Bertrand Russell (1872-1970) It isn’t too often that we think about or even explore the fundamental building blocks of mathematics. These building blocks are called axioms. Axioms are statements taken to be true, i.e. they cannot be proven. This causes mathematicians, whether they know it or not, to take a lot of things on faith. All of […]Read more "Axioms: Sets (Russell’s Paradox)"
It is a common occurrence in mathematics that when something does go wrong, it goes terribly wrong. This exact phenomenon occurs with the Banach-Tarski Paradox. Informally, it says that one can take a sphere (in 3 or more dimensional space) can be split into finitely many pieces and, using only rigid motions, can be rearranged […]Read more "Banach-Tarski Paradox"
As living beings we rely heavily day to day on our intuition. And most of the time it does not let us down. However, sometimes our intuition fails us and we feel compelled to call that event a paradox. This is the case with the birthday problem. I pose the following question. How many random […]Read more "Paradoxes: The Birthday Problem"
Gabriel’s horn is the function on the interval rotated around the x-axis. Intuitively, it should require less paint to fill the horn than to paint the surface (imagine painting a box or a ball). With Gabriel’s Horn this is not the case. In fact, There is an infinite surface area and only a finite volume. […]Read more "Paradoxes: Gabriels Horn"
Zeno of Elea was a Greek philosopher famous for paradoxes which assert that motion is nothing but an illusion. It is assumed that Zeno created the paradoxes in support of Plato’s Parminedes. We will present two of these paradoxes along with a refutation. 1. Achilles and the Tortoise Achilles was challenged to a race by […]Read more "Paradoxes: Zeno of Elea"