Richard Kaye's Home Page

Can a leech do maths? ... instinct tells you that this bloodsucker can no more "do maths" than it can play the trombone. This is a superficial view born of the bogus assumption that maths requires a mind.
(Editorial, New Scientist, 20 June 1998.)

    I am a Lecturer in Pure Mathematics. Recent teaching duties have included courses in logic, computability, analysis, and linear algebra. My research specialities are in mathematical logic. In particular in nonstandard models of arithmetic and related areas of model theory and nonstandard analysis. I am also interested in computer representation of mathematics, MathML and OpenMath in particular. To see a larger version of the picture here of me with my two sons in the Lake District (about 95K), click on the image.


By special request I have just put up on these web pages scans of my papers from the 1987 and 1988 Easter conferences in model theory in Berlin, DDR. These were not otherwose published and are difficult to obtain. They contain results on axiomatisations, quatifier complexity and parameter-free induction. Go to my "papers" page for more details.

Apart from mathematics I play the trombone a little, and if you didn't already know...

Trombonists do it in seven positions

You can also do it in seven positions by moving your mouse over the musical notation in this image. (A freely downloadable version of this graphic is available here.)

7 positions
1st position2nd position3rd position4th position5th position6th position7th position

You can try playing the correct note on the Trombone (moving your mouse over the music staff) and you might even find some hot-links there by clicking. (Don't worry if your embouchure is not up to it, since the same links are available as normal hyperlinks below.)


Bb Research interests

A   List of publications and access to some unpublished papers

Ab Current and recent undergraduate teaching duties

G   Postgraduate teaching

Gb Computer software, including information on and links for GLOSS

F   Trombone Jokes and Pictures

E   Administration duties

Other web pages

I list here other important groups of pages that I maintain on this server.

Sequences and series (real analysis) pages

A comprehensive set of pages on first-year real analysis, sequences and series.

Logic pages

A set of web pages to support my book The Mathematics of Logic, undergraduate courses and beyond, on logic, and in particular completeness and soundness theorems.

LaTeX pages

For information about LaTeX, go to my pages here. (These are looking rather long in the tooth now, sorry.)

GLOSS pages

GLOSS is a system for converting plain text to XML, XHTML, MathML, OpenMath and much more.

Linear Algebra home page

Robert Wilson and I have set up a page for our undergraduate text book Linear Algebra. At present this contains a fairly short list of known errors, but may well be expanded on in the future.

Minesweeper page

Minesweeper is NP-complete! Infinite Minesweeper is Turing complete! For further information, go to my Minesweeper page.

Other stuff

Some of my photographs are available via Flickr at

Square root

I have a webserver at Some other web pages or local copies of other web pages are available via

You can obtain My GPG/PGP public key here. (For PGP, go to The international PGP Home Page.)

My geek code is here.

Please contact me at:

Richard Kaye
School of Mathematics
The University of Birmingham
B15 2TT
Fax: +44 121 414 3389

or email me at R.W.Kaye AT

My personal blog (for not necessarily work-related things) is at