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Mathematical myths, legends and inaccuracies: some examples

I’m teaching a first-year module on the history of mathematics for undergraduate mathematicians this term. In this, I’m less concerned about students learning historical facts and more that they gain a general awareness of history of maths while learning about the methods used to study history.

Last week, I decided I would discuss myths and inaccuracies. Though I am aware of a few well-known examples, I was struggling to find a nice, concise debunking of one. I asked on Twitter for examples, and here are the suggestions I received, followed by what I did.

Happy Birthday Euler!

google doodle screengrab

Today is Euler’s $-306 \times e^{i \pi}$th birthday, and Google have chosen to celebrate (despite ignoring several other prominent mathematical birthdays, including Erdős’s centenary – see the @MathsHistory twitter feed for a full list) by creating a Google doodle on their homepage.

For anyone who isn’t aware, this is when Google changes the image above the search box on the homepage at, so it still says ‘Google’ but using an appropriate image, which sometimes has built-in interactive elements. I thought it was worth pointing out some of the fantastic maths they’ve included in today’s doodle.

Open Season – The Perfect Cuboid

In this short series of articles, I’m writing about mathematical questions we don’t know the answer to – which haven’t yet been proven or disproven. This is the second article in the series, and considers a less well-known variant on an extremely well-known problem.

Ask anyone to name a theorem, and they’ll probably come up with one of the really famous ones, like Pythagoras’ theorem. This super-handy hypotenuse fact states that for a triangle with sides A, B and C, where the angle between A and B is a right angle, we have $C^2 = A^2 + B^2$. This leads us on to a nice bit of stamp-collecting – there are infinitely many triples of integers, A, B and C, which fit this equation, called Pythagorean Triples.

One well-known generalisation of this is to change the value $2$ to larger values, and go looking for triples satisfying $C^n = A^n + B^n$. But don’t – Andrew Wiles spent a good chunk of his life on proving that you can’t, for any value of $n>2$, find any such triples. The statement was originally made by Pierre De Fermat, and while Fermat famously didn’t write down a proof, it was the last of his mathematical statements to be gifted one – hence the name ‘Fermat’s Last Theorem’ – and proving it took over 350 years.

Mathematics: a culture of historical inaccuracy?

Earlier this year, back when I somehow managed to find time to write blog posts (sorry!), I wrote a couple of pieces on incorrect but oft-repeated stories in history of mathematics, basically describing some issues and expressing my frustration. These were Apparently Gauss got in this bar fight with Hilbert… and Why do we enjoy maths history misconceptions?

Today Thony Christie wrote on Twitter (as @rmathematicus) with a link to this post by Dennis Des Chene (aka “Scaliger”): On bad anecdotes and good fun. As Thony points out, this is an “excellent piece of maths history myth busting” and I am writing this quick note to commend you to read it.

Interesting Esoterica Summation, volume 4

Dust off your thinking hat and do some mind-stretches because here’s another course of Interesting Maths Esoterica! It’s been several months since the last volume so this is quite a big post. I won’t mind if you skim it.

In case you’re new to this: every now and then I encounter a paper or a book or an article that grabs my interest but isn’t directly useful for anything. It might be about some niche sub-sub-subtopic I’ve never heard of, or it might talk about something old from a new angle, or it might just have a funny title. I put these things in my Interesting Esoterica collection on Mendeley. And then when I’ve gathered up enough, I collect them here.

The unplanned impact of mathematics

Time and again, pure mathematics displays an astonishing quality. A piece of mathematics is developed (or discovered) by a mathematician who is, often, following his or her curiosity without a plan for meeting some identified need or application. Then, later, perhaps decades or centuries later, this mathematics fits perfectly into some need or application.