Matt’s Reviews > Things to Make and Do in the Fourth Dimension > Status Update

Discussions about the Riemann Hypothesis and the zeta function are often guilty of a bait-and-switch. You’re promised a deep insight into how many prime numbers there are and their distribution, and suddenly you’re adding reciprocals of powers. Where did the prime numbers go? There is, however, a bizarre link between the two. And, once more, it comes down to Euler.

Despite the limited computing power available in the 1970s, [Kenneth Appel and Wolfgang Haken] were successful, and the four-colour theorem became the first major theorem to be proved by computer. People were not happy.
This was the first-ever maths proof in which some of the steps had been completed automatically by computer, unseen by human eyes. To this day, not all mathematicians are totally convinced.

A loop without a knot is known as an ‘unknot’[…]

With the scientists happily distracted by playing with their atoms, mathematicians took over knot theory and set about trying to find a way to calculate what is a knot and what is not.*

* Technically, the unknot is not not a knot, it’s a trivial knot. Glad I could clear that up.

Of the Platonic solids, only the cube can fill a 3D space. People often claim that the tetrahedron is also space-filling (including Aristotle, in his work On the Heavens) but, despite the fact that this, er, ‘fact’, is repeated again and again, it isn’t, in fact, a fact: it isn’t true. If feels like it should work but, if you stack tetrahedrons, there will always be some small gaps between them.

So you can count up to 1,073,741,824 with your fingers ... if you're flexible enough.