Natasha Billing: Everything is mathematical

I wanted to get in touch to let you know about a new maths website Everything is mathematical, a site that we’ve built to support a brilliant new book collection that explains how maths shapes the world around us. I can send you a PDF of the first book, ‘The Golden Ratio’ to preview, so please let me know, by emailing at

challenges.hothousedevelopments.com >>>at<<< mail.opal-solutions.com,

whether this is of interest.

Presented by Marcus du Sautoy, the 44-part series is aimed to introduce you to a range of mathematical topics in an approachable style, and is aimed at young and old alike – in fact the only requirement for enjoying these books is a curious mind and a thirst for understanding. The series approaches the subject of mathematics in a completely new, fresh and reader-friendly way, and covers a range of topics such as: the Golden Ratio, Prime Numbers, the Fourth Dimension, Fermat’s Enigma, the Secrets of Pi and Chaos Theory.

We’ve also built a website that goes along with the series that will feature news, videos and puzzles from the world of maths, as well as stories about maths innovators and heroes. We’ll be updating this every week, so please check it out.

We will be setting a weekly video maths challenge, the first of which is presented by Marcus du Sautoy, and will post the solution a week later. Visitors to the website will be able to enter a competition every week.

The first challenge video can be found here.

We were wondering if you would like to review the series for us, and we’d like to offer some copies of some books from the series to give away as a competition prize on your site or blog? We would love it if you wrote about the books and the site, as well as checking out the challenges and solutions on the website.

It would be great to hear your thoughts on the site and series, so please drop me a note and let me know what you think.

Bill Thurston: Mathematical Education

A link to Bill Thurston‘s paper Mathematical Education. This article originally appeared in the Notices of the AMS 37 (1990), 844–850.

Tony Gardiner said:

The best mathematicians – from Poincare to Thurston – are sometimes surprisingly sensitive to, and sensible about, educational issues.

The sad news is that Bill Thurston has just died.

He got his hands dirty with mathematics education from at least 1980, and wrote several articles which are quite inspiring.  Here is one that is easily to hand for some more refreshing reading than the stuff I usually highlight!

Bill Thurston died on 21 August 2012. Obituaries: The Mathematical Legacy of William Thurston (1946-2012) and Bill Thurston (October 30, 1946 – August 21, 2012)

Matilde Marcolli: Still life as a model of spacetime

Matilde Marcolli,  Still life as a model of spacetime. From the Introduction:

Still life is the most philosophical genre of traditional fi gurative  painting. It saw some of its most famous manifestations in the Flemish tradition of the XVII century, but it evolved and survived as a meaningful presence through much of XX century art, adopted by avantarde movements such as cubism and dadaism.

The purpose of this essay is to dig into the philosophical meaning behind the still life painting and show how this genre can be regarded as a sophisticated method to present in a pictorial and immediately accessible visual way, reflections upon the evolving notions of space and time, which played a fundamental role in the parallel cultural developments of Western European mathematical and scienti c thought, from the XVII century, up to the
present time.

A challenge for the artists of today becomes then how to continue this tradition. Is the theme of still life, as it matured and evolved throughout the dramatic developments of XX century art, still a valuable method to represent and reflect upon the notions of spacetime that our current scienti c thinking is producing, from the extra dimensions of string theory to the spin foams and spin networks of loop quantum gravity, to noncommutative spaces, or information based emergent gravity? Some may feel that the notions of spacetime contemporary physics and mathematics are dealing with nowadays are too remote from the familiar everyday objects that form the basic jargon of still life paintings. However, much the same could be said about the notions of relativistic spacetime and the bizarre world of quantum mechanics that were trickling down to the collective imagination
in the early XX century, and yet the artists of the avant-garde movements of the time were ready to jump onto concepts such as non-euclidean geometry, higher dimensions, and the like, and bring them into contact with a drastic revision of what it means to “represent” the everyday objects that surround us, and that come to occupy a profoundly altered concept of space and time. So, I believe, the challenge is a valid one, even in the light of the ever more complex landscape of today’s thinking about the concepts of space and time, and I take the occasion to make an open call here to the practicing artists, to take up the challenge and paint a new chapter of the “still life” genre, suitable for the minds of the current century.

Read the full paper.

Acceleration or Enrichment

Acceleration or enrichment: Report of a seminar held at the Royal Society
on 22 May 2000, The De Morgan Journal, 2 no. 2 (2012), 97-125.

Full title of the paper:

Acceleration or Enrichment?
Serving the needs of the top 10% in school mathematics.
Exploring the relative strengths and weaknesses of “acceleration” and “enrichment”.
Report of a seminar held at the Royal Society on 22 May 2000.

The report includes contributions from Tim Gowers, Gerry Leversha, Ian Porteous, John Smith, and Hugh Taylor.

Abstract:

This report was originally published in 2000 by the UK Mathematics Foundation (ISBN 0 7044 21828). It was widely red, and was surprising influential. However, it appeared only in printed form. Various moves made by the present administration have drawn attention once more to this early synthesis— which remains surprisingly fresh and relevant. Many of the issues raised tentatively at that time can now be seen to be more central. Hence it seems timely to make the report available electronically so that its lessons are accessible to those who come to the debate afresh.

While the thrust of the report’s argument remains relevant today, its peculiar context needs to be understood in order to make sense of its apparent preoccupations. These were determined by the gifted and talented policy’ adopted by the incoming administration in 1997, and certain details need to be interpreted in this context. There are indications throughout that many of those involved would probably have preferred the underlying principles to be applied more generally than simply to “the top 10%”, and to address the wider question of how best to nurture those aged 5–16 so as to generate larger numbers of able young mathematicians at age 16–18 and beyond. The focus in the report’s title and subtitle on “acceleration” and on “the top 10%” stemmed from the fact that those schools and Local Authorities who opted at that time to take part in the Gifted and Talented strand of the Excellence in Cities programme were obliged to make lists of their top 10% of pupils; and the only provision made for these pupils day-to-day was to encourage schools to “accelerate” them on to standard work designed for ordinary older pupils. The wider mathematics community was remarkably united in insisting that this was a bad move. This point was repeatedly and strongly put to Ministers and civil servants. But the advice was stubbornly resisted; (indeed, some of those responsible at that time are still busy pushing the same linez.

The present administration seems determined once more to make special efforts to nurture larger numbers of able young mathematicians, and faces the same problem of understanding the underlying issues. Since this report played a significant role in crystallising the views of many of our best mathematics teachers and educationists, it may be helpful to make it freely available—both as a historical document and as a contribution to current debate.

Read the whole paper. 

The Mathematical Legacy of William Thurston (1946-2012)

A post by  Evelyn Lamb on the Scientific American blog. A quote:

Thurston embraced efforts to make mathematics more accessible and enjoyable for students and the general public, especially in later years. In a 1994 article for the Bulletin of the American Mathematical Society, he wrote that the fundamental question for mathematicians should not be, “How do mathematicians prove theorems?” but, “How do mathematicians advance human understanding of mathematics?” He believed that this human understanding was what gave mathematics not only its utility but its beauty, and that mathematicians needed to improve their ability to communicate mathematical ideas rather than just the details of formal proofs.

He worked on projects to increase public understanding of mathematics and saw the mathematical sides of art and design. He co-developed a course called “Geometry and the Imagination” designed to introduce deep geometric concepts to people who did not necessarily have an advanced background in math.

Bill Thurston (October 30, 1946 – August 21, 2012)

Bill Thurston, the famous topologist and geometer, died on 21 August 2012.

The New York Times and The Atlantic published very warm obituaries. Edward Tenner writes in The Atlantic (he starts with a quote from The New York Times):

“Cosmologists have drawn on Dr. Thurston’s discoveries in their search for the shape of the universe.

On a more unlikely note, his musings about the possible shapes of the universe inspired the designer Issey Miyake‘s 2010 ready-to-wear collection, a colorful series of draped and asymmetrical forms. The fashion Web site Style.com reported that after the show, the house’s designer and Dr. Thurston “wrapped themselves for the press in a long stretch of red tubing to make the point that something that looks random is actually (according to Thurston) ‘beautiful geometry.’”

Mathematicians can cite many other examples of surprising applications. Could the 19th-century founders of mathematical logic have imagined where Alan Turing would take their new field a hundred years later? With the computer science that Turing founded, the once-abstract field of number theory became a foundation of cryptography. The mathematics of origami have contributed to designing solar sails and automotive airbags. In the 1980s, the topological subfield of knot theory became a powerful tool in particle physics. Symposia have already been held on applications of topology to the design of industrial robots. I’ve even read the statement — but haven’t been able to find the reference again — that every significant pure math idea has an application. We just haven’t discovered some yet.

All this is timely, because in some quarters of neo-mercantilist, managerial academia, some mathematics is considered too pure for the national economy, especially in the UK.

In a famous paper on the uncanny way that math describes reality, the physicist Eugene Wigner concluded:

“The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.”

Bill Thurston was one of the great bestowers of that gift.

 

Computer Science: A curriculum for schools

The Computing At School Working Group, a lobby group for IT industry (endorsed and supported by endorsed by BCS, Microsoft, Google and Intellect), proposed and published  Computer Science curriculum for schools. Other documents of interest on their website include

Tony Gardiner: Nurturing able young mathematicians

A. D. Gardiner, Nurturing able young mathematicians, The De Morgan Journal  2 no. 7 (2012), 87-96.

Abstract:

We summarise the developments of the last 20 years—highlighting the key underlying assumptions, and indicating certain unfortunate consequences. We show how official policy has been based on

  • persistent failure: (i) to develop and to implement a suitably challenging curriculum, and (ii) to provide ordinary teachers with good texts, suitable subject-specific professional development, and appropriate assessment targets;
  • a misconception of the curriculum as a one-dimensional ‘ladder’ (with each topic nominally the same for everyone, with uniform expectations for all pupils at a given ‘level’), up which pupils progress at their personal rate, and
  • associated accountability measures that have unintended consequences.

We then outline the alternative conception of a two-dimensional “*-curriculum”, in which each theme in the standard curriculum sequence is explored (and where necessary, assessed) to different depths, and where those who manage to dig deeper and to lay stronger foundations emerge naturally as the ones who are well-placed to subsequently progress further. In such a model, able pupils in Years 5 and 6 would not be pushed ahead to achieve a premature and superficial mastery of ‘Level 6’ material, but would spend time exploring harder problems at ‘Level 4’ and ‘Level 5’ (so-called 4* and 5* material). Similarly, able students in Years 10 and 11 would not be entered early for an accessible but superficial GCSE, but would instead be expected to master core GCSE material more deeply, so as to make the subsequent transition to A level in Year 12 straightforward.

Read the rest of the paper. 

Quality maths graduates flock to teaching

Press release from the Department of Education. A quote:

Our classrooms are now staffed by high-achieving maths graduates according to the latest figures released from the Teaching Agency (TA).  Data reveals that almost one in five maths graduates are becoming teachers. In addition, for the first time, over half of new maths trainee teachers have upper second-class degrees, or better .

The data, from the Higher Education Statistical Unit, shows that 18.5 per cent of maths graduates surveyed three and a half years after graduating chose to go into teaching. TA’s own data also shows that the proportion of maths graduates entering training with a 2:1 degree or better has risen from 44 per cent to 51 per cent in just three years.

From Notes to Editors:

Analysis of the HESA data was carried out by HECSU on behalf of the Teaching Agency.  The Destinations of Leavers of Higher Education (DLHE) survey is the official biannual follow-up to the annual national survey. It examines the careers of a sample of UK graduates, 3.5 years after they have graduated, and is designed to give a longer-term insight into the early career progression of graduates. [...] The census data is available online.