Today is St. Valentine’s Day, the day in much of Western culture arbitrarily designated to be the day for love. So let’s see what mathematics has to say on the subject. Finding a relationship with someone special is often about being introduced to people and sifting out the inappropriate. It seems clear that there is plenty of scope for the application of statistical techniques to the processes of meeting and weeding. First up is a great video from the ever-so-slightly geeky Amy Webb, who used mathematics to calculate the odds of finding a mate in Philadelphia. After producing a figure of 35 suitable men satisfying her criteria in a city of 1.5 million people she realized that she would have to turn to maths for help. There’s even a book, Data, a Love Story. Over on Wired, Chris McKinlay’s attempts to hack OKCupid’s online dating service is profiled. The article left me in two minds. Is this is great use of mathematics or is it just a bit creepy? Seemingly, the approach worked for him and no one is reported injured, so perhaps I shouldn’t judge. As a bonus, Wired also produced a handy infographic slideshow describing tips for improving online dating profiles. Top tips: Avoid Karaoke, get into surfing. My favourite though is that it is more attractive to mention “cats” than “my cats”. If everything goes well with the dating, then how do you arrange the wedding? “With maths” is not the standard answer. The Guardian reports on a statistically modelled wedding. This solves the centuries old problem of how to write the guest list. After all, you don’t want too few guests or too many accepting. Next post: Calculating the likelihood of...

## Rafael Araujo – A New Escher?...

posted by Kevin Houston

One needs only look at some of Fomenko’s monstrosities to see that mathematics and art don’t always mix well. Exceptions are rare with Escher the benchmark for excellence. A recent Wired article on the Venezuelan artist, Rafael Araujo, describes how he produces his mathematically constructed pictures. I can see these joining Escher’s pictures on the walls of mathematicians throughout the world over the next few years. The full article is here but you can also see stunning examples on his...

## Hilbert Hotel Video

posted by Kevin Houston

Belated Happy New Year! Here’s another of those short educational TED videos. This time on the Hilbert Hotel. (A cartoon Hilbert does seem to make an appearance but it is hard to tell as he isn’t wearing the hat. Do you think Hilbert wore that hat just once and had the misfortune of having it appear in his most famous picture?) Anyhow: You can find out more at the TED Education page for the video. Oh, and this week is the last chance to win a signed copy of Simon Singh’s book on The Simpsons! See...

## Maths and Magic on Radio 4...

posted by Kevin Houston

Should have posted this the other day: Last Friday Radio 4 transmitted a programme on maths and magic entitled, Maths and Magic! It features Jolyon Jenkins investigating the connection between the subjects in the title. You can hear it here for at least a few days. There are links on the web page but I thought I should add some. One of the magicians, Alex Stone, wrote one of my favourite books of the year, Fooling Houdini, which is about how he realized he was a terrible magician and devoted himself to changing that by immersing himself in the study of magic. He also does the same trick as Jenkins and there is a deeper explanation of it in the book. The Radio 4 website also lacks links to MathsJam and to James Grime, a contributor to Numberphile. Furthermore, the website cites Persi Diaconis as the sole author of Magical Mathematics when in fact it was co-authored by Ron Graham. And on the subject of Radio 4, today’s Infinite Monkey Cage isn’t about maths but is well worth a listen because of the excellent contributions from James...

## Singh, Simpsons and Skeptics...

posted by Kevin Houston

This is a rather belated review of Simon Singh’s talk on The Simpsons and Their Mathematical Secrets given for the Leeds Skeptics in the Pub in the Victoria Hotel pub. (There’s a chance to win the book, details below.) The Victoria is not a large pub so I did wonder where the audience was going to fit. In the end I counted nearly 100 people and this did not include those standing in the corridor or in the street outside. The Sardine Conjecture for @SLSingh at @leedsskeptics pic.twitter.com/XqE0p3lOs5 — Martin Iddon (@WalrusofComms) October 20, 2013 The talk is in two halves, the first covers the book and in the second Singh bravely invites questions on any topic connected to his work. The book part of the talk, accompanied by slides, delves into the mathematical backgrounds of the writers of The Simpsons and Futurama and how they inserted mathematical jokes into the programmes. Some of this was familiar as I’m a fan of both shows (though The Simpsons seems to have jumped the shark a while ago — Ned secretly married Mrs Krabappel!?) but Singh has done his homework and gained access to the writers so there is plenty here that was new to me. One of my favourite bits from the book wasn’t mentioned in the talk — there was a theorem invented purely for an episode of Futurama. So, the first part of the talk was about the book and during the interval Singh signed copies. Afterwards he did a question and answer session which amongst other things covered libel laws, Fermat’s last theorem, the Big Bang and quack medicine. The tour continues for another month, details can be found here. A great talk – you won’t be disappointed if you go. —-...

## Interview with Richard Elwes...

posted by Kevin Houston

In this post I interview Richard Elwes, author of a number of maths books in recent years. He has kindly agreed to give away signed copies his two most recent, Mathematics in 100 Key Breakthroughs and Chaotic Fishponds and Mirror Universes. For a chance to win all you have to do is sign up for my newsletter, see the right sidebar or the bottom of this post. I’ll get my daughter to randomly pick two winners from the list of subscribers in a couple of weeks. On with the interview… Hello Richard! I think we first met when you were a PhD student here at Leeds. Can you give a quick account of your background to help people get a feel for where you are coming from? I initially followed a conventional academic path: I studied maths as an undergraduate at Oxford, and then moved north to Leeds to start a PhD in 2001, where I met you among other excellent people. My research at that stage was in the general field of mathematical logic. Afterwards I held a postdoctoral position in Freiburg in Germany, and at some point after that I somehow found my way into writing about maths for the general public. Apart from books, I’ve written for the New Scientist, and for the excellent Plus magazine online. In fact I got my first break there, when I won their New Writers’ competition in 2006, with an article about the classification of finite simple groups (http://plus.maths.org/content/os/issue41/features/elwes/index). Your book Maths in 100 Key Breakthroughs came out last month. What’s it about? Who is it aimed at? It’s aimed at anyone who finds the idea of maths interesting and appealing, but who doesn’t want to drown in equations and jargon. So it’s written with...

## Simon Singh and the Simpsons...

posted by Kevin Houston

The week has been so busy that posting this has been delayed – I’ve been to London, Birmingham and Sheffield in the last three days. I did manage to install for a newsletter sign-up form for the blog. You can see it in the sidebar unless my hacks to the code have destroyed it for your browser. Please sign up if you want to know about maths articles, events, etc. Back to business. Simon Singh‘s new book, The Simpsons and Their Mathematical Secrets, is as the title suggests about the mathematics occurring in the long running cartoon The Simpsons. Now, I knew there were plenty of maths gags in the Simpsons but I’m surprised he has filled a whole book. Maybe he also includes stuff from Futurama which was packed with maths gags and even led to a lecture by Sarah Greenwald. This became a DVD extra on Bender’s Big Score (The audience features Simpsons and Futurama’s creator Matt Groening.) Singh’s book is not out yet but you can read an article about it in last Sunday’s Observer. He’ll be doing a (rather small) tour to promote the book, details are on his website. I’m planning to be at the Leeds event so maybe I’ll see you...

## How to Think Like a Mathematician

posted by Kevin Houston

It’s the blog’s birthday! It’s also the week before the start of the university year here and so it’s a good time to shamelessly advertise my best selling book. The success of How to Think Like a Mathematician has taken me by surprise. It has sold nearly 10,000 copies since it was published. Ok, I’m not going to rival JK Rowling but given that the statistic often quoted in the publishing world is that 95% of books sell less than 5000 copies, I am really happy that the book has found an audience and I get emails from all round the world saying how much they like the book. It has been translated into French, German, Turkish and a Korean version will appear soon. (See links below.) It has been adopted as a textbook throughout the world – I’ve lost count of the places that use it. Enough of the puff, what’s it about? Well, the book was written for anyone studying a mathematics degree or a mathematically based subject. My aim when I wrote it (it took me about 17 years but that’s another story) was to let students in on some of the secrets behind actually thinking like a mathematician so that learning mathematics becomes easier. The book has six parts: Study Skills for Mathematicians. This shows you how to read and write mathematics. The latter is an easy to learn skill and will set your work apart from most other students. How to Think logically. Mathematics is well known to be dependent on logic. Here you learn the basics from a very practical perspective. Definitions, theorems and proofs A key difference between university and pre-university level mathematics is that it is now not just about calculating. Definitions are made precise, mathematical truths (called theorems) are stated and they have to be shown to be unequivocally true by giving a proof. In this part you learn how to pull apart definitions, theorems and proofs so that you understand them. Techniques of proofs. Now that you have to prove things you need some techniques to bring out as the need arises. Mathematics that all good mathematicians need. The title is self-explanatory. Many other books introduce university level mathematics but then forget to include the maths you will be studying in your course. Closing remarks. We pull together everything learned so that rather than rely on superficial rote learning you develop deep understanding. Some of the tips in the book are simple but effective. The following is a taster: Many students asked to show that an equation holds will merely rearrange it an haphazard way to produce some other equation they know is true such as 1=1. (The reason why this is just plain wrong is given in Chapter 21, Some Common Mistakes. Hint: it is to do with logic.) Here’s a simple tip that works so much better: Take the most complicated side and do something to reduce it to the other side. This works. It stops you tying yourself in knots when randomly rearranging terms from one side to the other in the hope that something will happen. Instead it forces you to think about what you can do with the terms. It’s a simple trick that changes behaviour. If you are interested in owning a copy, then just follow the links below: How to Think Like a Mathematician: A Companion to Undergraduate Mathematics (UK) How to Think Like a Mathematician: A Companion to Undergraduate Mathematics (US) Wie man mathematisch denkt: Eine Einführung in die mathematische Arbeitstechnik für Studienanfänger (Deutschland) Comment penser comme un mathématicien (France) Matematikçi Gibi Düşünmek (Türkiye) How to Think Like a Mathematician: A Companion to Undergraduate Mathematics (Italia) How to Think Like a Mathematician Paperback: A Companion to Undergraduate Mathematics (España) (Some of the above are affiliate...

## Maths predicts – this time movie success

posted by Kevin Houston

In a previous post I talked about predictions using maths and Nates Silver‘s book on essentially that topic was one of my favourites books of last year. This next one is a bit of fun – predicting movie success. Film buffs will know William Goldman’s quote about making films “Nobody knows anything” which is taken to mean that no one can predict how a film will do at the box office. However, researchers have some good news. Mestyán, Yasseri and Kertész have published Early Prediction of Movie Box Office Success Based on Wikipedia Activity Big Data. As you can tell from the title the key is to use online data and activity. Their algorithm gives good predictive power up to a month before the film is released and hence will be of little use to Hollywood producers receiving pitches for new films. Of course, these are early days and even the Oxford Internet Institute news article uses the word predicts in quotes. Nonetheless the authors compare their results to those obtained using Twitter by other researchers and find it better. The paper is freely available and since the maths behind it is accessible to undergraduates it would be great for a student mini-project. (Talking of projects, over the summer I had an undergraduate studying symmetry matching and it has turned out very well so I’ll definitely be writing about that soon.) Photo attribution: Alex Eylar,...

## Glassified – Reinventing the ruler?...

posted by Kevin Houston

The ruler has remained unchanged for thousands of years. Now it has been updated! You can read more (but not much) at Anirudh Sharma’s website, Creative Applications, Gizmag, and...

## Maths Jam plug and Zeno’s Paradox (not together!)...

posted by Kevin Houston

First a plug for the next Maths Jam in Leeds: It will be on Tuesday 23rd at 7pm in the White Swan (it’s pretty much next to the City Varieties). I’ll be there (I know that if don’t publicly commit to it, then I’ll miss it) so maybe I’ll see you there! Here’s a link to a rather good Ted Ed video on Zeno’s paradoxes. I wish I had seen this before I gave my History of Maths course this year, it would have been quite useful despite its simple nature. There is a page for further information on the this...

## Sconic sections

posted by Kevin Houston

This is a strange one: How to make edible conic sections! You can find the details at Evil Mad Scientist. If you enjoy maths-related cooking, then see my post on Tau-nados. Does anyone else have any other...

## Wolfram on Leibniz

posted by Kevin Houston

The usual busyness at the end of the teaching term and a holiday last week have meant that I’ve not been posting for a while. Today’s post is a short one from me directing you to a fairly long post by Stephen Wolfram on his recent visit to the Leibniz archive in Hannover. Read it...

## Lagrange book sale

posted by Kevin Houston

I never miss a chance to rummage around in second-hand book shops. In the past bargains were easy to come by but now the internet has killed that off. Now all books are priced pretty much the same and I no longer have the experience of approaching the counter carrying a much-underpriced book with the feeling that I am stealing from the shop and am about to be discovered. Those days are gone. As they are not experts, unfortunately charity shops price their books by consulting the web. This leads to setting the price of some dog-eared copy at just below the price of a mint condition one. Also, I miss the end-of-search feeling as I come across a long sought-after book. These days if I want a book I can find it on Amazon or Abebooks in minutes. The latter is my favourite second-hand book-seller site. They often send me emails about books and a recent one is worth sharing. One of the most expensive sales on the site in March was a book by Lagrange. The relevant part of the article is the following. Our list also includes an historic textbook from 1788 that has had a lasting influence on mathematics. Sounds a bit dull? Not at all. Méchanique Analitique by Joseph Louis Lagrange sold for $13,112. Born in Italy, Lagrange became a famous academic in France and Germany, and managed to survive the French Revolution despite the carnage surrounding him. Méchanique Analitique advanced analytical mechanics beyond the work of Isaac Newton and Galileo Galilei. He wrote the book while in Berlin where he was director of mathematics at the Prussian Academy of Sciences. It was his greatest piece of work, although he contributed widely to mathematics and astronomy. He laid down...

## Colin Wright and the mathematics of juggling...

posted by Kevin Houston

Recently, an acquaintance from my days as a researcher at Liverpool University alerted me to the existence of the Museum of Mathematics in New York. My acquaintance, Janet West, was a PhD student when I was at Liverpool and is now involved in the museum. There’s plenty of stuff online to look at but I would like to draw your attention if you have not already seen it to a lecture by Colin Wright. Colin is well-known in the mathematics communication community as he probably does more mathematics talks in schools around the country than anyone else. His main talk is about the mathematics of juggling. You can see him talking on to the BBC about it by clicking this link. (Note that the headline says he is a teacher whereas in fact his job is in marine navigation!) Colin gave a talk at the Museum of Maths in New York which was recorded and is on YouTube. You can even buy a DVD version. Teachers: If you are interested in seeing his talk at your school, then go to his...

## What is the Best Proof of Cauchy’s Integral Theorem?...

posted by Kevin Houston

My book on Complex Analysis is now available! You can find it at xtothepowerofn.com. The material below is there along with other sample chapters on Common Mistakes and on Improving Understanding. Today’s post may look as though I’m going all Terry Tao on you with a long post with lots of mathematical symbols. It’s really about the learning and teaching of Cauchy’s integral theorem from undergraduate complex analysis, so isn’t for everyone. If it’s not your cup of tea/coffee, then pop over here for some entertainment. Cauchy’s Integral Theorem Cauchy’s Integral Theorem is one of the greatest theorems in mathematics. There are many ways of stating it. Here’s just one: Cauchy’s Integral Theorem: Let be a domain, and be a differentiable complex function. Let be a closed contour such that and its interior points are in . Then, . Here, contour means a piecewise smooth map . In my years lecturing Complex Analysis I have been searching for a good version and proof of the theorem. My definition of good is that the statement and proof should be short, clear and as applicable as possible so that I can maintain rigour when proving Cauchy’s Integral Formula and the major applications of complex analysis such as evaluating definite integrals. Many of the proofs in the literature are rather complicated and so time is lost in lectures proving lemmas that that are never needed again. Here’s a version which I think has a good balance between simplicity and applicability. I’ve highlighted the difference with the version above. Cauchy’s Integral Theorem (Simple version): Let be a domain, and be a differentiable complex function. Let be a simple closed contour made of a finite number of lines and arcs such that and its interior points are in . Then, . Here an important point is that the curve is simple, i.e., is injective except at the start and end points. This means that we have a Jordan curve and so the curve has well-defined interior and exterior and both are connected sets. With this version I believe one can prove all the major theorems in an introductory course. I would be interested to hear from anyone who knows a simpler proof or has some thoughts on this one. Proof of Simple Version of Cauchy’s Integral Theorem Let denote the interior of , i.e., points with non-zero winding number and for any contour let denote its image. First we need a lemma. Lemma Let be a simple closed contour made of a finite number of lines and arcs in the domain with . Let be a square in bounding and be analytic. Then for any there exists a subdivision of into a grid of squares so that for each square in the grid with there exists a such that for all Proof of Lemma The set up looks like the following. For a contradiction we will assume the statement is false. Let and divide into 4 equal-sized squares. At least one of these squares will not satisfy the required condition in the lemma. Let be such a square. Repeat the process to produce an infinite sequence of squares with .By the Nested Squares Lemma (which is just a generalization of the Nested Interval Theorem) there exists . As is differentiable there exists such that for . But as the size of the squares becomes arbitrarily small there must exist such that is contained in the disk . This is a contradiction. Main part of proof Given there exists a grid of squares covering . Let be the set of squares such that and let be the set of distinguished points in the lemma. Define by Then as is differentiable, is continuous (and hence integrable). Without loss of generality we can assume that is positively oriented. Let be the union of positively oriented contours giving the boundary of . Since is made of a finite...

## Mary Cartwright article...

posted by Kevin Houston

Mary Cartwright is fairly well-known amongst mathematicians in the UK but less widely known amongst the general public. A recent BBC online article about her and her work may be the beginning of a change in this situation. There is even a Radio 4...

## Estimating large numbers the Fermi way...

posted by Kevin Houston

Here’s a really good introduction to estimating numbers and includes Enrico Fermi‘s famous “How many piano tuners are there in Chicago?” You can see more like this at...

## Matt Parker Number Ninja...

posted by Kevin Houston

This is mainly one for those local to Leeds (although see the bottom of the post). As part of the Leeds Festival of Science, Matt Parker will be giving a talk at the University. From the advertising: Direct from BBC Radio 4’s Infinite Monkey Cage with Brian Cox and Robin Ince, with research featured on QI, Leeds will be welcoming stand-up Maths comedian Matt Parker. Expect everything from debunking number nonsense and flagrant sudoku abuse to the mysterious patterns in the locations of ancient monuments and defunct Woolworths stores. Suitable for ages 16 plus. Entry to the show is strictly by ticket only. Book early as places are limited. Tickets can be booked via the University of Leeds website I’ll be doing my own little bit for Leeds Science Week with a visit to at least one school. See the Schools Programme. Teachers and pupils: Although it’s too late to book me for science week, if you want me to visit your school, then get please get in touch. I’ll travel further afield than just...

## Maths problems tweets...

posted by Kevin Houston

I’m not a big user of twitter as I prefer to read material that has more than 140 characters. Nonetheless, often something interesting appears. Dan Meyer set off an intriguing set of responses to his call for maths problems that can be posed within Twitter constraints. The results can be seen here: Tweet-sized...

## Mathematics of the mosh pit...

posted by Kevin Houston

Rock music fans are aware of the phenomenon of the mosh pit at concerts — a riotous area, usually close to the stage, where concert-goers, in lieu of learning complicated dance steps, slam violently into each other (and hence an alternative name for moshing is slam dancing). Until now the fascinating mathematics of this emergent property of crowds has been unjustly ignored. However, this has changed with the advance publication on the arXiv Collective Motion of Moshers at Heavy Metal Concerts by Silverberg, Bierbaum, Sterna and Cohen. The abstract states Human collective behavior can vary from calm to panicked depending on social context. Using videos publicly available online, we study the highly energized collective motion of attendees at heavy metal concerts. We find these extreme social gatherings generate similarly extreme behaviors: a disordered gas-like state called a mosh pit and an ordered vortex-like state called a circle pit. Both phenomena are reproduced in flocking simulations demonstrating that human collective behavior is consistent with the predictions of simplified models. The authors model the behaviour of the mosh pit (and circle pit), provide source code and Java script interactive moshpit The conclusions will be surprising to many: If we increase the self-propulsion coefficient (decrease ), we find the motion, though random, is no longer fit by a Maxwell-Boltzmann distribution. Instead, collisions between active and passive MASHers [Mobile Active Simulated Humanoid] on the boundary of the simulated mosh pit removes energy faster than collisions among active MASHers can rethermalize the system. Consequently, measurements in silico show a radial temperature gradient is established with a higher effective temperature at the core of the simulated mosh pit and a lower effective temperature at the edge A valuable and timely addition to the literature. Ok, let’s...

## Archimedes and 3D printing...

posted by Kevin Houston

3D printing seems to have some sort of turning point in the last few months. Lots of people know what it is and many are experimenting with it. This week I began teaching on my History of Mathematics module; yesterday’s lecture was about Archimedes. I would never imagined that the two could be combined but today I saw a preprint on the arXive on the combination of Archimedes and 3D printing. The paper has a brief history of Archimedes and his works (and quite a few elementary typos) and focusses on how to make models of his inventions, for example his water screw, and more mathematical objects using a 3D printer. I don’t have access to 3D printing but would be intrigued to give some of the Archimedes models a go. Certainly, it would be great to have a supply of Platonic and Archimedian solids to show students. Has anyone out there tried something...

## Mathematics of Lego

posted by Kevin Houston

Obviously the first post of the year should be a serious one about the year ahead, New Year’s resolutions and such. Not this time. This time I urge you to have a look at the mathematics of Lego via Wired. Read the article here. To be honest I’m not sure if this really is a good example of a log-log plot (could I use it in class) or if it even tells us something deep about Lego but I think it’s worth a...

## End of the year…...

posted by Kevin Houston

It’s the end of the year. It seems only like yesterday we were all saying “What? I can’t believe it’s the end of January already”. So what was the year like? I feel I’ve had a good year – I’ve been having a lot of fun trying to understand discrete surfaces and if I hadn’t succumbed to a virus just shortly before Christmas I might have written the bulk of my first paper on the subject. I also had fun with the Beatles story which garnered a lot of attention. Interestingly the most read blog entry was on the passing of Vladimir Zakalyukin. In the world of science the big story was not in mathematics but in the discovery of the Higgs boson. Given that the evidence is hardly overwhelming, it wouldn’t surprise me if the big story in 2013 was its ‘undiscovery’ and the scientists admit a mistake or a misreading of the data. For 2013 one of my top resolutions is to finish my next book. Feel free to write and remind me of that at the end of 2013 if it remains uncompleted. It will be tricky as this coming semester I have a lot of teaching (if there are any of my History of Maths students reading, then watch The Two-Thousand-Year-Old Computer, there are two days left to watch.) Have a good...

## Nate Silver Talk at Google...

posted by Kevin Houston

Nate Silver has come to prominence recently through the seemingly simple method of predicting election results through statistics. I’ve just finished reading his book, The Signal and the Noise and it’s certainly one of my favourite books of the year. It covers all sorts of predictions, in baseball, chess, politics, earthquakes, terrorism, stocks, and more besides. If I were to recommend a Christmas book for a maths geek, then this would be the one. He recently gave a Google talk which you can see...

## Scott Young on Lectures...

posted by Kevin Houston

I follow a number of education writers and those who write about learning. One of these, Scott Young, is a high achieving recent graduate who seems to be making a living by giving learning advice. His latest claim to fame is his MIT Challenge where he studied a complete 4-year MIT course in one year as a way of learning new skills but also, presumably to prove the effectiveness of his methods. My opinion is that some of the methods are debatable as they don’t foster really deep understanding of a topic, a number are just ways of quickly mastering the necessary ideas to pass an exam. As an example, in one of the key documents he uses to advertise his Learning on Steroids programme he shows how someone used his methods to learn the mathematical concept of limits. There is a scan on page 7 of the notes. The student writes in a section headed “What is a limit, REALLY?” that “A limit is like a stalker, forever getting close to the target. Forever trying to close the distance between it and the target, but rarely ever succeeds.” This analogy is deeply flawed. Worse than that, leaving aside the word stalker, it is precisely what I have to stop students thinking a limit is. When I set an exam question on the definition of a limit, many students will give rather incoherent answers about “numbers getting close to other numbers but never quite reaching”. However, what I want students to realize is that the limit of 0,0,0,0,0,0,… is 0, i.e., every element of the sequence is equal to the limit — the sequence doesn’t get closer and closer to the limit. Another good example is interweaving this sequence with 1/n. I.e., 0, 1,...

## Lancelot Hogben

posted by Kevin Houston

No post last week – I seem to have spent the last two weeks on trains or motorways going from one part of the country to the next on various academic related missions so have not had the time to write a post. So back to business. Dara O’Briain’s Science Club is a new TV series that takes a Top Gearish approach to scientific topics (I often wondered why no one had attempted such an approach before). Last night one of the guests was Lucy Cooke who I’d never come across before but was very entertained by. As her unsung scientific hero she selected Lancelot Hogben as he pioneered the use of the African clawed frog in scientific investigation, including an early method of testing for pregnancy in humans. I had not known this side of him, I know him as the author of Mathematics for the Million. I bought a copy of this book from the thirties from a second-hand book shop in Ilford when I was an undergraduate. In its time it was a popular maths best-seller, though I doubt such an equation-packed book would do so well now. To give some idea of the content it starts with mathematics in ancient antiquity and gets up to calculus, modern algebra and probability. I have to confess that I have not read it cover to cover but have read chapters, dipped in here and there and used some material for my own courses. I would love to be able to teach the chapter on Mathematics for the Mariner as it covers a lot of interesting spherical geometry. Maybe some...

## XKCD on the maths of elections...

posted by Kevin Houston

Too much going on this week to post anything sensible so I’ll point in the direction of the latest xkcd:

## William Tutte and Tommy Flowers...

posted by Kevin Houston

On Monday night I unexpectedly came across a TV programme about the code-crackers at Bletchley Park during World War II. Usually such a programme focuses on Turing and the cracking of Enigma but this was about two of the lesser known players: William Tutte who was a mathematician like Turing and Tommy Flowers, a Post Office engineer who arguably built a programmable computer before anyone else. Seeing Tutte was a coincidence as just last week I was trying to understand his graph embedding theorem. [I’d met the theorem before but had forgotten all about it until I was trying to understand the “No Free Lunch Theorem” for discrete Laplace operators by Wardetzky et al, see here. Well, I think I understand the theorem but I don’t understand the proof. In my attempt to understand the basics of discrete Laplace-Beltrami operators I set aside a day last week to understand the proof and perhaps attempt to give a different one. Unfortunately after three days I still didn’t understand all the details of their proof and didn’t have a version of my own either! If anyone knows the details, then get in touch. But I digress…]I found a good description of the theorem on a site by Graham Farr at Monash. You can find it here. It’s a bit long but the important bits are in the first part. I liked the programme, for a start it didn’t assume you were stupid (even though it assumed I wouldn’t have heard of Tutte). The codebreakers programme is of course available for the next few days on the...