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The Mathematical Beauty of the Game SET

Three SET cards, forming a 0-alike SET

If you are like me, you have played the game SET and have probably been perplexed at how quickly some people can play the game! Even as the game is quite easy to explain, it takes some time to build various strategies and pattern recognition to play the game effectively. If you have never heard of SET, don’t fret because we will soon review its layout. For my final masters project at Texas A&M University, we had the autonomy to research any higher-level mathematical topic and I felt SET would be a great venue to tap into some deeper mathematics. Little did I know how truly complex and elegant SET really is with connections to combinatorial geometry, finite affine geometry, and vector spaces over finite fields, some of these problems still open in research-level mathematics. All of these topics (and more) are included in a great resource I highly recommend for some summer reading. Check out The Joy of Set by McMahon, et al. to dig deeper into what is presented below.

Wikiquote edit-a-thon – Saturday, May 12th, 2018

TL;DR: We’re holding a distributed Wikipedia edit-a-thon on Saturday, May 12th, 2018 from 10am to improve the visibility of women mathematicians on the Wikiquotes Mathematics page. Join in from wherever you are! Details below, and in this Google Doc.


Extension and abstraction without apparent direction or purpose is fundamental to the discipline. Applicability is not the reason we work, and plenty that is not applicable contributes to the beauty and magnificence of our subject.
– Peter Rowlett, “The unplanned impact of mathematics”, Nature 475, 2011, pp. 166-169.

Trying to solve real-world problems, researchers often discover that the tools they need were developed years, decades or even centuries earlier by mathematicians with no prospect of, or care for, applicability.
– Peter Rowlett, “The unplanned impact of mathematics”, Nature 475, 2011, pp. 166-169.

There is no way to guarantee in advance what pure mathematics will later find application. We can only let the process of curiosity and abstraction take place, let mathematicians obsessively take results to their logical extremes, leaving relevance far behind, and wait to see which topics turn out to be extremely useful. If not, when the challenges of the future arrive, we won’t have the right piece of seemingly pointless mathematics to hand.
Peter Rowlett, “The unplanned impact of mathematics”, Nature 475, 2011, pp. 166-169.

Now, don’t get me wrong. I have every admiration for Peter and his work; his is a thoughtful voice of reason, and it’s not at all unreasonable for the Wikiquote page on mathematics to cite his writing.

Taming the AGM

This post is in response to Peter’s post introducing the Approximate Geometric Mean.

The approximate geometric mean $\mathrm{(AGM)}$ is a nice approximation of the geometric mean $\mathrm{(GM)}$, but it has some quirks as we will see. After a discussion at the MathsJam gathering, I was intrigued to find out how good an approximation it is.

To get a better understanding, we first have to look again at its definition. For $A=a\cdot 10^x$ and $B=b \cdot 10^y$, we set

\[ \mathrm{AGM}(A,B):=\mathrm{AM}(a,b)\cdot 10^{\mathrm{AM}(x,y)} \]

where $\mathrm{AM}$ stands for the arithmetic mean. This makes also sense when $a$ and $b$ are not just integers between 1 and 10, but any real numbers. Note that we won’t consider negative $A$ and $B$ (i.e. negative $a$ and $b$), as the geometric mean runs into issues if we do so. The values of $x$ and $y$ may be negative, though. The $\mathrm{AGM}$ looks like a mix between the $\mathrm{AM}$ and the $\mathrm{GM}$, so what can possibly go wrong?

Gerrymandering Gives Mathematics’s Moon a Day in the Sun

If you pay attention to United States politics you have probably noticed that mathematics is currently enjoying a rare moment of relevance. You probably also know this is not happening because all of a sudden politicians have decided that mathematics is clearly the coolest thing in the world, even though it clearly is, but instead because gerrymandering has become one of the major issues du jour.

I’ve re-recorded Alan Turing’s “Can Computers Think?” radio broadcasts

On the 15th of May 1951 the BBC broadcast a short lecture by the mathematician Alan Turing under the title Can Computers Think? This was a part of a series of lectures on the emerging science of computing which featured other pioneers of the time, including Douglas Hartree, Max Newman, Freddie Williams and Maurice Wilkes. Together they represented major new projects in computing at the Universities of Cambridge and Manchester. Unfortunately these recordings no longer exist, along with all other recordings of Alan Turing. So I decided to rerecord Turing’s lecture from his original script.

Review: Geometry Snacks, by Ed Southall and Vincent Pantaloni

Geometry Snacks cover

Exams have a nasty habit of sucking the joy out of a subject. My interest in proper literature was dulled by A-Level English, and I celebrated my way out of several GCSE papers – in subjects I’d picked because I enjoyed them – saying “I’ll never have to do that again.”

Geometry is a topic that generally suffers badly from this – but fortunately, Ed Southall and Vincent Pantaloni’s Geometry Snacks is here to set that right.

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