David Singerman: X + Y the movie

[To appear in the LMS Newsletter]

There are now an increasing number of movies where mathematics plays an important role. Usually we are let down by the parts featuring the maths because the makers of the film have little knowledge about our subject. So it is a real pleasure to review x+y a beautiful film where the mathematics is carefully done but not in a way that will put off a non-mathematical audience. The director is Morgan Matthews who also made the BBC4 documentary Beautiful Young Minds about the Mathematical Olympiad and the film is clearly based on this documentary. This documentary can be seen on Youtube.

The main character is Nathan. From the BBC synopsis

Preferring to hide in the safety of his own private world, Nathan struggles to connect with people, often pushing away those who want to be closest to him, including his mother, Julie. Without the ability to understand love or affection, Nathan finds the comfort and security he needs in numbers and mathematics.

Even though there are similarities between this film and the documentary, the main story line is totally fictitious. Near the beginning, Nathan, who has Asperger’s syndrome, is involved in a car crash which kills his father to whom he was very close. He is then mentored by his maths teacher Martin Humphreys, who when young had taken part in the Mathematics Olympiad. He was diagnosed with multiple sclerosis but also has other problems to do with self worth and soft drugs and ended up being a secondary school teacher.

Humphreys recognizes Nathan’s abilities and persuades him to enter for the Olympiad. He goes to the preliminaries in Taipei.

One of the scenes where there is actual maths is when Nathan is brought to the board to explain how to solve a problem. This involves playing cards which can be face up or face down.

Nathan’s solution is to model this with binary arithmetic involving 0s and 1s and he then turns the problem into an arithmetic one which is easy to solve.

In Taipei he meets Zhang Mei, a girl on the Chinese team. The film concentrates on two relationships. One between Nathan and Zhang Mei and the other between Martin Humphreys and Julie.

The scene moves from Taipei to Cambridge where the Maths Olympiad takes place.

There is real pathos in the final scenes. One where Nathan finally opens himself up to his Mother, and another when Nathan and Zhang Mei while travelling back from Cambridge by train see a rainbow and the viewer feels that their relationship will last. At last, Nathan feels and understands love and affection. Some critics have thought that this ending is too soapy, but if you see the documentary on which this film is based, the rainbow really was there!

One should also mention the excellent cast. Nathan was played by Asa Butterfield, Martin by Ralf Spall, Julie by Sally Hawkins and Zang Mei by Jo Yang. A lovely film where mathematics plays a central role.

Geoff Smith on X + Y

Reposted from the UKMT’s Newsletter:

In March 2015, the film  X + Y  will appear in cinemas all over the UK. This is a romantic drama, and explores a collection of intense personal relationships. One of the main characters is a teenaged boy (played by Asa Butterfield) who competes enthusiastically in UKMT competitions, and who dreams of going to the International Mathematical Olympiad. Several leading actors decorate the cast (Sally Hawkins, Eddie Marsan, Rafe Spall, Jo Yang). The film was made with the co-operation of UKMT and the IMO, and logos and flags appear accordingly. The film has secured international distribution contracts, and will be seen in many countries, and on airlines.

This film grew out of the BBC2 documentary “Beautiful Young Minds”, and the common director is Morgan Matthews. If UKMT were to make such a film (an exceptionally bad suggestion), the emphasis would be much more on the mathematics and less on the relationships. Morgan Matthews has become very interested in the way people on the autistic spectrum can prosper in mathematics. There has been a natural concern in the maths community that portraying some mathematicians as being less than socially fluent is dangerous, because it could lead to the misapprehension that mathematicians are all strange.

My personal view is that the prefix “mis” in the previous sentence can be deleted. All mathematicians are strange because they place such an exceptional value on thought, ideas and understanding. I think that the maths community should be proud of the way it embraces people on the basis of their enthusiasm for and interest in mathematics. University maths departments are happy places, where the socially adroit rub along in harmony with people who live in more private spaces. The trick is mutual respect and affection. This is equally true of UKMT maths camps. Most students are relaxed and outgoing, with the full set of skills that allow them to prosper in the teenage social maelstrom. Some others are not, but everyone gets along almost all of the time, united by a passion for ideas and ingenuity. We all know maths people who sometimes appear confused and nervous, but who have beautiful mathematical insights.

Things would be even better if women and all racial groups were richly represented in the maths community, and UKMT has done excellent work on the gender issue by founding the European Girls’ Mathematical Olympiad and running the annual talent search examination, the UK Maths Olympiad for Girls. The mentoring schemes make an excellent education in mathematical problem solving available to all social groups. However, while social inclusion is very much “work in progress”, the incorporation of people on the autistic spectrum into the wider maths community seems to be a great success, and in my view, a cause for celebration.

Geoff Smith, Chair of the BMO and the IMO, University of Bath.

Disclaimer: Geoff was involved in assisting to make X + Y, so his views are not impartial.

Book Review: “What the Best College Teachers Do” by Ken Bain, 2004

Book review by Richard Elwes:

Open a typical book on the theory of pedagogy, and all too often one is confronted by a morass of impenetrable and, one often suspects, unnecessary jargon. So it is a particular pleasure to read Ken Bain’s “What the Best College Teachers Do”. The book is the outcome of a fifteen year study in which Bain and colleagues identified and analysed around a hundred excellent teachers at US Colleges and Universities. Through extensive observations, discussions, and interviews with the teachers and their students, Bain arrives at a range of conclusions regarding the practice of good teaching. His findings are laid bare in a series of straightforwardly entitled chapters: “How do they conduct class?”, “How do they treat their students?”, and so on.

Few of his discoveries come as complete surprises, yet many are genuinely enlightening. For instance, the best teachers “have an unusually keen sense of the histories of their disciplines, including the controversies that have swirled within them, and that understanding seems to help them reflect deeply on the nature of thinking within their fields”.

Many of the insights within this book derive from the removal of extraneous and superficial aspects of education. How do good teachers speak to their students? Obviously, there are countless possible answers. But what do these approaches have in common? “Perhaps the most significant skill the teachers in our study displayed in the classroom… was the ability to communicate orally in ways that stimulated thought.”

The author often allows his educators to speak for themselves, and as one might expect, they are a thoughtful and frequently amusing group. Thus we read the Harvard political theorist Michael Sandel opining that teaching is “above all… about commanding attention and holding it… Our task… is not unlike that of a commercial for a soft drink”. On the other hand, Jeanette Norden, professor of cell biology at Vanderbilt University, “told us that before she begins the first class in any semester, she thinks about the awe and excitement she felt the first time anyone explained the brain to her, and she considers how she can help her students achieve that same feeling.”

The teachers analysed come from a wide range of Colleges and academic disciplines; some teach only elite students, others specialise in assisting strugglers; while several are eminent researchers, a few have no research publications at all; they deploy a variety of educational techniques. Among this diversity, the conclusions that Bain avoids are as interesting as those he draws. “[P]ersonality played little or no role in successful teaching. We encountered both the bashful and the bold, the restrained and the histrionic…. We found no pattern in instructors’ sartorial habits, or in what students and professors called each other. In some classrooms first names were common; in others, only titles and surnames prevailed.”

All the same, some common traits are apparent. “Exceptional teachers treat their lectures… and other elements of teaching as serious intellectual endeavors, as intellectually demanding and important as their research and scholarship.”

Particularly important, Bain argues, is the fostering of a “natural critical learning environment”. This is the closest the book ever comes to jargon, but that judgement would be unfair: “‘natural’ because students encounter the skills, habits, attitudes, and information they are trying to learn embedded in questions and tasks they find fascinating… ‘critical’ because students learn to… reason from evidence, to examine the quality of their reasoning… and to ask probing and insightful questions about the thinking of other people”.

At this stage, the reader might worry that this catalogue of heroic deeds could be dispiriting to the rest of us. Not so. Whilst Bain is full of admiration for his teachers, he by no means deifies them. “Even the best teachers have bad days… they are not immune to frustrations, lapses in judgement, worry, or failure.” On the contrary, their ability to confront their own shortcomings is one thing which sets the best teachers apart from those others who “never saw any problems with their own teaching, or they believed they could do little to correct deficiencies”. Good teachers show humility and willingness to improve.

In comparison, the teachers identified as the “worst” by their students often appear to carry the attitude, as one of Bain’s subjects puts it, that only “smart men can possibly comprehend this material and that if you can’t understand what I’m saying, that must mean I’m a lot smarter than you are”. As the biologist Craig Nelson says “The trouble with most of us… is that we teach like we were god.” Contrast this to the view of Dudley Herrschbach, another of the teachers in the study (as well as being a Nobel Prize-winning Chemist) that “You have to be confused… before you can reach a new level of understanding anything.”

In summary, this short book is far more readable and entertaining than a text on educational theory has any right to be. It offers every Higher Education teacher an invaluable opportunity: to learn from the best.

Ken Bain, What the Best College Teachers Do, Harvard University Press, 2004. ISBN-10: 0674013255. ISBN-13: 978-0674013254.

David Mumford on Grothendieck and magazine “Nature”

Can one explain schemes to biologists

December 14, 2014

John Tate and I were asked by Nature magazine to write an obituary for Alexander Grothendieck. Now he is a hero of mine, the person that I met most deserving of the adjective “genius”. I got to know him when he visited Harvard and John, Shurik (as he was known) and I ran a seminar on “Existence theorems”. His devotion to math, his disdain for formality and convention, his openness and what John and others call his naiveté struck a chord with me.

So John and I agreed and wrote the obituary below. Since the readership of Nature were more or less entirely made up of non-mathematicians, it seemed as though our challenge was to try to make some key parts of Grothendieck’s work accessible to such an audience. Obviously the very definition of a scheme is central to nearly all his work, and we also wanted to say something genuine about categories and cohomology. Here’s what we came up with:

Continue reading

Andreas Schleicher: Seven big myths about top-performing school systems

A paper by Andreas Schleicher, , at the BBC website. The list of “seven big myths”:

  1. Disadvantaged pupils are doomed to do badly in school
  2. Immigrants lower results
  3. It’s all about money
  4. Smaller class sizes raise standards
  5. Comprehensive systems for fairness, academic selection for higher results
  6. The digital world needs new subjects and a wider curriculum
  7. Success is about being born talented

In my [AB] humble opinion,  this appears to be the case when the negations of myths are myths, too (with a possible exception of no. 7). School systems cannot, and should not, be compared without first having a close look at socio-economic, cultural, and political environments of their home countries.


No, it is not the Queen’s Honours list. It stands for Outcomes Based Education, the latest pedagogical fad. The EU has practically adopted it as its official educational project. Which probably means that to bid successfully for EU funded projects you’d stand a better chance if you insert the OBE here and there.

But I am writing this because in the Wikipedia page Outcomes-based education

I was somewhat amused to (re)read a paragraph such as this:

In a traditional education system, students are given grades and rankings compared to each other. Content and
performance expectations are based primarily on what was taught in the past to students of a given age. The goal of traditional education was to present the knowledge and skills of an older generation to the new generation of students, and to provide students with an environment in which to learn. The process paid little attention (beyond the classroom teacher) to whether or not students learn any of the material.

and guess what reference they cite at the end of this paragraph? The
Constance Kamii and Ann Dominick 1998 paper on the “harmful effects” of algorithms in Grades 1-4. They also quote this gem from the paper:

“The teaching of algorithms is based on the erroneous assumption that mathematics is a cultural heritage that must be transmitted to the next generation.”

And whole countries build their educational policies on such “findings”.

The beginning of the end?

Is this beginning of the end of the traditional model of mathematics education?

This advert for PhotoMath gone viral:  and enjoys an enthusiastic welcome.

Mathematical capabilities of PhotoMath, judging by the product website, are still relatively modest. However, if the scanning and OCR modules (“OCR” here refers to “Optical Character Recognition”, not to the well–known examination board). of PhotoMath are combined with the full version of Yuri Matiasevich‘s “Universal Math Solver“, it will solve at once any mathematical equation or inequality,  or evaluate any integral, or check convergence of any series appearing in the British school and undergraduate mathematics. Moreover, it will produce, at a level of detail that can be chosen by a user, a complete write-up of a solution, with all its cases, sub-cases, and necessary explanations (with slight Russian accent, but that can be easily fixed).

In short, smart phones can do exams better, and the system of mathematics education based on standard written examinations is dead. Perhaps, we have to wait a few years for a formal coroner’s report, but we cannot pretend that nothing has happened.

In my opinion, a system of mathematics education which focuses on deep understanding of mathematics and treats mathematics as a discipline and art of those aspects of formal reasoning which cannot be entrusted to a computer is feasible. But such alternative system cannot be set-up and developed quickly, it is expensive and raises a number of uncomfortable political issues. I can give an example of a relatively benign issue: in the new system, it is desirable to have oral examinations in place of written ones. But can you imagine all the complications that would follow?

PhotoMath gives a plenty of food for thought.

An Open Letter: To Andreas Schleicher, OECD, Paris

An Open Letter: To Andreas Schleicher, OECD, Paris

Heinz-Dieter Meyer and Katie Zahedi, and signatories – 5th May 2014

Dear Dr. Schleicher,

We write to you in your capacity as OECD’s director of the Programme of International Student Assessment (PISA). […]

Read the rest of the letter in the Global Policy journal.

To signt the open letter please go to  http://oecdpisaletter.org/.