What is the Poincare Conjecture?

Is it possible to deduce the shape of the universe without stepping outside of it? Henri Poincaré thought so. Similar to how the Greeks were able to discern the spherical nature of the earth (and even its rough diameter) using mathematics, he proposed that we should be able to make conclusions about our universe. Stanford University mathematician Keith Devlin explains the Poincaré Conjecture, which became a legendary problem in mathematics, with the help of a short animation.

Original Program Date: June 3, 2011

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[dzeplous]

After watching the spaceman and the rope, now i can proclaim myself as a Guru of Poincare Conjecture.

[compellingpoint]

Well, it's basically a statement about whether or not some shapes can be turned into other shapes by twisting them. It sounds like something that would have been discovered in kindergarten. But... no one has found any shape which disproves it.

It's a really hard problem because it involves comparing two shapes to see if they are the same or not. How do you compare two things if they don't have any properties in common? For example, how does one compare the number 2 with the color blue? They are completely different!


There are many mathematicians who work on the Poincare Conjecture. What is interesting about these people is that, unlike most professionals in other fields, they are not very interested or concerned with fame and money. The only thing they care about is solving problems such as this.
The Poincare Conjecture is a statement of the fundamental nature of reality, as well as being one of the most elegant mathematical conjectures. The conjecture is best phrased in terms of the concept of homotopy.



A sphere is a two dimensional object, with no holes. It has a certain amount of curvature that can be quantified mathematically.


A doughnut is also a two dimensional object, with no holes. It has the same amount of curvature as a sphere.


Now a hole in a doughnut is the same as the region inside a sphere. But if you replace part of the sphere with an equivalent amount of doughnut, then you have two objects that are homotopic.


In other words, the sphere and the doughnut are structurally equivalent in some sense. This is a very powerful concept that allows you to explore all sorts of ideas.

In short, the conjecture is that any loop drawn through a solid sphere must intersect itself. The sphere may be sliced up into many pieces and rearranged in an arbitrary way; it will still retain the property that each loop cut out from one piece can be continuously deformed to become another identical loop on another piece.
The reason that most people don't understand math and science is because they are not taught properly. You know when you were in elementary school your teacher probably just told you a bunch of formulas to memorize, instead of teaching you how to think.


For example, in math class they should teach you how to ask questions, instead of just giving you the answer and wondering why no one understands it. They should also give you examples that relate to your life.

[robertkrohn]

Condescending to Perelman and his reasons for not accepting the prize, while also being an inaccurate explanation of what the conjecture actually is. Astounding lol

[seraphik]

imagine being smarter than anyone else on the planet and then a bunch of so called experts call you a very weird man. 🙄

[mr.rupees]

The guy that solved it was offered the highest math award and a prize of 1million in money. He refused. The last thing heared from him was when a journalist found his phone number and called him. The guy said "leave me alone I'm picking mushrooms". Also when he had handed it his answer, it took the math institution 1 year to double check his work to see if it was correct

[KaliFissure]

I have figured out the topology of the universe. I don’t have the math yet but soon. Props Geocalc.

The universe is a hypercardioid. The point 0;0 represents the highest energy density point/ event horizon. This is a hyperbolic mapping. The least curved point, the tangent of the sphere the cardioid sits within 180deg opposite, represents the lowest energy points, deep voids, basically the vacuum energy and nothing more. All mass moves from point 2, 0 least energy over time rolling/falling over time (literally) until eventually there is event horizon. The neutrons of neutron star which invert at collapse leave behind event horizon and re emerge via infinitesimal time back at lowest energy points. Conservation of Hamiltonian, In one way drawn by gravity, in the other way drawn by the immense energy pressure differential between event horizon and deepest voids. They then these neutrons decay from neutron to amorphous atomic hydrogen. Increasing in size 10^14 times. This is expansion. This is dark energy. This is the topology which regulates the universe. This is why the perfect balance. This is why asymmetric aspects re chirality and charge.

All points are connected via an infinitesimal Planck moment of time. We are the energetic surface membrane of that infinitesimal. There are infinite points on the surface of an infinitesimal.

Negative charge is inflow from past to present. Positive charge is outflow from present to future. This is why mass is linked to positive charge i this dimension. On other side of time membrane, antimatter universe. Everything manifesting as inverted. An inflow here is an outflow there. Clockwise is anti from other side of universe.

[EGarrett]

This video had the opposite of the intended effect. I thought I knew what the Poincare Conjecture was, and after listening to that explanation, I now don't understand it.

[mattwinward]

I love how I knew that was Robert taking in the first few seconds without even having to check.

[RobbyBoy]

I've been looking at the explanations of poincare conjecture using the ricci flow but this one simplifies it soo much better

[sonicbroom]

What is Newman from Seinfeld doing sitting there, with sandals?

[saurabhkhanduri]

Also, it were Indians not Greeks who concluded that Earth is a sphere(sanskrit word for globe has always been ' भूगोल', which literally means Round Earth), in fact more or less like Egg-shaped.

[paulg]

Any man that can wear sandals from the 2nd century BC has to be recognized as a giant in any field!

[antoniogonzaga]

The best explanation of the Poincare topology, very good in did!

[erkanturan]

Since Perelman has already solved the problem then what is the answer now??

[BrookBowenVideos]

Very well done. It seems about as difficult to explain these things in easy to understand terms as it is to actually solve the original question.

[rohank]

Finally I understood the poincare conjecture

[BlueSoulTiger]

0:13 Another crass comment from another glib journalist. Perelman is who he is. QED

[ionutpopescu]

is a non conjecture
that rusian guy that refused the medal figured out
that s why he did not accept the price
a true caracter

[Hoodratliker]

if the universe is shaped like an inner tube, whats outside the inner tube? and what are the walls of the inner tube made out of? Can they be punctured?

[Differenshit]

How do we know that we would reach the tail of the rope at all?