Tony Gardiner: David Willetts and “Robbins Revisited”

David Willetts (Minister of State for Universities and Science) has just published a possibly significant pamphlet with the Social Market Foundation called Robbins Revisited:

Robbins was an LSE economist whose committee examined the future of the ish university system – reporting in 1963. The report was unusually perceptive and its recommendations influenced policy for the next 30 years. This report is interesting in that it indicates the relevant Minister’s desire to place current HE policy in a historical context. Half of the time the contextualising makes sense; but half of the time it seems to be influenced by the need for post hoc self-justification.

As so often with high level documents, the data are wilfully distorted (whether deliberately or through wishful thinking one cannot know) in order to fit a required political perspective. Willetts repeatedly interprets data as demonstrating “improvement” even where we know it does no such thing. And where the uncomfortable explanation is to hand, he prefers to express puzzlement – as on p.69 where he observes

“an apparent mismatch between the supply and demand for high-level computer skills. Employers currently say they cannot find the skills they need yet computer science graduates find it relatively hard to find graduate-level work”

but then fails to infer that perhaps many computer science undergraduates are accepted onto courses, and graduate, without the relevant “high-level skills”.

He makes no mention of the botched attempts to broaden studies at age 16-18 (e.g. Tomlinson), or of the fact that the A level ‘gold standard’ his colleagues defend makes sense only if it supports specialisation. He then misinterprets the English fudge of continuing with A levels while abandoning specialisation (Table 5.1) as if it were a move in the direction of the kind of breadth Robbins advocated.

However, he has a relevant qualification (pp.50-1):

“there is an important distinction to be made between the need for breadth in general, and the need for maths skills in particular. In an interview with The Listener in 1967 Robbins was asked why the numbers opting for applied and pure sciences had fallen below expectations. He blamed what he called “the terror of mathematics”, caused by poor teaching and a preoccupation in university maths departments with producing “aces”.

This issue has not gone away. Last year the Lords Science and Technology Committee expressed its shock that many Science, Technology, Engineering and Mathematics (STEM) undergraduates lacked the mathematical skills required to cope with their course at university. The National Audit Office has warned that this is an issue for student retention. Maths is a core part of science and engineering subjects – but it comes into many others […] it is the universal analytical tool which matters more and more in today’s higher education.”.

“Robbins Revisited” by David Willets

The Rt Hon. David Willetts MP has just published a pamphlet with the Social Market Foundation called Robbins Revisited: Bigger and Better Higher EducationHere are quotes where he mentions mathematics.

Women are still under-represented in sciences (maths and physics) and the applied sciences (computing, engineering, technology and architecture), but the margin has narrowed from the 1960s when only three per cent of students studying “applied science” were women. (p.26)

We want scientists with an awareness of historical context; historians with the maths to handle statistics; mathematicians who can speak another language. (p.50)

Nonetheless, there is an important distinction to be made between the need for breadth in general, and the need for maths skills in particular. In an interview with The Listener in 1967 Robbins was asked why the numbers opting for applied and pure sciences had fallen below expectations. He blamed what he called “the terror of mathematics”, caused by poor teaching and a preoccupation in university maths departments with producing “aces”.

This issue has not gone away. Last year the Lords Science and Technology Committee expressed its shock that many Science, Technology, Engineering and Mathematics (STEM) undergraduates lacked the mathematical skills required to cope with their course at university. The National Audit Office has warned that this is an issue for student retention (pp. 50-51)

Maths is a core part of science and engineering subjects – but it comes into many others. As Liz Truss argues with great passion, it is the universal analytical tool which matters more and more in today’s higher education. It matters to the politics student who has to grapple with difficult statistical data, or the nursing student performing a drug calculation. And after leaving university many graduates will find themselves faced with numerical reasoning tests when competing for jobs. Yet only 16 per cent of undergraduates studying subjects other than maths have an A-level in maths under their belt. Often they will have forgotten much of what they once knew, and even if they haven’t, their confidence in their own abilities may be low. (p.51)

This is why Michael Gove’s moves to ensure that everyone continues some level of mathematical study until the age of 18 are so important. Another important initiative is “sigma”, a Hefce funded project. It is establishing approachable maths support services at institutions across the country. Thanks to their work, politics students suddenly confronted with a regression analysis have someone to turn to. STEM (Science, Technology, Engineering and Mathematics) undergraduates too are receiving expert support to bring their maths skills up to speed. (p.52-52)

GeoGebra Conference Budapest 23-25 January 2014

GeoGebra conference in 2014. We will meet in Budapest, Hungary on 23-25 January 2014 for a promising conference:

Plenary talks will be delivered by Markus Hohenwarter, Zsolt Lavicza , Celina Abar, Tomas Recio, and Balazs Koren. Also, there will be parallel sessions with talks and workshops.

The deadline for abstract submission is 1 December and registration is already open: Payment methods will be announced later, but register for early bird fees and to receive further information.

If you have any questions please contact Balazs Koren (, Zsolt Lavicza ( and

MathJax v2.3 beta release

From Peter Krautzberger of The MathJax Team:

We are entering beta testing for MathJax v2.3 today. This release focused on new webfonts options and improvements. It also includes improved localization features and improvements to our Native MathML output (to work around shortcomings in Firefox and Safari).

A copy of the beta release is available via our CDN at and also via a stable https address. Please note that the beta now has its own subdomain. You can also download the beta as a zip file at

If you are able to test the release, we would very much appreciate your feedback. I’ve copied the upcoming announcement with more information below.

Continue reading

Dominic Cummings: Some thoughts on education and political priorities

Dominic Cummings, the former special adviser to the Secretary of State for Education Michael Gove, published a 237 page document, Some thoughts on education and political priorities. It is a very interesting paper, and it is much concerned with mathematics education and deserves attention from the mathematical community — even if some readers might find some points raised controversial.

The paper is written by a thoughtful and well-informed person who is passionate about mathematics and mathematics education. However, the paper’s most striking feature is that it bears the hallmarks of “the voice of one crying in the wilderness” (John 1:23). The pages overflow with untested (although frequently brilliant) ideas, that have apparently blossomed outside any structurally sound referential framework. These 237 pages effectively document the absence of a proper public discourse on mathematics education policy.

And it is something we should not blame Dominic Cummings for; it is we in mathematics education community who are largely responsible for the silence that replaces policy discussions relating to mathematics education in this country.

The De Morgan Forum and The De Morgan Gazette have been set up with the aim to provide a space for voicing opinions — and maybe raising controversies — about issues in education policy which affect mathematics. Despite 500,000 hits over the last two years and some excellent papers and curriculum documents published in The De Morgan Gazette, we are still far from reaching this objective. We wish to invite the readers to face the challenge and use Dominic Cummings’ paper as an opportunity for a well-informed discussion of mathematics education.

Pierre Deligne: Early Years

Some quotes from  Interview with Abel Laureate Pierre Deligne, by Martin Raussen (Aalborg, Denmark) and Christian Skau (Trondheim, Norway), European Mathematical Society  Newsletter, September 2013, pp. 15-23.

You were born in 1944, at the end of the Second World War in Brussels. We are curious to hear about your first mathematical experiences: In what respect were they fostered by your own family or by school? Can you remember some of your first mathematical experiences?

I was lucky that my brother was seven years older than me. When I looked at the thermometer and realized that there were positive and negative numbers, he would try to explain to me that minus one times minus one is plus one. That was a big surprise. Later when he was in high school he told me about the second degree equation. When he was at the university he gave me some notes about the third degree equation, and there was a strange formula for solving it. I found it very interesting.

When I was a Boy Scout, I had a stroke of extraordinary good luck. I had a friend there whose father. Monsieur Nijs, was a high school teacher. He helped me in a number of ways; in particular, he gave me my first real mathematical book, namely Set Theory by Bourbaki, which is not an obvious choice to give to a young boy. I was 14 years old at the time. I spent at least a year digesting that book. I guess I had some other lectures on the side, too.

Having the chance to learn mathematics at one’s own rhythm has the benefit that one revives surprises of past centuries. I had already read elsewhere how rational numbers, then real numbers, could be defined starting from the integers. But I remember wondering how integers could be defined from set theory, looking a little ahead in Bourbaki, and admiring how one could first define what it means for two sets to have the “same number of elements”, and derive from this the notion of integers.

I was also given a book on complex variables by a friend of the family. To see that the story of complex variables was so different from the story of real variables was a big surprise: once differentiable, it is analytic (has a power series expansion), and so on. All those things that you might have found boring at school were giving me a tremendous joy.

Then this teacher, Monsieur Nijs, put me in contact with professor Jacques Tits at the University of Brussels. I could follow some of his courses and seminars, though I still was in high school.

It is quite amazing to hear that you studied Bourbaki, which is usually considered quite difficult, already at that age.

Can you tell us a bit about your formal school education? Was that interesting for you, or were you rather bored?

I had an excellent elementary school teacher. I think I learned a lot more in elementary school than I did in high school: how to read, how to write, arithmetic and much more. I remember how this teacher made an experiment in mathematics which made me think about proofs, surfaces and lengths. The problem was to compare the surface of a half sphere with that of the disc with the same radius. To do so, he covered both surfaces with a spiralling rope. The half sphere required twice as much rope. This made me think a lot: how could one measure a surface with a length? How to be sure that the surface of the half sphere was indeed twice that of the disc?

When I was in high school, I liked problems in geometry. Proofs in geometry make sense at that age because surprising statements have not too difficult proofs. Once we were past the axioms, I enjoyed very much doing such exercises. I think that geometry is the only part of mathematics where proofs make sense at the high school level. Moreover, writing a proof is another excellent exercise. This does not only concern mathematics, you also have to write in correct French – in my case – in order to argue why things are true. There is a stronger connection between language and mathematics in geometry than for instance in algebra, where you have a set of equations. The logic and the power of language are not so apparent.

You went to the lectures of Jacques Tits when you were only 16 years old. There is a story that one week you could not attend because you participated in a school tip…?

Yes. I was told this story much later. When Tits came to give his lecture he asked: Where is Deligne? When it was explained to him that I was on a school trip, the lecture was postponed to the next week.

He must already have recognised you as a brilliant student. Jacques Tits is also a recipient of the Abel Prize. He received it together with John Griggs Thompson five years ago for his great discoveries in group theory. He was surely an influential teacher for you?

Yes; especially in the early years. In teaching, the most important can be what you don’t do. For instance, Tits had to explain that the centre of a group is an invariant subgroup. He started a proof, then stopped and said in essence: ‘An invariant subgroup is a subgroup stable by all inner automorphisms. I have been able to define the centre. It is hence stable by all symmetries of the data. So it is obvious that it is invariant.”

For me, this was a revelation: the power of the idea of symmetry. That Tits did not need to go through a step-by-step proof, but instead could just say that symmetry makes the result obvious. has influenced me a lot. I have a very big respect for symmetry, and in almost every of my papers there is a symmetry-based argument.

Can you remember how Tits discovered your mathematical talent?

That I cannot tell, but I think it was Monsieur Nijs who told him to take good care of me. At that time, there were three really active mathematicians in Brussels: apart from Tits himself, Professors Franz Bingen and Lucien Waelbroeck. They organised a seminar with a different subject each year. I attended these seminars and I learned about different topics such as Banach algebras, which were Waelbroeck’s speciality, and algebraic geometry.

Then, I guess, the three of them decided it was time for me to go to Paris.Tits introduced me to Grothendieck and told me to attend his lectures as well as Serre’s. That was an excellent advice.