D’Arcy Thompson has been of interest to me since I was a teenager. There was recently a programme on BBC World Service. Have a listen on the BBC iPlayer if it’s available in your area: Science Stories: D’Arcy...

A New Book I’ve been working on a new book about sequences and series. The original plan for my book How to Think Like a Mathematician was to include some few chapters on epsilon-delta proofs. These were written but for reasons of space I left them out and had always intended to put them into a book. That intention is now being honoured. The bare bones of my thoughts on sequences have been uploaded to my website www.sequencesandseries.com. The design is not finished and there are no exercises, specially recorded videos or extra explanations. Also, there is nothing on series yet! Only sequences so far. My plan is to make the website the best place to go for information on sequences and series. Furthermore, I want to make a public commitment to finishing the book this year. So if I don’t, then please feel free to mock me on 1st January 2019! If you are interested in this experiment of writing a book and having some of it online, then please have a look and sign up for updates. The other project I’m working on is I’m gearing up for a proper launch of my latest book Complex Analysis: An...

Here’s a question for which the answer doesn’t seem to be widely known. Certainly, no one I’ve asked so far has known. They all found the answer interesting though! Why is a matrix called a matrix? If we consult www.etymonline.com for the origins of the word matrix we find matrix (n.) late 14c., “uterus, womb,” from Old French matrice “womb, uterus,” from Latin matrix (genitive matricis) “pregnant animal,” in Late Latin “womb,” also “source, origin,” from mater (genitive matris) “mother” (see mother (n.1)). That doesn’t seem to be much help (but does explain the word matriarchy and why surgeons sometimes refer to the matrix). However, surprisingly “womb” is the origin of the word in mathematics. To see this we go back to JJ Sylvester‘s 1850 article Additions to the articles in the September number of this journal, “On a new class of theorems,” and on Pascal’s theorem in which it is used in this context for the first time. He says For this purpose we must commence, not with a square, but with an oblong arrangement of terms consisting, suppose, of m lines and n columns. This will not in itself represent a determinant, but is, as it were, a Matrix out of which we may form various systems of determinants by fixing upon a number p, and selecting at will p lines and p columns, the squares corresponding to which may be termed determinants of the pth order. So what is Sylvester talking about here? Well, his interest is in developing what we now think of as Linear Algebra. In particular, he cares about determinants and is thinking of them as arising from a square array of numbers. In the passage above he notes that from an m by n array of numbers...

Posts have been a bit scarce round here recently. Something’s coming soon…

My new book, Complex Analysis: An Introduction, is nearly finished. To help my students with revision I created a list of common mistakes and this forms a chapter in the book. As a lecturer with many years of experience of teaching the subject I have seen these mistakes appear again and again in examinations. I’m sure that, due to pressure, we’ve all written nonsense in an exam which under normal conditions we wouldn’t have. Nonetheless, many of these errors occur every year and I suspect something deeper is going on. What follows is not intended to be a criticism of my students, who, luckily for me, are generally hard-working and intelligent. Nor is it an attempt to mock or ridicule them. Instead the aim is to identify common mistakes so that they are not made in the future. And if this post seems negative in tone, the a later one is more positive as it delves into techniques that improve understanding. Imaginary numbers cannot be compared The first mistake is the probably the most common: the comparison of imaginary numbers. For example, students write for a complex number. This cannot be right. If were what does it mean for to be less than ? What is usually intended is the modulus of , i.e., . The point is, unlike real numbers, we cannot order the complex numbers. For example, which is bigger or ? This is difficult to decide! Since complex numbers can be identified with the plane ordering them is equivalent to ordering the points of the plane and clearly this can’t be done — at least not in any useful or meaningful way. One last point needs to be made. Although is incorrect, note that expressions like can be true if is...

The web comic xkcd is well-known for its humour. I’ve also got a soft spot for the educational infographics, such as the following. (Not all the information should be...

This week the joint Gresham College and London Mathematical Society lecture will take place. Reidun Twarock of the University of York will give a talk Geometry: A New Weapon in the Fight Against Viruses. The details are on the Gresham College website. In case you can’t make the talk on Wednesday, then maybe there is a MathsJam near you on Tuesday. And if you can’t make either, then maybe you would like to see last year’s Gresham/LMS talk by Marcus du...

It has been a while since I posted a TED talk. There haven’t been many good ones in recent years. I enjoyed the one below (though I think he could have made clear that men respond the same way as women after asking the “What do you do?” question!). Further Reading The paper on the Honeycomb Conjecture by Thomas Hales starts off with a very good introduction before getting down to the higher level mathematics. Pappus of Alexandria Freeform Honeycomb Structures Not directly related but is an interesting paper from a conference I was at last...

The line up for this year’s London Mathematical Society Popular Lectures has finally been announced. As this year marks the 150th year of the LMS there are four lecturers instead of the usual two. We have Professor Martin Hairer, FRS – University of Warwick (and recipient of a Fields Medal last year) Professor Ben Green, FRS – University of Oxford Dr Ruth King – University of St Andrews Dr Hannah Fry – University College London The lectures will be at different times and different places, see the Popular Lectures webpage. Last year’s lectures are available...

The last post was a monster post. This one is a bit shorter as it exam time at my university so I’m a bit busy. Students these days have it easy with regards to exams. They are given far too much information about how to get good marks. When I was a lad we had to guess what an examiner wanted. Just look at the rubric of this 1980s exam (click to enlarge): I just love “Full marks may be obtained for complete answers to about FIVE questions”! And this is not an isolated case, I have a stack of exam papers like...

Usually I am against books offering general study advice, I favour those that focus on a particular subject. (Which is why I wrote How to Think Like a Mathematician. Mathematics students may also be interested in Lara Alcock’s How to Study for a Mathematics Degree.) I’ll make an exception for Cal Newport’s How to Become a Straight-A Student. Let’s get the bad stuff out of the way first. The subtitle is The Unconventional Strategies Real College Students Use to Score High While Studying Less which, along with the book’s other marketing, makes the scam-like sounding promise that you can do less work and get better grades. This can of course happen but does lend the book a feeling of too-goo-too-be-true. Furthermore, the book could do with some trimming of excess material though, at 216 pages, it is quite short for this type of book. The book could do without the regular mentions of partying and beer swigging but I suspect I’m not the target market for those bits. But leave aside those problems. Why would I recommend the book? Essentially, most of the advice is good. There is the standard stuff that all students know that they should do: get plenty of rest, eat properly, do your work in the morning between lectures to gain a sense of accomplishment. The non-standard stuff is good too. He doesn’t advocate lots of highlighter pens or even a highly detailed to do list. Instead he mostly focusses on the methods for efficient and effective learning. For example, on page 105, he talks of the Quiz-and-Recall method, [emphasis mine] Whether it’s philosophy or calculus, the most effective way to imprint a concept is to first review it and then try to explain it, unaided, in your own words....

My unscheduled summer hiatus from blogging arose from a family emergency that meant I was in stuck in Brazil for about 5 weeks. Not a bad place to be stuck but under the circumstances it was difficult to find time to finish my planned summer posts. For example, I had planned to post about the Fields Medals and as it happened lost the opportunity to report from Brazil about a Brazilian winner. The short story is that, to me, the Brazilians seemed mostly proud but surprised that a Brazilian was even in the running. The hiatus also meant that the deadline for my next textbook wooshed by. Ok, in reality I was never going to make it but I’m even further behind than expected. Anyhow, service will resume when I get back on track after all the time lost. For instance, I’ll let you know what the book is...

The London Mathematical Society runs a regular Popular Lectures Series. These are mathematics lectures by (usually) research mathematicians. In recent years a pair of lecturers has performed in London and Birmingham. This year they will be given by Julia Gog and Kevin Buzzard. (The London performance was last night and the Birmingham one is in September.) If you haven’t got tickets, then the good news is that the lectures are recorded and put online. Currently, an admittedly incomplete, collection of previous lectures is hosted in two different places: Lectures from 2008-2013 Lectures from 1986-1996 Previous speakers have included Sir Tim Gowers, Sir Roger Penrose, Reidun Twarock, Matt Parker, Mark Miodownik, Ray Hill, Vicky Neale and Dorothy...

I haven’t posted in a while for many reasons. One of which is that I’ve been trying to finish a textbook. My target date is July 31 to have the final draft finished. I’m not sure I’m going to make it… Anyhow, I noticed that the Beatles’ first film A Hard Day’s Night is being rereleased. ‘But what’s the opening chord to the title song?’ I hear you say. Funny you should ask, that gives me a chance to show again my modest attempt at solving the...

The name Martin Gardner is familiar to most mathematicians. He wrote numerous on mathematics from a culture and leisure viewpoint. (You can find his books on Amazon.) Next week Persi Diaconis will give a talk at the British Mathematical Colloquium (BMC) on the life and work of Martin Gardner. The BMC is an annual gathering of research mathematicians in the UK and beyond. Diaconis’ talk is a public lecture so anyone may attend but a (free) ticket is required. Details of the talk are here. I’ll be attending so do say hello if you see me. For all of those unable to attend but want to know a bit more about Gardner then Diaconis has co-written a biography of Gardner (as well as a great mathematical magic book). There is also a recent article in the New York...

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...

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...

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...

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...

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. —-...

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...

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...

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...

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...

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...