Featured Challenges of the Anthropocene


John Von Neumann: The Mathematician. 1947

John von Neumann wrote The Mathematician which was published in Works of the Mind Vol. I no. 1 (University of Chicago Press, Chicago, 1947), 180-196. It has also been published in von Neumann’s Collected Works. A discussion of the nature...

/ May 27, 2019

Cool Number Tricks

Let’s admit it, most of us are intellectually lazy, and thinking is a strange and hard activity, because it requires effort. Even philosophy, the prime discipline devoted to thinking, mostly circulates the ideas of other people, and has some similarity to journalism. Real thinking...

/ September 13, 2016

Hyperbolic Space

Here are two computer-animated videos from Youtube that demonstrate some properties of knots, the relations between knots and space, and how we arrive at hyperbolic space. Easy to watch, and very informative.   Part Two:  

/ January 13, 2013

Nature by Numbers

Below there is  an interesting video inspired by numbers, geometry and nature, created by Cristóbal Vila. Nature looks complex, but the underlying principles are simple, for instance the Fibonacci Series of numbers.  The natural beauty and complexity we see all...

/ March 3, 2012

Mathematical Realism

How does mathematics and reality relate to each other? Some mathematicians believe that mathematical entities are “real”, and this view can be characterized as a version of Platonic philosophy. Quine and Putnam developed an argument in support of mathematical realism,...

/ February 19, 2012

Mathematical Infinity

"There are two approaches to mathematical infinity. It can be seen as defining limiting cases that can never be realized or as existing in some philosophical sense. These mathematical approaches parallel approaches to meaning and value that I call absolutist...

/ February 12, 2012

Unsolved Millenium Problems

The Clay Institute offers a prize to anyone who can solve one of these Millenium problems.  Here is a description of the problems from the Institute’s website: Birch and Swinnerton-Dyer Conjecture Mathematicians have always been fascinated by the problem of...

/ November 23, 2011

Fibonacci Sequence

Definition A Fibonacci sequence is easily constructed:  Start with 0 and 1, and for each following number, add the previous two: 0, 1, 0+1=1, 1+1=2, 1+2=3, and so on. Here is the beginning of the sequence:  0, 1, 1, 2, 3, 5,...

/ November 22, 2011

Poincaré Conjecture

This explanation is quoted from the  The Clay Mathematics Institute, Poincaré Conjecture. (solved by: Grigoriy Perelman, 2002-3) “If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving...

/ November 22, 2011

Knot theory

Knot theory is a very fast growing field of mathematics.  Knots are not natural phenomena, and there exists only a finite number of distinct knots in three-dimensional space. Knots define spaces, because we can think of a knot as a...

/ November 22, 2011

Prime Numbers

Prime numbers are the basic units of the system of numbers, since every natural number is either a prime, or can be expressed as a composite of prime numbers. Here are some excerpts from the Wikipedia article about Prime numbers:...

/ November 21, 2011