(Apologies that the last few seconds of the video cut off – apparently the 10-minute limit is actually a 9:49 limit and YouTube declined to notify me of this, or that they’d cut the end off.)

]]>I quite enjoyed describing about what I do, so I’ve decided to reproduce my answers here. Enjoy!

**Your Name: **Christian Lawson-Perfect

**Your Age: **31

**Your Work Place: **Newcastle University

**Your Job Title: **Mathematician / e-learning officer *(officially it’s only the second one of those two, but that’s a hopelessly vague title; ‘mathematician’ gets you much closer to imagining what I do all day)*

**Secondary school: **Dame Allan’s. GCSE Maths, Statistics, French, German, Physics, Chemistry, Biology, IT, History. (I hope they don’t notice I didn’t do GCSE English!)

**College**: Dame Allan’s *(again. Sorry, I went to one of those posh schools.)* A-Level Maths, Further Maths, French, Physics.

**Apprenticeship**: None.

**University: **Newcastle University. Master’s degree in Mathematics and Statistics.

**First Job: **Newcastle University. Tutor and e-learning officer.

**Are there any tips you would give someone who wants a career in your field?**

Maths is much more about persistence than natural ability – everybody gets stuck, and it’s **much** more than just doing sums – in fact, some of us are hopeless at doing actual calculations. Doing puzzles and playing games is the best way to develop your thinking skills.

**Best thing about your job?**

I get to solve interesting maths problems, and travel around the world to meet people who use the software I make.

**Not-so-good thing about your job?**

Like all jobs, there are forms to fill in and meetings to attend. On busy days when I’m interrupted a lot, it makes it hard to get any good maths done.

While we’re not massively bothered by the pricing, the articles do raise, and then completely fail to address, an interesting point: an oval pizza is harder to cut into equally sized pieces! Luckily, maths is here to save the day. I found a nice method and made a video explaining how it works:

Take a look and improve your future pizza cutting technique!

Cheesed off! Families roundly cheated by trendy oval pizzas as experts warn they are smaller in size… And how CAN you slice them into equal portions, anyway? in The Daily Mail

Why those trendy new oval pizzas you see in major supermarkets may not be worth it, in The Mirror

(Sadly, all proper newspapers have declined to comment)

]]>The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.

]]>Back in 2013, Evelyn Lamb (@evelynjlamb, first on our list) beat us to the punch with a comprehensive list of women on Twitter fitting the adjective ‘mathy’; we can’t guarantee all the account handles are still accurate or they’re still tweeting, but it’s a nice place to start. The list is also available as a Twitter List you can subscribe to.

This week, the #womeninmaths hashtag is kicking off with details of all the events and talks going on to celebrate women, and there are several Twitter accounts dedicated to tweeting about women in maths all year round – including @womeninmaths (the Twitter account of the LMS’s Women in Maths committee) and more generally @STEMWomen. International Women’s Day has its own Twitter account @womensday.

And finally, here’s a (far too short) list of some more cool mathematical women I’ve recently met/heard of/worked with, and their Twitter handles.

- Eugénie von Tunzelmann (@eugenieVT): works in computer graphics and 3D rollercoaster design, and has a tattoo of a hypercube on her arm
- Laura Taalman (@mathgrrl): met her while she was mathematician in residence at MoMATH in New York, and does lots of interesting stuff with 3D printing and maths
- Sam Durbin (@samdurbin1): coordinator of maths masterclasses at the Royal Insititution, and an unstoppable force of nature when it comes to promoting maths
- Finally, Nalini Joshi (@monsoon0): mathematician at the University of Sydney, and (as of today) the first ever woman to have her portrait hanging in the prestigious MacLaurin Hall at the university:

On #internationalwomensday , the amazing Nalini Joshi has her official portrait unveiled! A beautiful work by artist Celeste Chandler. pic.twitter.com/wwEPS8wqMj

— Sydney Science (@Sydney_Science) 8 March 2017

The Mathematical Association of America also helpfully tweeted this collection of handles:

Happy #InternationalWomensDay! #Follow mathematicians: @evelynjlamb @alittlestats @EricaNWalker @doctor_talitha @jennapcarp @jennapcarp

— MAA (@maanow) March 8, 2017

]]>More #Womeninmath: @AWMmath @WVUMathDoc @mathcirque @csquaredd13 @KelseyAHE @EKTBenn @kristinheysse @KristinLauter @mathyadriana

— MAA (@maanow) March 8, 2017

The film is a painstaking and at times brutally realistic depiction of the struggles faced by African-Americans, and by women, during the era of the early space missions.

It’s the first film I’ve ever seen where the BBFC certificate at the start warns, where you’d usually see “scenes of violence/nudity/strong language”, a warning for “discrimination theme” – and it’s justified, as you find yourself battered by the repeatedly unfair and horrible treatment received by the clearly brilliant and lovely main characters, and worst of all how that is completely normal and widespread for the time. Langley, where NASA HQ is located, is in Virginia, a state where segregation continued in many aspects until the Civil Rights Act of 1964 – this meant ‘coloureds’ had to use separate bathrooms, drink from separate water fountains, sit in a separate section at the back of the bus and attend separate schools, all of which (and their horrible demoralising effects) are seen clearly in the film.

It also doesn’t shy away from the discrimination received by women, which is another layer of problems these characters face – even within their own community, they encounter people with a ‘do they let women do that?’ attitude. When one character arrives in her new department to provide her mathematical expertise and is immediately handed a bin which needs emptying, it’s not clear whether it’s because she’s female or black (or both).

But you’re here for the maths, right? This is at its core a film about a mathematician, an engineer and a computer scientist and how they helped America put a man into space. The maths and science is well incorporated into the story and doesn’t feel awkward, and serves to display the brilliance of the main characters, as well as the difficulty of the work everyone at NASA was doing – it was groundbreaking, and in some cases involved inventing new mathematical techniques to solve problems nobody imagined they’d have to solve (and this aspect of the space race is even mentioned as a justification for the huge cost and effort of the programme).

In one early scene, Katherine Johnson (as a child) demonstrates her mathematical brilliance by, having skipped two grades in school, being called up to the blackboard in front of a room of older students. She demonstrates that the product of two quadratics, set equal to zero on the board, can easily be solved by noting that if a product of two things equals zero, it means one of the two terms must equal zero so you can factorise each of the two quadratics, set each of the four resulting components to zero and find four solutions. It’s a beautiful piece of maths, well explained and displayed in full, front and centre in the scene. While some filmmakers might worry about this, it completely works and demonstrates her brilliance – the looks on the other students’ faces tell the story too.

Elsewhere in the film, Katherine is required to do Analytic Geometry, studying the trajectories of the space flights and their take-off and landing. The initial calculations for the earlier low-Earth orbit flights were simpler, and it’s when they start considering the more complex orbital flights – in which the trajectory of the capsule changes from an elliptical orbit of the Earth to a parabolic trajectory as it comes down, where they needed to work out something new. Together the team realises they can use numerical integration – Euler’s Method, which has been known for a long time but hadn’t been used at NASA for years – to obtain a solution which works numerically, without having to actually solve the differential equations. Johnson’s brilliance in helping come to this realisation is clear, and anyone watching who didn’t understand the maths can maybe even get a sense of the beauty and satisfaction mathematicians find in their work, especially when it has such amazing applications.

The other main characters demonstrate their excellence in their own fields too. Mary Jackson, clearly a brilliant engineer, is encouraged by her boss to join the NASA engineer training programme, but finds her bachelor’s degree in maths and physics is insufficient; the administrator’s veiled joy in telling her she doesn’t qualify could just be a true bureaucrat relishing in the rules, but as with many of the things people do in the film it’s in line with the standards of the era, and advancement seems an impossible dream.

The third amazing role model in this film is Dorothy Vaughan, who runs the computing department (at the time, a team of human ‘computers’ who perform all the calculations by hand). She notices that the new IBM supercomputer coming in to do the calculations will make all their jobs obsolete, so she educates herself and her team, getting books on Fortran from the library and using her skills with machinery and numbers to understand how it works.

I’m glad this film exists, and I’m double glad that it’s such a well-made piece of cinema, with well-developed characters, a gripping story and emotional tugs which work regardless of whether you’re interested in maths – because it means lots of people will see it. I hope that as well as telling these women’s stories – something badly needed – and reminding us of how painfully recent these attitudes held sway (and warning us not to let them take hold again now!) this film will also help people to see the wonder of maths and science, and show that people who do these things struggle the same as everyone else, and are all part of the same world.

It looks like the film is having this effect – many people are now talking about it, and Katherine Johnson also features in this new LEGO set, recently approved, of Women Pioneers at NASA. I’d recommend going to see it, but also taking along some tissues and being prepared to come out energised and angry that people were treated this way, and, I’d hope, ready to take on injustice now.

]]>We each have fairly sizeable collections of maths books, which prompted CLP to wonder how many of them are by female authors. A quick scan of our respective bookshelves later, here’s what we found.

I’ve found four books I know for sure are by female authors – several others just have a surname or initial/surname. I’m also convinced I used to have a copy of Hannah Fry’s TED book The Mathematics of Love, which I owned from when I reviewed it for this site, but I must have passed it on to someone else.

Of these five books, precisely one was bought by me as a book I’d like to read – Timandra Harkness’s witty and light-hearted analysis of *Big Data – Does Size Matter*, and the rest I all own for technical reasons. *Maths in 30 Seconds* by Anne Rooney is a book on which I consulted on technical aspects of, and they sent me a copy; I bought Masha Gessen’s excellent *Perfect Rigor*, which is a biography of Grigori Perelman and the story of his proof of the Poincaré Conjecture, in order to read up on the topic for a talk I was writing, and Daina Taimina’s *Crocheting Adventures with Hyperbolic Planes* was (genuinely) a wedding present Paul and I received.

I have a total of 59 maths books on my shelf which are a mixture of books I’ve bought for myself, books I’ve bought for work purposes, books I’ve been sent to review for this site and books I’ve inherited from others who review books for a living. This means my females make up around just under 7% (8% if I can find my Hannah Fry book) of my collection. For the record, I have 5 Martin Gardner books, and am duly ashamed of myself. I can only conclude I really need to step up my game and spend less of my reading budget on classic sci-fi, and look up some more diverse maths authors.

When I taught maths to forensic science a few years ago, the recommended book was one of the classic maths for engineers textbooks. Forensic science students study bits of chemistry, biology, physics and some computing, maths and stats. I felt quite awkward recommending a book targeted to engineers, but found *Maths for Science* by Sally Jordan, Shelagh Ross and Pat Murphy to be written at the right level and targeted to the right audience – explaining things simply and clearly using examples that would appeal to scientists.

*Thinking Mathematically* is a classic by John Mason. The revised second edition is by John Mason, Leone Burton and Kaye Stacey, and I was introduced to it by Noel-Ann Bradshaw, who wrote this review. I used some of its ideas and problems with our first years this year in a problem-solving session.

I recommend *The Oxford Handbook of the History of Mathematics* by Eleanor Robson and Jackie Stedall in my history of maths module, along with Jackie Stedall’s *The History of Mathematics: A Very Short Introduction*. The handbook, a collection, provides a look at the history of maths with special focus on the contribution of different cultures. The *Very Short Introduction*, I tell my students, has a clear advantage – it is Very Short. At a little over 100 pages, it gives a good clear overview of some issues to consider when studying history of mathematics, and presents a little history along the way. Students tend not to read recommended books, but I implore them to at least read the barely-three-page introduction (available on Google Books), saying if they do then it would enhance their understanding of the study of history of maths considerably.

The photo also shows the most recent book I read, *The Indisputable Existence of Santa Claus* by Hannah Fry and Thomas Oléron Evans, which I was delighted to receive and read over the Christmas break. It is silly and fun, with some series maths at its core.

Also pictured are *George Green, Miller and Mathematician*, one (not the best) of a series of increasingly-detailed books about Nottingham’s famous mathematician by D. Mary Cannell; the LMS’s *The Book of Presidents* by Susan Oakes, Alan Pears, and Adrian Rice; and *Numericon* by Marianne Freiberger and Rachel Thomas of Plus Magazine.

I also have a bunch of older books that go “initial. surname” which I haven’t assumed to be female in my response.

I do have more maths books by female authors than by Martin Gardner, though this may be due to paucity of Martin in my collection rather than a great number of female-authored books. These 8 books sit in a cupboard of 112 mathsy books, meaning they represent a mere 7% of my collection.

I have between four and six books definitely by female authors, out of 83. I can’t decide whether to count the excellent *Genius at Play* by Siobhan Roberts, because it’s a biography by a non-mathematician, or *An Introduction to the Theory of Groups* because it’s a translation by Hazel Perfect of an original Russian text by Paul Alexandroff.

The others are a mixed bag: *Making Mathematics with Needlework* by sarah-marie belcastro and Carolyn Yackel is the classic crafty maths book; *Playing with Infinity *is a very good pop maths book of the whirlwind-tour-of-the-undergrad-syllabus sort by Rózsa Péter (if you’re going to read a pop maths book, they’re all pretty much the same so you might as well make it this one); *A first course in Modern Mathematics* by Marie Anderson is an unremarkable textbook; and *Instant Maths* by Ann Cutler is all about the Trachtenberg system for mental maths, about which the less said the better.

I own four books by Martin Gardner, so I *just* reach Martin-to-Mrs parity.

$n=3$ is not a big sample, so let’s take a look at the most-read maths books on Goodreads this week. Not all of the books are really about maths – there are some pop science and computer science books in there – and we’ll exclude the children’s books as well. That leaves just over 40 maths books, give or take a couple, of which four are written by women:

*Weapons of Math Destruction*by Cathy O’Neill comes highly recommended – pity it hasn’t made more of a splash over here!*A Mind for Numbers*by Barbara Oakley seems to be the companion book for a big Coursera MOOC.*Mathematical Mindsets*by Jo Boaler is the hot education craze of the moment. If you’re a teacher, you’ve probably heard of Jo Boaler, and even if you’re not, you might have heard some of the fairly heated arguments for and against the ideas in this book.*How to Bake Pi*by the ubiquitous Eugenia Cheng rounds off our list. By all accounts it’s a good read!

The Goodreads list has a heavy US slant, but the proportion of books by female authors is still just under 10%.

*So, do you own more books by Martin Gardner than by female authors? Have you broken the 10% female authors barrier? What book by a female author should no mathematician be without?*

“Life moves very fast. It rushes from Heaven to Hell in a matter of seconds.”

― Paulo Coelho

This week, I was suddenly reminded of a fact I’d been meaning to keep track of, and I was disappointed to discover that even though I always endeavour to remember birthdays and holidays (mainly due to a system of elaborate reminders, notes and excessive list-making), I’d missed a hugely significant anniversary. Shortly after the clock struck midnight on New Year’s eve, I had passed one billion seconds old.

While not one of the usual anniversaries to celebrate, I’d been looking forward to this one – it turns out that one billion seconds works out to somewhere between 31 and 32 years (my ‘just-after-midnight’ statement assumes I know the exact time I was born, which I don’t, but I have a reasonable estimate) . If you’d like proof, here’s a breakdown:

\[ 1000000000\ \mathrm{seconds} = 1000000000 \div 60\ \mathrm{minutes}\\

16666666.\dot{6}\ \mathrm{minutes} =16666666.\dot{6} \div 60\ \mathrm{hours}\\

277777.\dot{7}\ \mathrm{hours} =277777.\dot{7} \div 24\ \mathrm{days}\\

11574.\overline{074}\ \mathrm{days} =11574.\overline{074} \div 7\ \mathrm{weeks}\\

1653.\overline{43915}\ \mathrm{weeks} =1653.\overline{43915} \div 52\ \mathrm{years}\\

= 31.\overline{796906} \ \mathrm{years} \]

This quantity may mildly surprise you – partly because humans in general can be quite bad at interpreting numbers like a million and a billion. We know what the number means, and can calculate with it, but intuition can fail us when trying to put it into context.

It turns out that a second is quite a nice way to contextualise large numbers – for example, here’s an interesting fact I heard about the number of seconds in six weeks:

\[ \begin{eqnarray}

6 \ \mathrm{weeks} &=& 6 \times 7 \ \mathrm{days}\\

&=& 6 \times 7 \times 24 \ \mathrm{hours}\\

&=& 6 \times 7 \times (8 \times 3) \ \mathrm{hours}\\

&=& 6 \times 7 \times (8 \times 3) \times 60 \ \mathrm{minutes}\\

&=& 6 \times 7 \times (8 \times 3) \times (10 \times 3 \times 2) \ \mathrm{minutes}\\

&=& 6 \times 7 \times (8 \times 3) \times (10 \times 3 \times 2) \times 60 \ \mathrm{seconds}\\

&=& 6 \times 7 \times (8 \times 3) \times (10 \times 3 \times 2) \times (3 \times 5 \times 4) \ \mathrm{seconds}\\

&=& 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times (3 \times 3) \times 10 \ \mathrm{seconds}\\

&=& 10! \ \mathrm{seconds}\\

\end{eqnarray} \]

The number of seconds in six weeks can be expressed as a product of the numbers one to ten – that is to say, there are 10! seconds in six weeks. Large factorials like this ($10! = 3,628,800$) are similarly difficult to quantify, so this is a nice fact to have in your pocket.

A million is a more manageable number; a million seconds is just over 11 and a half days, which might be the length of a single short project you work on in your lifetime, or how long a holiday lasts, or somewhere at the long end of how long you might reasonably expect a banana to keep for (if it was really fresh when you got it).

So my 1 billion seconds = 31 years milestone makes a nice distinction between a million and a billion – a couple of weeks versus a good chunk of my life. Another reason I’m disappointed not to have properly celebrated (I mean, I was celebrating, but not necessarily this) is because this is probably the biggest power of ten I’ll reach in my lifetime. I’ll probably survive to 2 billion seconds, and if I’m lucky maybe even 3 billion, but there’s no way I’ll make it to 10 billion and certainly not a trillion.

But here’s some you might manage:

- 1 year on the planet Jupiter is about 11.86 years
- 10 million minutes (aka 10 MEGAMINUTES) is about 19.01 years
- 1000 fortnights is about 38.33 years
- 1000 months is about 83.4 years, if you’re lucky!

So raise a billion glasses for me, and celebrate your milestones in seconds not years (as long as it doesn’t make you feel too old).

]]>Forget pepperoni – mushroom is Britain's most liked pizza topping (65%), followed by onion (62%) and then ham (61%) https://t.co/5kYikXOEtF pic.twitter.com/AJezMfJHbk

— YouGov (@YouGov) March 6, 2017

Actually, for the purposes of criticism and comment, here’s a local copy of the image:

It should immediately set your data presentation colly wobbling.

- It’s not a pie chart: the slices are all the same size…
- … and some slices have more than one percentage linked to them.
- The percentages don’t add up to 100: each one is the proportion of respondents who liked that item.
- The percentages aren’t in order. You can’t immediately see which toppings were most popular, and which were least.
- In fact, several quite popular toppings were left off the graphic, and only mentioned in the small text underneath. Apparently anchovies (18%) are the least popular of the items listed, while onions are the second most popular.

But these are only problems if the point of the graphic is to convey useful information about people’s preferences for toppings, in a way that you can immediately apply. What else could it be for? If it’s just to give you a smattering of information about the results of their survey, maybe it’s not so bad?

**It is.**

The question asked respondents to tick any toppings that they like on a pizza. If you want to use this data, you might decide that a pizza with the three most popular toppings is sure to be a winner.

But the data don’t tell you two important things:

- How many people
*actively disliked*each topping? - Which toppings do people particularly like or dislike
*together*?

The first point is even more subtle – each respondent has to decide on their threshold for saying they like a particular topping. Do they pick their three favourite toppings, or just any topping they wouldn’t object to having on a pizza? So “most liked” has a few different interpretations – does it mean ‘strongly liked by the most people’, or ‘disliked by the fewest people’? The first interpretation might pick a highly controversial topping, while the second is likely to return a very bland topping as the ‘most liked’.

Knowing which toppings people actively dislike would help to identify the most controversial items – for example, I reckon spinach (26% like) is much less controversial than olives (very similar, at 33% like), so the presence of olives on a pizza is much more likely to be a deal-breaker than spinach.

And knowing which toppings go well – or badly – together would also really help. Ham (61%) and pineapple (42%) is a classic combination, while I don’t think I’ve ever seen a mushroom (65%) and pineapple pizza on a menu.

So did YouGov capture any of this data, but leave it out because it’s not easily presented in a graphic that can spread on social media?

Not really. The full results of the survey are available from YouGov; there are a couple of questions about pineapple and whether it should go on a pizza, and a final question asking which ingredients the respondent would ban if they had the chance. If the answers to this question are ‘dislikes’, then you could define ‘controversiality’ to be ‘likes + dislikes’. By that measure, I was right to say olives (33+20 = 53) are more controversial than spinach (26+12 = 38), but you’re still missing a lot of complexity.

The phrasing of the last question, and the accompanying blog post, mention the president of Iceland, who recently said he’d like to ban pineapple on pizzas. So after all, this seems to be a stunt survey to get some fluff statistics which can be reproduced in news articles, with YouGov’s name attached. The context of the question somewhat explains the data collected – if you were the president of Iceland, which topping would you ban – but instead of presenting the toppings most Britons would like to ban, the graphic showed the topping the most Britons ‘like’. That might be because the most popular topping is not surprising – it’s anchovies, followed by olives – while I don’t think anyone would expect mushrooms to come first in a ranking of favourite toppings.

To finally return to the question of why this graphic was constructed the way it was, one clue might be the stock photo used, which shows some of the toppings mentioned in the survey. I tracked it down in iStockPhoto – the original is a collage of eight one-sixth slices of pizza with different toppings. It looks like the person who made the graphic has just arranged six of them in a circle, and picked out the ingredients mentioned in the survey. Note that the stock photo has a slice with prawns, but they don’t seem to have been mentioned in the survey at all!

*Could prawns be the nation’s favourite pizza topping?*

What’s that? It’s this:

… if $B_1$, $B_2$, $\ldots$, $B_n$ are $n$ bases of an $n$-dimensional vector space $V$ (not necessarily distinct or disjoint), then there exists an $n \times n$ grid of vectors ($v_{ij}$) such that

1. the $n$ vectors in row $i$ are the members of the $i$th basis $B_i$ (in some order), and

2. in each column of the matrix, the $n$ vectors in that column form a basis of $V$.

Easy to state, but apparently hard to prove!

If the Polymath project is new to you, it’s the name for a series of collaborative research endeavours to solve long-standing problems by sharing lots of contributions, of any size, from people all over the world. Previous Polymath projects have successfully led to proofs of the density version of the Hales-Jewett theorem, the Erdős discrepancy problem, and famously reduced the bound on the smallest gaps between primes to within shouting distance of the ultimate goal.

On the Polymath blog, Chow suggests three ideas for ways to make progress, based on previous work on the conjecture.

Even if you can’t make an intelligent contribution, Polymaths are an excellent opportunity to see the messy business of how maths is made – something that you don’t get by reading only finished papers and textbooks.

Rota’s Basis Conjecture: Polymath 12? on the Polymath blog

Timothy Chow’s original proposal on MathOverflow

Papers published under the collective pseudonym “D.H.J Polymath” on the arXiv

]]>