Black Holes

It took a long journey for scientists to prove that black holes exist. John Mitchell was the first person to come up with the idea that a black hole could exists in 1783, he developed the theory of black holes when he accepted Newton's theory that light consists of small material particles, called photons. He wondered how the movement of these light particles is impacted by the gravitational pull of the star they are escaping. He referred to them as "dark stars", however he doubted that such objects could exist and after publishing his information, he abandoned further research on the subject.

Mitchell’s research was further enhanced by Pierre Simon Laplace in 1795. Using Newton's Theory of gravity, Laplace calculated that if an object was compressed into a small enough radius, then the escape velocity of that object would be faster than the speed of light.

Then all this research took a turn of events as Einstein himself wrongly thought that black holes would not form, because he held that the angular momentum of collapsing particles would stabilize their motion at some radius. This led the general relativity community to dismiss all results to the contrary for many years, and black holes were considered nothing more than abstract mathematical concepts.

But in 1915, Einstein's theory of general relativity predicted the existence of black holes, which ended up proving his previous statement wrong. And then in 1967 John Wheeler, an American theoretical physicist, applied the term "black hole" to these collapsed objects.

Now I'll get to the point and explain how black holes are created. To keep it as simple and straightforward as possible, we can say that black holes are created when a massive star dies.But I would like to go into a bit more detail because a one line definition isn't enough!

A common type of black hole is produced by certain dying stars. A star which has a mass greater than approximately 20 times the mass of our Sun may produce a black hole at the end of its life.

In the normal life of a star there is a constant tug of war between gravity pulling in and pressure pushing out. Nuclear reactions in the core of the star produce enough energy and pressure to push outward. For most of a star’s life, gravity and pressure balance each other exactly, and so the star is stable. However, when a star runs out of nuclear fuel, gravity gets the upper hand and the material in the core is compressed even further. The bigger the core of the star causes the greater the force of gravity that compresses the material, making it collapse under its own weight.

For small stars, when the nuclear fuel is exhausted and there are no more nuclear reactions to fight gravity, the repulsive forces among electrons within the star eventually create enough pressure to halt further gravitational collapse. The star then cools and dies peacefully. This type of star is called a "white dwarf."

When a very massive star exhausts its nuclear fuel it explodes as a supernova. The outer parts of the star are expelled violently into space, while the core completely collapses under its own weight. If the core remaining after the supernova is very massive (more than 2.5 times the mass of the Sun), no known repulsive force inside a star can push back hard enough to prevent gravity from completely collapsing the core into a black hole.

Rubik's Cube. The "toy" which amused 5 year old's yet inspired mathematicians!

Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Erno Rubik. The puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980. And as of January 2009, 350 million cubes have been sold worldwide making it the world's top selling puzzle game.

In the mid-1970's, Erno Rubik worked at the Department of Interior Design at the academy of Applied Arts and Crafts in the capital of Hungary, Budapest. In an interview with CNN he states that he planned to make it a teaching aid for his class of design students and he also had an interest himself in trying to build a structure that would permit individual blocks to move independently without the whole thing falling apart. It should be noted that there was no three-dimensional printing and CAD (computer-aided design) back then and he made the first Rubik Cube prototype with wood, elastic bands and other very simple things. He did not realize that he had made a puzzle until the first time he scrambled his Cube and then tried to restore it!

The Rubik's Cube is a cube consisting of 6 sides with 9 individual pieces on each side. The objective of this puzzle is to recreate its original position which is a solid colour for each side. Although it looks colourful and looks like a children's toy, an association by the name of The World Cube Association maintains a history of world records for the Rubik's Cube completion in different categories. For example the current world record for single time on a 3×3 Rubik's Cube was set by Mats Valk of the Netherlands in March 2013 with a time of 5.55 seconds and the record for blind solving is held by Marcin Zalewski of Poland, who solved a cube blindfolded in 23.80 seconds.


Math classes to this day study the complexity of the Cube. This is because the Cube can't be easily solved as it doesn't have a definite scrambled point. In simpler words, there's is only one completed solution, which is where all the sides have one colour each, and if the Cube is anything but that, it is considered scrambled. To put this into perspective, when the Cube is complete and one simple rotation is made it's scrambled even though it would be easy to undo that. Therefore, the Cube had an astonishing 43 Quintilian possible position and wait for it.... only one is right!!  And it has been calculated that if every person on earth randomly twisted a Cube once every seconds, about once every three centuries one Cube would return to its original state. So don't be too hard on yourself if you can't solve a Rubik's Cube.


The simple Rubik's Cube is a harder problem than most people realize. Using the currently provided best algorithm for solving the Cube, would take the computer you are reading this on now about 35 years to perform, and that's just for a basic 3x3 Rubik's Cube. However, mathematicians at MIT have found a breakthrough, they've developed a standard algorithm that can determine how many moves are needed to solve a Rubik's Cube and they've developed a more efficient algorithm for solving cubes that start out in their worst state.

Last August, nearly 40 years after the Rubik’s cube first appeared, an international team of researchers consisting of Erik Demaine, an associate professor of computer science and engineering at MIT; his father, Martin Demaine, a visiting scientist at MIT’s Computer Science and Artificial Intelligence Laboratory; graduate student Sarah Eisenstat; Anna Lubiw, who was Demaine’s PhD thesis adviser at the University of Waterloo; and Tufts graduate student Andrew Winslow using computer time lent to them by Google have found every way the Rubik's Cube can be solved and on top of that they proved that no matter how scrambled a cube got, it could be solved in no more than 20 moves!

Mathematicians have tried to find the shortest method of unscrambling the Rubik's Cube, which became known as God's algorithm. The way God's algorithm works is by drawing up a tree structure of all possible scrambles position. The root of the tree is the single initial position where the cube is solved. The algorithm searches for the matching scrambled position from the root of the tree and a solution is found by going over the actions leading to the path found. 


This international team of researchers showed that the maximum number of moves required to a Cube with N squares per row is proportional to N^2 / log. The research published online, ends a 30 year search for the most efficient way to correctly align the Rubik's Cube. "It took 15 years after the introduction of the Cube to find the position that provably requires 20 moves to solve" the team said, "it is appropriate that 15 years after that, we can prove that 20 moves suffice for all positions." The team crunched through billions of Cube positions, solving each one over a period of "just a few weeks."

In an interview online about his time trying to solve the Rubik's Cube Demaine says "The aesthetic is not just to look at things that are fun but also look at problems that are simple. I think the simpler the mathematical problem, the more likely that it’s going to arise in some important practical application in the future. And the Rubik’s cube is kind of the epitome of simplicity.”