The Quixotic Search for a “Fair” Math Test

Math with Bad Drawings

It’s happened again: a math question made students cry.

This time it was in Scotland—very discouraging, as I’ve always assumed the Scottish raise a tougher, more stoic, northerly breed of mathematician. Alas; it seems they’re as skittish and frightened as the rest of us.

Here’s the offending question:


(My two cents? This question is more than just fair; it’s really good!)

But students panicked. Then they tweeted their panic. The BBC quoted a former examiner denouncing this question as “unfit for purpose.” And commentators leered at the spectacle—by this point routine—of students freaking out about a hard math question.

This sort of ordeal threatens to confirm our darkest and most cynical suspicions about students. They’re incurious. They’re mercenaries. They’re on a witch hunt for anything that pushes them out of their comfort zone. They worship at the Church of the Right Answer.

So who do we blame? The students?…

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Where the Laws No Longer Hold

Somehow, I suspect I wouldn’t survive long on the frontier.

Drop me in the American West, circa 1850, and I fear my math-blogging and bad-drawing skills might not carry me far. I need indoor plumbing. I need the rule of law. I need chain coffee shops. I’m not cut out for the frontier.

And yet the frontier is exactly where I found myself the other day, when I came across this formula in the wonderful Penguin Book of Curious and Interesting Numbers, by David Wells:


I decided to play around with this product a bit. After all, what are products for, if not playing around?

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Donuts, math, and superdense teleportation of quantum information

Quantum teleportation has been achieved by a number of research teams around the globe since it was first theorized in 1993, but current experimental methods require extensive resources and/or only work successfully a fraction of the time. Now, by taking advantage of the mathematical properties intrinsic to the shape of a donut — or torus, in mathematical terminology — a physicists have made great strides by realizing ‘superdense teleportation.’

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Cakes, Custard and Category Theory: Easy Recipes for Understanding Complex Maths, by Eugenia Cheng

Noel-Ann Bradshaw is inspired by a book with all the right ingredients for explaining a tricky subject.

Apart from alliteration, what on earth do cakes, custard and category theory have in common? As a recent winner of the Best Mathematical Cake prize at MathsJam, the recreational mathematics conference, I feel I am fairly qualified to understand the connections that mathematician Eugenia Cheng illustrates here.

Cheng – the only female category theorist in South Yorkshire, she quips – has written this deliciously lively text with the aim of showing that “mathematics is there to make difficult things easy”. It is a book of two halves: the first explains the mathematical concepts needed to understand category theory, and the second describes the rudiments of category theory itself, a branch of abstract mathematics often described as the “mathematics of mathematics”. She combines these definitions to deduce that “category theory is there to make difficult mathematics easy” – in a neat contrast to the warning in the title of Carl E. Linderholm’s memorably mischievous look at the subject, Mathematics Made Difficult (1972).

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Questions aren’t the enemy. They’re the ammo.

In grad school, my wife took a class that assigned no homework. The topic was an advanced, hyper-specific area of research—the only plausible problems to give for homework had literally never been solved. Any answer to such a question would have constituted novel research, advancing the field and meriting a publication in a professional journal. The professor assigned no homework for the simple reason that there was no practical homework to assign.

This tickled me. I’d never thought of good questions like a fossil fuel. A nonrenewable resource. Built up over eons and consumed in minutes.


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