# Popularisation and Teaching

## Mathematics and the imagination

Mathoetic mode, Article, LMS Newsletter, January 2008

Sonya Kovaleskaya on mathematicians, imagination and poets.

The role of the poet, by W. Shakespeare. Is this role analogous to that of the mathematician?

Albert Einstein on the relevance of considering the Theory of knowledge.

Gian-Carl Rota on disclosing new worlds.

Alexander Grothendieck on speculation.

Barry Mazur has articles on Mathematics and the Imagination on his home page.

Are there famous problems in Category Theory?

Mathematics and the Imagination: A Brief Introduction This is a scholarly Introduction by Arielle Saiber and Henry S. Turner to the 17 (2009) issue of the journal Configurations.

Math-Overflow: how do you decide whether a question in abstract algebra is worth studying?

## Aims in University Mathematics Education

``Carpentry: a fable'', R. Brown,
*Mathematical Intelligencer*, 11, no.4 (1989) 37.

What should be the
output of mathematical education?

This is an edited web version of the article published in: *Mathematics
education as a research domain: a search for identity*, ed. Kilpatrick,
J. and Sierpinska, A., Kluwer, Lancaster (1997) 459-476.

What should be the *context* of an adequate specialist
undergraduate education in mathematics?, Ronnie Brown and Tim Porter,
The De Morgan Journal 2 no. 1, (2012) 411--67.

An examination paper from a
University Staff Training College, Mathematics
Division, has turned up, and may be found here. It was first presented
at an evening discussion session on `The Public Image of Mathematics', led
by the writer, at the British Mathematical Colloquium at St. Andrews in 1987.
No answers were handed in! Related comments and quotations have been added,
and some additional questions. Comments welcome! Following up the ideas here
led to our courses:

**
What is the best way to develop mathematical intuition?**

Here is a true story. One year a student questionnaire on my first year analysis course wrote: "Professor Brown gives too many proofs."
I thereupon decided that next year the course would have **no theorems, and no proofs**. It would however, have "Facts" and "Explanations".
(I got this idea from an engineer!) Part of the deal of course would be that an Explanation should explain something.
Another point is that unlike the good old days when Euclidean Geometry was studied at school students have no previous experience
of the words "Theorem" and "Proof". Also the study of Grammar has gone as well, so they are unfamiliar with the structure of language.

What is called a "proof" is really an explanation but written very carefully.

In other second year lectures which needed an explanation of a particular case of *A* is contasined in *B*,
I asked the class "What is the first line of the proof?" and then,
to be written further down on the board, "What is the last line?". By the end of the course, they got the idea!

Also students need training in writing carefully. See a course called Ideas in Mathematics I gave.

I also found that the best way to develop intuition was to write things out very carefully, and explain them to others. When you have written something out 5 times, you may see how to improve it a bit. Then another bit. And so on.

The idea that a proof is found one step after another is just not so. For 9 years I had an idea of a proof in search of a theorem. It took that long, and lots of
talking and writing, to piece together the gadgets needed to make the idea of the proof actually work and prove a theorem.

The composer Ravel said that you should copy. If you have some originality, this may appear as you copy. If not never mind! Your new ideas also may only appear at the 5th copy, as the wheels of the brain start to unclog. In fact it has been said that Newton was an inveterate copier!

Mathematics in Context description of a
course given at Bangor. Have a look also at this interesting
link
to a Didsbury student paper.

`Ideas in mathematics'. Here are details of a first
year math course.

What is mathematics? Please debate these issues!

Best Practice, THES Article, 22/10/04

Promoting mathematics , pdf of article in EMS Newsletter June 2010, 17-21, revised version of article published in MSOR Connections, vol 7, No 2, May 2007.

"Why study mathematics", by R. Brown and
T.Porter, *Mathematics for the future* IMA/Hobsons 1995.

The Methodology of Mathematics.
Versions of this article have been published in *Bulletin International Commission
of Mathematical Instruction*, 37 (1994) 23-37; *Math. Gazette*, 79
No 485 July, 1995, 321-324. It has also been published in Lithuanian (Alfa
+ Omega, 1 Nr 5 (1998) 71-84 ), in the J. Transfigural Mathematics, in CUBO,
and in the European Mathematical Society Newsletter in two parts, June and
September, 2001.
The latest version was published in
The De Morgan Gazette, and is at Methodology: 16 October, 2017, (pdf) .

Towards a Philosophy of Real
Mathematics, by David Corfield. Do look up other links on this excellent
book.

`Mathematicians struggle for truth'

Discussion on mathoverflow on "How do you decide whether a question in abstract algebra is worth studying?"

Mathematics and humour: since this is not an aim of mathematics education, here are some cartoons of David Piggins to cheer you up!

A Warning.

Here is my answer to the stackexchange question Getting students not to fear confusion. The methods of "errorless lerning", and of learning from success, inclduing learning to tolerate failure, apply at all stages of learning.

## People

Click here for links to the life and work of Alexander Grothendieck.

George W. Mackey : this is a brief account of how he encouraged me in work on groupoids by telling me of his interest in them.

Donald Coxeter's
90th
Birthday celebration at the Fields Institute, February 9, 1997; photos
of the occasion, and link to my presentation on

The
Symbolic Sculptures of John Robinson: Geometry, values, form and structure

## Research Assessment

Quality in Higher Education: a discussion document, including an analogy with business and commerce. It seems Government practice is the opposite of recognised quality management, which should be about investment, training, people and attitudes, and not about systems nor paperwork!

Banquo on the seeds of time:

Letter on Science Funding to `Science and Public Affairs', August 1999.

A senseless system: On the RAE, by Simon Caulkin, Management Editor of the Observer, December, 2008.

MetricsREF A document prepared for the LMS by Charles Goldie analysing the problems of using `metrics' as a basis for research evaluation by the HEFC. pdf file

Assesment of articles, journals and Thomsons ISI

Quality management in business, by J. Varey

## Articles

Category theory and higher dimensional algebra: prospective tools in theoretical neuroscience. (pdf file)

The intuitions of higher dimensional algebra for the study of structures space. (pdf file)

`Out of Line' Link to pdf and html files of a new version of a presentation as a Friday Evening Discourse to the Royal Insititution of Great Britain in May, 1992. The title refers both to the area being non traditional and to the idea of higher dimensional algebra.

Pdf file of presentation on
Mathematics and Knots
at *
Visual Representations and Interpretation*s: Liverpool, Sept 22-24, 1998.

``Making a mathematical exhibition'', by
R. Brown and T. Porter, in *The popularization of mathematics*, edited
A.G.Howson and J.-P. Kahane, ICMI Study Series, Cambridge University Press,
(1990) 51-64.

`Analogy, concepts and methodology in mathematics', by Ronnie Brown and Tim Porter. pdf file Eureka, (September 2006) 23-27.

`Category Theory: an abstract setting
for analogy and comparison', by R. Brown and T. Porter, pdf file In:
*What is Category Theory?* Advanced Studies in Mathematics and Logic,
Polimetrica Publisher, Italy, (2006) 257-274.

The five Ds - necessities for any writer! (Learned from a novelist talking on the radio.)

Some remarks on research in Mathematics Extract from one of the Prefaces to `Topology and Groupoids'.

Review of ``History of Topology'' Edited I.M. James, North Holland, 1999. LMS Newsletter, January 2000.

The origins of symbolicity. This is an article by the distinguished Auatralian palaeontologist Robert Bednarik on the use of symbols by early hominids. I find this relevant to mathematics, in which symbols play a key role. In any case, I find it fascinating!

##
John Robinson, Sculptor

Conversations with John Robinson (pdf)

John Robinson's Official web site>

de Laszlo Collection of John Robinson Sculpture Maquettes at Durham University (pdf)

Symbolism in the sculptures of John Robinson

A discussion in the context of
`Knowledge:
representation and interpretation' . Published in Theoria et Historia
Scientiarum, the International Journal of Interdisciplinary Studies, issue
on `Knowledge: representation and interpretation.', edited W. Meyer and R.
Paton, 6 (2002) 55-73.

"Symbolic sculptures and mathematics", Views of the four John Robinson Sculptures at Bangor; though they are not all in these positions or on view.

"Symbolic Sculptures and Mathematics", Web Site Presented by the Centre for the Popularisation of Mathematics and Edition Limitée.

John Robinson, Sculptor, May 5, 1935 - April 6, 2007. Article in Hyperseeing, June 2007.

A recent presentation on My Friend John Robinson, Sculptor ; pdf file, 26MB.

Seventeen great videos of sculptures may be found on YouTube by searching for `John Robinson sculptor'.

There is much very well presented material on John's official site: Bradshaw Foundation; the main site reflects John's long standing interest in Rock Art, and the history of makind.

Updated April 9, 2016