Infinity Ring. A ring built from the Julia Sets that lie along the main cardioid of the Mandelbrot Set. By Matt Henderson, Matt Henderson, used with permission.

Infinity Ring. A ring built from the Julia Sets that lie along the main cardioid of the Mandelbrot Set. By Matt Henderson, Matt Henderson, used with permission.

15,306 次观看

$Mathematics. A close look at the infinite swirling of the Rössler Attractor, which exhibits chaotic dynamics and fractal properties. Like a cosmic taffy-pulling machine. By Marcus Volz, Used with permission.$

Mathematics. A close look at the infinite swirling of the Rössler Attractor, which exhibits chaotic dynamics and fractal properties. Like a cosmic taffy-pulling machine. By Marcus Volz, Used with permission.

17,598 次观看

Technology. A vision of our future. Our AI overlords. Bowling. Robots. Power. By Tom Coben, CGI, used with permission.

Technology. A vision of our future. Our AI overlords. Bowling. Robots. Power. By Tom Coben, CGI, used with permission.

18,257 次观看

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Mathematics, physics. We live in a chaotic, unpredictable universe. This is a grid of 812 double pendulums, each with slightly different initial conditions for the two angles of the pendulum. By Jonathan Nafziger, Used with permission

Mathematics, physics. We live in a chaotic, unpredictable universe. This is a grid of 812 double pendulums, each with slightly different initial conditions for the two angles of the pendulum. By Jonathan Nafziger, Used with permission

1,818,377 次观看 • 3 年前

→ Math, physics, reality. Imagine showing this animation to scientists 200 years ago, and accelerating the growth of knowledge. Credit: I didn’t upload this video to 𝕏. I’m pointing to a video residing in the 𝕏 stream of “raz_akram” (Mar 17, 2025).

→ Math, physics, reality. Imagine showing this animation to scientists 200 years ago, and accelerating the growth of knowledge. Credit: I didn’t upload this video to 𝕏. I’m pointing to a video residing in the 𝕏 stream of “raz_akram” (Mar 17, 2025).

14,086 次观看 • 8 天前

Mathematics clock. By Daniel Mentrard, Daniel Mentrard, Used with permission. Source:

Mathematics clock. By Daniel Mentrard, Daniel Mentrard, Used with permission. Source:

107,475 次观看 • 3 个月前

Roger Penrose's cyclic universe theory, called Conformal Cyclic Cosmology (CCC), proposes the universe goes through infinite cycles, where the end of one "aeon" (a universe's lifespan) smoothly transitions into the Big Bang of the next. Art: Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission

Roger Penrose's cyclic universe theory, called Conformal Cyclic Cosmology (CCC), proposes the universe goes through infinite cycles, where the end of one "aeon" (a universe's lifespan) smoothly transitions into the Big Bang of the next. Art: Andrea Belloni, Water flowing | anbello.eth | anbello.tez, Used with permission

82,851 次观看 • 4 个月前

Astronomy, mathematics, physics. The evolution in our thoughts and models: Heliocentrism and Geocentrism. By Malin Christersson, source: (CC BY-NC-SA 4.0)

Astronomy, mathematics, physics. The evolution in our thoughts and models: Heliocentrism and Geocentrism. By Malin Christersson, source: (CC BY-NC-SA 4.0)

470,060 次观看 • 3 年前

Mathematics. Hidden inside every square is a 3-4-5 right triangle, which humans can reveal in the following manner. By math educator Tim Brzezinski, Tim Brzezinski, Used with permission.

Mathematics. Hidden inside every square is a 3-4-5 right triangle, which humans can reveal in the following manner. By math educator Tim Brzezinski, Tim Brzezinski, Used with permission.

70,753 次观看 • 5 个月前

Mathematics. Physics. Magnetic Chaotic Pendulum: adding magnetic forces to gravity gives this pendulum chaotic motion (sensitivity to slight differences in initial launch conditions). By Physicsfun, Used with permission.

Mathematics. Physics. Magnetic Chaotic Pendulum: adding magnetic forces to gravity gives this pendulum chaotic motion (sensitivity to slight differences in initial launch conditions). By Physicsfun, Used with permission.

333,372 次观看 • 3 年前

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:

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:

30,941 次观看 • 2 个月前

Mathematics, topology, geometry, simulation, algorithms. Watch this Cosmic Eversion Loop. Particle Tube Metamorphosis. Notice how the interior surface of the tube evaginates to become the "exterior." By Acid Boy 💊, Used with permission.

Mathematics, topology, geometry, simulation, algorithms. Watch this Cosmic Eversion Loop. Particle Tube Metamorphosis. Notice how the interior surface of the tube evaginates to become the "exterior." By Acid Boy 💊, Used with permission.

56,197 次观看 • 5 个月前

The year is 2020. This infographic animation caught my eye today. Covid-19. Source: CC BY-NC-SA 4.0

The year is 2020. This infographic animation caught my eye today. Covid-19. Source: CC BY-NC-SA 4.0

38,169 次观看 • 4 个月前

Mathematics, astronomy, physics. Dance of Earth and Mercury. By Engaging Data, Used with permission.

Mathematics, astronomy, physics. Dance of Earth and Mercury. By Engaging Data, Used with permission.

42,168 次观看 • 5 个月前

Mathematics, Physics. "Dirac's Belt Trick is a clever way to remove two full twists in a ribbon by simply moving it around. This gives a way of connecting cables to a rotating object without them twisting or tangling." By Matt Henderson, Matt Henderson, used with permission.

Mathematics, Physics. "Dirac's Belt Trick is a clever way to remove two full twists in a ribbon by simply moving it around. This gives a way of connecting cables to a rotating object without them twisting or tangling." By Matt Henderson, Matt Henderson, used with permission.

50,251 次观看 • 7 个月前

Mathematics. The beauty of September 27, 2025. By Jerome White, Jerome White, Used with permission.

Mathematics. The beauty of September 27, 2025. By Jerome White, Jerome White, Used with permission.

50,129 次观看 • 8 个月前

Mathematics, physics. Straight stick fits through curved holes. By Andreas Wannerstedt, Andreas Wannerstedt, Used by permission.

Mathematics, physics. Straight stick fits through curved holes. By Andreas Wannerstedt, Andreas Wannerstedt, Used by permission.

10,078 次观看 • 1 个月前

$Math. Truchet tiles. As you randomly orient the tiles, is a closed smooth curve always produced? (For random orientations, what is the fraction of closed circles?) By Frédéric Vayssouze-Faure, Used with permission.$

Math. Truchet tiles. As you randomly orient the tiles, is a closed smooth curve always produced? (For random orientations, what is the fraction of closed circles?) By Frédéric Vayssouze-Faure, Used with permission.

30,895 次观看 • 5 个月前

Math. The 3n+1 Heavens. Don't you love thinking about the Collatz Conjecture? It's a problem that children can understand, while providing a lifelong challenge for mathematicians. By Algoritmarte, Source: Used by permission.

Math. The 3n+1 Heavens. Don't you love thinking about the Collatz Conjecture? It's a problem that children can understand, while providing a lifelong challenge for mathematicians. By Algoritmarte, Source: Used by permission.

15,803 次观看 • 2 个月前

→ Science, simulation, math, chance, reality. Credit: I didn’t upload this video to 𝕏. I’m pointing to a video residing in the 𝕏 stream of “mikefc”, 𝕏 ID “coolbutuseless” (Aug 20, 2020).

→ Science, simulation, math, chance, reality. Credit: I didn’t upload this video to 𝕏. I’m pointing to a video residing in the 𝕏 stream of “mikefc”, 𝕏 ID “coolbutuseless” (Aug 20, 2020).

21,566 次观看 • 4 个月前

Mathematics. Fractals. Mandelbrot. Infinity. Created by iterating simple formulas, revealing the mystery of math. How chaos theory and iteration can birth entire universes that look alive. By Trips, Used with permission.

Mathematics. Fractals. Mandelbrot. Infinity. Created by iterating simple formulas, revealing the mystery of math. How chaos theory and iteration can birth entire universes that look alive. By Trips, Used with permission.

14,271 次观看 • 3 个月前

Mathematics, physics. We live in a chaotic, unpredictable universe. This is a grid of 812 double pendulums, each with slightly different initial conditions for the two angles of the pendulum. By Jonathan Nafziger, Used with permission

Mathematics, physics. We live in a chaotic, unpredictable universe. This is a grid of 812 double pendulums, each with slightly different initial conditions for the two angles of the pendulum. By Jonathan Nafziger, Used with permission

54,185 次观看 • 1 年前