With a surprising new proof, two young mathematicians have found a bridge across the finite-infinite divide, helping at the same time to map this strange boundary. The boundary does not pass between ...

Simple mathematical concepts such as counting appear to be firmly anchored in the natural process of thinking. Studies have shown that even very young children and animals possess such skills to a ...

In mathematics, real numbers are everywhere; but are they so real? Let me propose the following hypothetical game. The host has several point objects that can move with constant speeds; I like to ...

The laws of physics imply that the passage of time is an illusion. To avoid this conclusion, we might have to rethink the reality of infinitely precise numbers. Strangely, although we feel as if we ...

One question has preoccupied humankind for thousands of years: Do infinities exist? More than 2,300 years ago Aristotle distinguished between two types of infinity: potential and actual. The former ...