Wolfram Alpha, a year later

On 1 April 2011 I wrote to Wolfram Research:

I had a look at Wolfram Alpha and was slightly surprised that [it] returned, among many useful information about the matrix


the assertion that it had eigenvectors

(1,0) and (0,0).

You and I, of course, understand how to interpret the answer, but it could be quite confusing for a first year student.

I tried it again today, I got the same answer; see for yourself.

Eigenvectors as returned by Wolfram Alpha


GCHQ releases two Turing papers

From ZDNet UK:

GCHQ has released two mathematical papers written by cryptographer Alan Turing after keeping the works secret for over half a century.

The intelligence agency believes the handwritten papers were produced by Turing during his time at Bletchley Park, the World War Two code-breaking centre, GCHQ said in a press release on Thursday. […]

One of the papers, the informal ‘Paper on Statistics of Repetitions‘, seeks a means to tell whether two enciphered messages with different plaintext and an overlap of characters used the same encipherment key during the overlap.

The second paper, ‘The Applications of Probability to Cryptography‘, was possibly written between April 1941 and April 1942, as it contains the reference ‘Hitler is now of age 52’. The paper uses probability analysis to look at four problems: ‘Vigenère’, ‘A Letter Substitution Problem’, ‘Theory of Repeats’, and ‘Transposition Ciphers’, said GCHQ. […]

The two papers have not been digitised, and only currently exist in handwritten form. People wishing to read the papers need to travel to the National Archives at Kew with the reference numbers of the papers, and two forms of ID — a picture ID, and proof of address. People who do this will probably be given a reader ticket number, which will then allow them to request the papers for viewing.

Programming project comes to primary schools

BBC about the Code Club project. A quote:

Volunteers have kicked off a project to set up after-school clubs that teach young children how to programme computers.

Called Code Clubs, the sessions will aim to instil the basics of computer programming into children aged 10-11.

The clubs will be built around practical hands-on tasks that will include children making games and eventually controlling robots.

It aims to have 25% of the UK’s primary schools running a Code Club by 2014.

And more from BBC: Learning to code. A quote:

Alasdair Blackwell, our main tutor and the co-founder of Decoded, is an impressive evangelist for the open web, and the need to give ourselves the tools to make best use of it.

He argues that today’s teenage iPad users, far from being digital natives, actually have less understanding of what makes computers tick than his generation, who got their hands dirty with machines like the BBC Micro. “The children playing on iPads, I actually despair for them because they’re just using software, not creating software for themselves.”

Meanwhile, First Raspberry Pi computers to be delivered.

Cultures of Mathematics and Logic (China)

9-12 November 2012
Institute for Logic and Cognition
Sun Yat-Sen University
Guangzhou, China

All researchers working on various aspects of “Cultures of Mathematics and Logic”, including, but certainly not limited to, philosophers, sociologists, historians of mathematics, mathematicians, and researchers in mathematics education, are cordially invited to submit their one page abstracts by the submission deadline of 30 June 2012 (see below for details).

DESCRIPTION OF THE CONFERENCE. Mathematics and formal reasoning are fundamental building blocks of knowledge, essential for science, technology, policy-making and risk-management. Mathematical practice is a rich phenomenon of human activity, with subtle differences between various cultures: here, the word culture can refer to national cultures, but also cultural differences in different historical periods, in different strata of a given society, in different social settings.

And yet, the public perception of mathematics is of an apersonal subject with little or no human interaction, based on a false picture of a science of pure thought and deduction, with almost no interaction or visible activity.

In a move away from these traditionalist positions, philosophers and social scientists have recently become more interested in studying mathematical and logical practice, or, to be precise, different mathematical and logical practices. Our conference will focus on this plurality of viewpoints, studying the various cultures of mathematics and logic, and involve several disciplines such as philosophy, sociology, psychology, cognitive science, history of mathematics, mathematics education, and linguistics.


* Andrea Bender. Universität Freiburg, Freiburg, Germany.
* Karine Chemla. Equipe Recherches Epistémologiques et Historiques sur les Sciences Exactes et les Institutions Scientifiques (REHSEIS), Paris, France.
* Christian Greiffenhagen. University of Manchester, Manchester, United Kingdom.
* Shirong Guo. Inner Mongolia Normal University, Hohhot, China.
* Juan Pablo Mejía Ramos. Rutgers University, Piscataway NJ, United States of America.
* Reviel Netz. Stanford University, Stanford CA, United States of America.
* Zhaoshi Zeng. Sun Yat-Sen University. Guangzhou, China.


Abstract submission deadline: 30 June 2012
Notification of authors: 30 July 2012
Conference: 9-12 November 2012

ABSTRACT SUBMISSION. All researchers are encouraged and invited to submit their abstracts until the deadline of 30 June 2012 via the easychair submission page at


Please submit the abstract either in the “abstract” field of the easychair submission site or as a one-page PDF submission.

POST-CONFERENCE PUBLICATION. All authors of papers presented at the conference will be encouraged to submit a full version to a post-conference publication volume. The deadline for submission of full papers will be in early 2013. All papers submitted to the post-conference proceedings will be refereed to high journal standards, and acceptance as a presentation is no guarantee that the post-conference paper will be published.

PROGRAMME COMMITTEE. Mihir Chakraborty, Jadavpur University, India; Shuchun Guo, Chinese Academy of Science, China; Joachim Kurtz, Ruprecht-Karls-Universität Heidelberg, Germany; Brendan Larvor, University of Hartfordshire, United Kingdom; Benedikt Löwe, Universiteit van Amsterdam, The Netherlands; Martina Merz, Universität Luzern, Switzerland; Dirk Schlimm, McGill University, Canada; Ju Shier, Sun Yat-sen University, China

LOCAL INFORMATION. Guangzhou, known historically as Canton, is located in southern China on the Pearl River, about 120 km north-northwest of Hong Kong. With over 12 million inhabitants, it is the third largest city in China (after Shanghai and Beijing) and the largest city of southern China.
In the month of November, expected temperatures are between 15 and 24 degrees. Baiyun International Airport is a major transportation hub with many national and international airlines (for instance, Air France, China Southern Airlines, Emirates, Lufthansa, etc.). In addition, Guangzhou is easy to reach from Hong Kong with its international airport.

David Pierce: Induction and Recursion

D. Pierce, Induction and Recursion, The De Morgan Journal, 2 no. 1 (2012),  99-125.

From the Introduction:

In mathematics we use repeated activity in several ways:

  1. to define sets;
  2. to prove that all elements of those sets have certain properties;
  3. to define functions on those sets.

These three techniques are often confused, but they should not be. Clarity here can prevent mathematical mistakes; it can also highlight important concepts and results such as Fermat’s (Little) Theorem, freeness in a category, and Goedel’s Incompleteness Theorem.
The main purpose of the present article is to show this.

In the `Preface for the Teacher’ of his Foundations of Analysis of 1929, Landau discusses to the confusion just mentioned, but without full attention to the logic of the situation. The present article may be considered as a sketch of how Landau’s book might be updated.

David Wells: Response to the paper “What should be the context of an adequate specialist undergraduate education in mathematics?”, by Ronnie Brown and Tim Porter

D. Wells, Response to the paper “What should be the context of an adequate specialist undergraduate education in mathematics?”, by Ronnie Brown and Tim Porter, The De Morgan Journal  2 no. 1 (2012), 85-98. The link to the paper by Brown and Porter.

Further comments are welcome — all posts on this blog are open to comments.


Government abolishes Technology Policy Unit

The Department for Education (DfE) has confirmed that the unit charged with developing the technology in schools policy will no longer exist after April. [More]

This quote is repeated in many online publications:

“We want schools to be free to use curricula and teaching resources that properly equip pupils for the 21st Century and we want experts like Microsoft, Google and Cambridge University to be involved in the development of ICT teaching,” the DfE spokeswoman said.

“Excellent developments such as Raspberry Pi and Computing at School have taken off in schools precisely because government has stepped back and let the experts take the lead.”