How to tie a tie? There are various knots and depending on the tie one will look better than the other. The instructions and illustrations may seem confusing at first but the good news is that once you've got any particular knot in your fingers you won't forget it. It's like swimming or cycling.

This weekend’s Financial Times features an article about the comeback of the Windsor knot. I was instantly reminded of an article in Nature of some years ago, Designing Tie Knots by Random Walks, about the mathematics of tie knots. Along with the mathematics of juggling and origami it is still one of my favourite examples of how mathematics can prove practical and fun.

The authors, physicists Thomas Fink and Yong Mao, realized that a tie knot consists of a sequence of moves, which can be described as a random walk on a triangular lattice. Don’t panic if this sounds difficult, the ideas and diagrams are surprisingly simple and easy to follow. This formal approach led them to the discovery of 85 tie knots, 13 of which satisfied additional aesthetic criteria of balance and symmetry.

At the time of publication, in 1999, the article spawned a wave of media attention and Fink and Mao subsequently wrote a fun little book, The 85 Ways To Tie a Tie. It contains a brief history of tie knots and a short introduction to knot theory, the mathematics of knots. The 13 aesthetically pleasing knotted are illustrated with clear diagrams and advice as to which knot to use with which type of tie. My personal favourite is the knot the authors named St Andrew. It’s the one I use most often.

Every now and then you read about the tie being old fashioned, its days being counted and so on. But the tie is still around. I wear my own ties both professionally and as a fashion accessory, depending on the occasion.

If you're looking for a nice tie, my own collection consists of ties from Charvet, Richard James, Brioni, Zegna and Duchamp. Victoria Richards does beautiful hand painted ties. Paul Smith also has some nice ties in his collection, they're special in that the rear side also has a nice design.

Update: Of course, you can now find instruction videos on YouTube, which make life a whole lot easier.