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Cliff Pickover

@pickover • 233,333 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

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.

1,467,585 views

Mathematics. Rubik's Cube for Higher-Dimensional Aliens. Poincaré disk model. 24-color puzzle based on the regular {7,3} tiling. Info: By Roice, used with permission.

Mathematics. Rubik's Cube for Higher-Dimensional Aliens. Poincaré disk model. 24-color puzzle based on the regular {7,3} tiling. Info: By Roice, used with permission.

52,097 views

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.

24,072 views

Mathematics and Mystery. Fourier Decomposition of a Pentagram. By George Savva, Used with permission.

Mathematics and Mystery. Fourier Decomposition of a Pentagram. By George Savva, Used with permission.

54,335 views

Mathematics. The infinite race. The "Penrace Triangle." Eternity, hyperspace, forever. By Linus Dahlgren, Linus Dahlgren, Used with permission,

Mathematics. The infinite race. The "Penrace Triangle." Eternity, hyperspace, forever. By Linus Dahlgren, Linus Dahlgren, Used with permission,

33,434 views

Electronics, physics. → What is the name of this kind of switch, and what purpose does it serve? Credit: I didn’t upload this video to 𝕏. I’m pointing to a video residing in the 𝕏 stream of “412Couchloc” (Jul 20, 2026).

Electronics, physics. → What is the name of this kind of switch, and what purpose does it serve? Credit: I didn’t upload this video to 𝕏. I’m pointing to a video residing in the 𝕏 stream of “412Couchloc” (Jul 20, 2026).

17,625 views

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.

85,161 views

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.

41,176 views

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

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

15,424 views

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

53,426 views

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

72,707 views

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, 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, Used with permission.

17,098 views

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.

28,834 views

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

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

52,351 views

Mathematics. Two spheres, rolling on a strange track, for an eternity. By Matthew Hughes, Matthew Hughes, Used with permission.

Mathematics. Two spheres, rolling on a strange track, for an eternity. By Matthew Hughes, Matthew Hughes, Used with permission.

19,446 views

Geometry from another world. "The universe buries strange jewels deep within us all, and then stands back to see if we can find them." - Elizabeth Gilbert, Big Magic Art by Joseff, Used with permission.

Geometry from another world. "The universe buries strange jewels deep within us all, and then stands back to see if we can find them." - Elizabeth Gilbert, Big Magic Art by Joseff, Used with permission.

15,689 views

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.

136,491 views

Mathematics. This is a walkable trefoil knot. © Dr. Robert Fathauer, Robert Fathauer, Used with permission,

Mathematics. This is a walkable trefoil knot. © Dr. Robert Fathauer, Robert Fathauer, Used with permission,

16,889 views

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.

17,951 views

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 views

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For the mathematicians you love.... Examples of parametric curves. By Jerome White, Jerome White, Used with permission.
0:21
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For the mathematicians you love.... Examples of parametric curves. By Jerome White, Jerome White, Used with permission.

Cliff Pickover

67,751 views • 2 days ago

Strange Universe. Math, Physics, Reality. "6 belts are anchored on the outside to a fixed frame, and on the inside to a spinning cube. Although the cube spins continuously in one direction the belts never become tangled. The belts return to their original configuration when the cube has rotated 720 degrees." - Jason Hise,
0:59
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Strange Universe. Math, Physics, Reality. "6 belts are anchored on the outside to a fixed frame, and on the inside to a spinning cube. Although the cube spins continuously in one direction the belts never become tangled. The belts return to their original configuration when the cube has rotated 720 degrees." - Jason Hise,

Cliff Pickover

886,473 views • 1 month ago

Mathematics. Rubik's Cube for Higher-Dimensional Aliens. Poincaré disk model. 24-color puzzle based on the regular {7,3} tiling. Info: By Roice, used with permission.
0:20
pickover's profile picture

Mathematics. Rubik's Cube for Higher-Dimensional Aliens. Poincaré disk model. 24-color puzzle based on the regular {7,3} tiling. Info: By Roice, used with permission.

Cliff Pickover

52,097 views • 14 days ago

Mathematical Coalescence. Math machine. A strange pattern emerges in these Archimedean Spirals with interconnecting tubes. "The pattern 東南西北 can be displaced, but remains conserved." By Raven Kwok, Raven Kwok, Used with permission
1:11
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Mathematical Coalescence. Math machine. A strange pattern emerges in these Archimedean Spirals with interconnecting tubes. "The pattern 東南西北 can be displaced, but remains conserved." By Raven Kwok, Raven Kwok, Used with permission

Cliff Pickover

166,455 views • 1 month ago

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
0:33
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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

Cliff Pickover

1,842,942 views • 3 years ago

Mathematics. Epicycles. Fourier series. Polar bear synthesis. By Daniel Mentrard, Daniel Mentrard, Used with permission.
1:23
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Mathematics. Epicycles. Fourier series. Polar bear synthesis. By Daniel Mentrard, Daniel Mentrard, Used with permission.

Cliff Pickover

67,671 views • 2 months ago

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.
0:24
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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.

Cliff Pickover

10,801 views • 11 days ago

Mathematics clock. By Daniel Mentrard, Daniel Mentrard, Used with permission. Source:
0:31
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Mathematics clock. By Daniel Mentrard, Daniel Mentrard, Used with permission. Source:

Cliff Pickover

107,709 views • 6 months ago

Astronomy, mathematics, physics. The evolution in our thoughts and models: Heliocentrism and Geocentrism. By Malin Christersson, source: (CC BY-NC-SA 4.0)
0:35
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Astronomy, mathematics, physics. The evolution in our thoughts and models: Heliocentrism and Geocentrism. By Malin Christersson, source: (CC BY-NC-SA 4.0)

Cliff Pickover

496,323 views • 3 years ago

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
0:26
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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

Cliff Pickover

20,609 views • 1 month ago

Strange Universe. Math, Physics, Reality. "12 strands are anchored on the outside to a fixed frame, and on the inside to a spinning dodecahedron. Although the dodecahedron spins continuously in one direction, the strands never become tangled. The strands return to their original configuration when the dodecahedron has rotated 720 degrees." - Jason Hise,
0:59
pickover's profile picture

Strange Universe. Math, Physics, Reality. "12 strands are anchored on the outside to a fixed frame, and on the inside to a spinning dodecahedron. Although the dodecahedron spins continuously in one direction, the strands never become tangled. The strands return to their original configuration when the dodecahedron has rotated 720 degrees." - Jason Hise,

Cliff Pickover

21,703 views • 1 month ago

Mathematics. Our complicated, seemingly unpredictable universe. This is chaos theory in action. The motion of a "quadruple pendulum" (simulation with no friction). Source 1 (Reddit u/tmanchester): Source 2 (Matlab code):
0:22
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Mathematics. Our complicated, seemingly unpredictable universe. This is chaos theory in action. The motion of a "quadruple pendulum" (simulation with no friction). Source 1 (Reddit u/tmanchester): Source 2 (Matlab code):

Cliff Pickover

381,341 views • 3 years ago

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
0:26
pickover's profile picture

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

Cliff Pickover

83,083 views • 7 months ago

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.
0:45
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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.

Cliff Pickover

333,438 views • 3 years ago

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.
0:24
pickover's profile picture

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.

Cliff Pickover

70,753 views • 8 months ago

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, Daniel Mentrard, Used with permission.
1:05
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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, Daniel Mentrard, Used with permission.

Cliff Pickover

21,997 views • 2 months ago

Beauty of mathematical chaos and infinite complexity. Mandelbulb: higher-dimensional extension of the Mandelbrot Set. Central floral-like formation with radiating, recursive details are characteristic of fractals. By Trips, Used by permission.
0:20
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Beauty of mathematical chaos and infinite complexity. Mandelbulb: higher-dimensional extension of the Mandelbrot Set. Central floral-like formation with radiating, recursive details are characteristic of fractals. By Trips, Used by permission.

Cliff Pickover

21,512 views • 2 months ago

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.
0:25
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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.

Cliff Pickover

56,316 views • 8 months ago

Mathematics, physics, chaos. Apparent unpredictability. Life explained. The "Lorenz Attractor." Little blue butterflies, circulating forever. Source: CC BY-NC-SA 3.0
0:58
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Mathematics, physics, chaos. Apparent unpredictability. Life explained. The "Lorenz Attractor." Little blue butterflies, circulating forever. Source: CC BY-NC-SA 3.0

Cliff Pickover

22,346 views • 3 months ago

Math: Strange Infinite Universe. Using mathematics to create perfect circles from whip-like tendrilous spirals. Infinite sums. By Tungsteno, Tungsteno, Used with permission. Info:
0:29
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Math: Strange Infinite Universe. Using mathematics to create perfect circles from whip-like tendrilous spirals. Infinite sums. By Tungsteno, Tungsteno, Used with permission. Info:

Cliff Pickover

16,178 views • 2 months ago