The Lives of the Mathematical Ninja: Bourbaki

Dangerous bends sign

Nicolas Bourbaki published a series of books in the middle of the 20th century, in an attempt to put maths on a firmly rigorous footing. So far, so completely antithetical to Mathematical Ninjary, which is all about getting good answers quickly without worrying too much about the details.

But there’s one thing about Bourbaki that makes him stand out as a Ninja of the highest order: he didn’t exist.

Or rather, the person Bourbaki didn’t exist. Instead, ‘he’ was a group of mathematicians who got together in 1935 in Paris to write a textbook — explicitly, the textbook that would render all other textbooks obsolete1. It would treat all of the important areas of maths in a rigorous, logical manner.

It’s still — or at least was, when my ex-colleague Jean was a student there — very influential in France: he has stories of doing a simple subtraction in his first year at university and being marked down because he hadn’t proved that subtraction was a valid operation.

Bourbaki’s main legacy for me is that they introduced the Ø symbol  to mean the null (empty) set and, better still, a sort of diagonal N like the one you see on a ‘dangerous curves’ sign, meaning… well, dangerous curves: they’d put it next to any section of the textbook they thought was difficult.

Colin

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.

  1. Naturally, this didn’t happen, but you have to admire their chutzpah. []

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