Udo of Aachen: Lives of the Mathematical Ninja

This is an excerpt from my upcoming book, The Maths Bible, (which will eventually be available from all good bookstores.)

Udo of Aachen (c. 1200-1270) was a Benedictine monk, scholar, poet and mathematician. His best-known poetical work is Fortuna Imperatrix Mundi, which is usually know by its choral title, O Fortuna from Carmina Burana.

That’s not the most remarkable thing about Udo, though: when retired professor Bob Schipke visited Aachen cathedral, he noticed something incredible about a nativity scene. The Star of Bethlehem appeared to be in the shape of the Mandelbrot set.

He tracked down some of Udo’s original writings, which had been discovered in the 19th century and immediately filed away, presumably by a curator with no mathematical training. In them, Udo described the basics of probability theory, performed Buffon’s needle experiment, and wrote down rules for working with ‘profane’ and ‘spiritual’ numbers — which correspond precisely to what we call ‘real’ and ‘imaginary’ numbers. The process of repeatedly multiplying and adding them together, as in the Mandelbrot set, was seen as an allegory to determining who would be drawn to God, and who would be cast into darkness.

Udo of Aachen was a remarkable mathematician, many centuries ahead of his time, making use of techniques that weren’t widely adopted in Europe for many decades to come.


Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.


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