Resources for Non-Specialists
The Mathsters
YouTube channel of short maths videos aimed at sixth formers interested in doing maths at university, and other interested adults.
The Maths of Cream tea
Mathematical proof that clotted cream is better than whipped cream! Note: the papers are reporting that this “research” was commissioned by a clotted cream company. However I was not paid by them, nor did I even receive any clotted cream – and I couldn’t find any in Sheffield so I clotted my own in the rice cooker! Read the full story here.
The Maths of Pizza
The Maths of Doughnuts
The Maths of Mince Pies
The Maths of Popping Open a Bottle of Bubbly
Higher-dimensional category theory: the architecture of mathematics
An introduction to my field and my research as of November 2001. Written for non-specialists in any discipline (originally as part of a job application), it is very non-technical and includes various flights of fancy and copious analogies.
Mathematics and Lego: the untold story
Approximate text from a seminar I gave at Newnham College in November 2001 aimed at students and researchers of all levels and all disciplines. This is not a formally presented document, and it doesn’t include the slides, so some of it is a bit hard to imagine. Also, a radio interview I did on the subject in December 2012, on BBC Radio 4’s “More or less”.
Mathematics, Morally
A talk I gave at the Cambridge University Society for the Philosophy of Mathematics, and in a modified version later at the University of Chicago.
Abstract:
A source of tension between Philosophers of Mathematics and Mathematicians is the fact that each group feels ignored by the other; daily mathematical practice seems barely affected by the questions the Philosophers are considering. In this talk I will describe an issue that does have an impact on mathematical practice, and a philosophical stance on mathematics that is detectable in the work of practising mathematicians.
No doubt controversially, I will call this issue ‘morality’, but the term is not of my coining: there are mathematicians across the world who use the word ‘morally’ to great effect in private, and I propose that there should be a public theory of what they mean by this. The issue arises because proofs, despite being revered as the backbone of mathematical truth, often contribute very little to a mathematician’s understanding. ‘Moral’ considerations, however, contribute a great deal. I will first describe what these ‘moral’ considerations might be, and why mathematicians have appropriated the word ‘morality’ for this notion. However, not all mathematicians are concerned with such notions, and I will give a characterisation of ‘moralist’ mathematics and ‘moralist’ mathematicians, and discuss the development of ‘morality’ in individuals and in mathematics as a whole. Finally, I will propose a theory for standardising or universalising a system of mathematical morality, and discuss how this might help in the development of good mathematics.
Is mathematics easy?
Are Lectures a Waste of Time?
Build Your Own 5-Associahedron!
Here is a serious piece of mathematics that you can also cut out and make. All you need is scissors and tape, and the handy template linked.
Thanks are due to Aaron Lauda for making this when we were working together on Higher-Dimensional Categories: An Illustrated Guidebook. You can find more explanation in there (for specialists) or (for non-specialists) in my book How to Bake Pi.
Make your own Eckmann-Hilton Clock!
How to Write Proofs: A Quick Guide
This is a 17 page pamphlet aimed at mathematics students who are perplexed about how to write proofs, having never written proper mathematical proofs before. It’s chatty, with examples of good proofs and bad proofs. Here are the contents:
- What does a proof look like?
- Why is writing a proof hard?
- What sort of things do we try and prove?
- The general shape of a proof
- What doesn’t a proof look like — popular ways to write a bad proof
- Practicalities: how to think up a proof
- Some more specific shapes of proofs
- Proof by contradiction
- Exercises: What is wrong with the following “proofs”?
I wrote it for an evening “workshop” I ran for my calculus students at the University of Chicago, so the examples are taken from the beginning of that course: field axioms, functions etc. All the examples of erroneous proofs come from recurring problems I’ve seen from students in both Cambridge and Chicago. The aim of this pamphlet is to help iron out those problems.
I would be interested to hear your comments about it, whether you’re a student or faculty member. You’re welcome to distribute it to your students – in which case I’d be particularly interested to hear if it’s useful.