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Guesting on the ‘Wrong, But Useful’ first anniversary episode

You may recall that Samuel Hansen and I used to have a weekly conversation about mathematics in the news and news in mathematics, which we called the Math/Maths Podcast and released through the (still going!) science communication project Pulse-Project. When we put Math/Maths on hiatus (the length of which is still an open question), this left a gap in the lucrative ‘two blokes talking about maths-y stuff’ market. Leaping on the opportunity, plucky young podcasters Colin Beveridge and Dave Gale started Wrong, But Useful (as you may recall from a previous post here). Well, that was a year ago now and, as creatures whose outlook is tied to this planet, that is apparently worth celebrating. Through a careful constructed mock-feud, Colin and Dave reeled in first Samuel and then me to join them in an anniversary recording.

‘Development and evaluation of a partially-automated approach to the assessment of undergraduate mathematics’

Next month I will present at the 8th British Congress of Mathematics Education, the “largest mathematics and mathematics education conference in the UK” which “brings together teachers from early years to higher education, researchers, teacher educators, CPD providers, consultants, policy makers, examiners and professional and academic mathematicians”, according to its website.

My talk is part of the research strand of the conference, organised by the British Society for Research into Learning Mathematics. This society is “for people interested in research in mathematics education”, and I am a member.

I’m presenting the ‘what I did’ portion of my PhD; well, most of it. Anyway, the peer-reviewed proceedings have now been published (not true! See edit below). My article is ‘Development and evaluation of a partially-automated approach to the assessment of undergraduate mathematics’. The abstract is below.

The neuroscience of mathematical beauty, or, Equation beauty contest!

Neuroscientists Semir Zeki and John Paul Romaya have put mathematicians in an MRI scanner and shown them equations, in an attempt to discover whether mathematical beauty is comparable to the experience derived from great art.

They’ve detailed the results in a paper titled “The experience of mathematical beauty and its neural correlates”. Here’s a bit of the abstract:

We used functional magnetic resonance imaging (fMRI) to image the activity in the brains of 15 mathematicians when they viewed mathematical formulae which they had individually rated as beautiful, indifferent or ugly. Results showed that the experience of mathematical beauty correlates parametrically with activity in the same part of the emotional brain, namely field A1 of the medial orbito-frontal cortex (mOFC), as the experience of beauty derived from other sources.

BBC News puts it: “the same emotional brain centres used to appreciate art were being activated by ‘beautiful’ maths”. This is interesting, according to the authors, because it investigates the emotional response to beauty derived from “a highly intellectual and abstract source”.

As well as the open access paper, the journal website contains a sheet of the sixty mathematical formulae used in the study. Participants were asked to rate each formula on a scale of “-5 (ugly) to +5 (beautiful)”, and then two weeks later to rate each again as simply ‘ugly’, ‘neutral’ or ‘beautiful’ while in a scanner. The results of these ratings are available in an Excel data sheet.

This free access to research data means we can add to the sum total of human knowledge, namely by presenting a roundup of the most beautiful and most ugly equations!

Martin Gardner Testimonials

21 October 2014 is the centenary of the birth of Martin Gardner, the supreme populariser of mathematics (amongst much else) who sadly passed in 2010. Those behind the Martin Gardner Centennial website and associated Twitter account @MGardner100th are collecting testimonials from people inspired by his work.

What does his extensive written legacy mean to you? Are you one of the many who can say things like “I only read Scientific American for Martin’s column” or “The reason I became a [insert profession/hobby here] is because of Martin”?

We’d love you to submit your comments here please. Feel free to say a little about yourself; if you taught physics for 27 years, tell us. If you are an artist or puzzle maker, or a student of computer science or psychology or linguistics, let us know. If you were lucky enough to correspond with or meet the great man, share your story. If you’ve already written elsewhere about Martin’s influence on you, please don’t be shy about giving details (web links, etc). If you’re a well-known author yourself, who knew Martin, please chime in too. Martin didn’t care if his sources or correspondents were amateurs or professionals, and we’re equally broadminded. We actively seek a good cross-section of comments, but we don’t mind repetition either. So many people have similar stories to tell, and we want them all.

Currently testimonials include Keith Devlin (testimonial #29), Cliff Pickover (#24), George Hart (#9), Max Maven (#3), John Allen Paulos (#30) and Colm Mulcahy (#7).

The website says all submissions will be posted following review. Testimonials can be submitted via the website or by email to gardnercentennial@gmail.com.

More information

Martin Gardner Testimonials.

For more about Martin Gardner, listen to the All Squared interview with Colm Mulcahy.

Via John Read on Twitter, who submitted testimonial #38.

Why do $0!$ and $a^0$ equal $1$?

The last two weeks my first year mathematicians and I have covered Taylor series.This means that several times I’ve had the conversation that goes “What’s $0!$?” “It’s $1$.” “Oh, erm, right. Why again?” “Because it works.” This may not be a completely satisfactory answer!

One of my students, Callum Mulligan, tweeted this question.

Saying “by definition” or “because it makes a bunch of stuff work” won’t cut it. So how to answer this question? To give a somewhat intuitive understanding of why this should be the case to a first year undergraduate. It may be obvious, but it wasn’t immediately obvious to me how to explain this, so I share some thoughts here.