Public and other lectures
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A note of 28th March 2017. On Wed 8th of this month I gave a talk (one which I dedicated to the memory of Jon Borwein (1951-2016)) to the student Mathematics society at Trinity College Dublin. Some weeks beforehand I had provided the following description to give a flavour of my intentions for my talk:

Title. The (remarkable and beautiful) binomial coefficient theorem of Gauss, and more besides.

Abstract. One of Gauss's most memorable and beautiful discoveries (with an extremely difficult proof) is his so-called 'binomial coefficient congruence' (it's a mod p congruence, prime p = 1 mod 4). One might think he had discovered it by doing ... see what Karl Dilcher and I outlined in our American Mathematical Monthly paper An Introduction to Gauss Factorials (which is the fourth paper at this page), but a reading of his original Latin paper (1828, when he was 51) one sees he discovered it by a quite different approach.

In any event, Gauss's original mod p theorem seemed a dead end until Karl Dilcher and I discovered the most general extended version of it (i.e., mod palpha, again for prime p = 1 mod 4, and all alpha = 2, 3, 4, ... ). What I would like to attempt is not just to state what this general extension, but rather show how this extension first occured to us, before we eventually made a proof of it. Not even the mod p2 extension had ever been guessed. All of this can be described in quite simple language. " [END]

A html version may be accessed here.

During the academic year 1995-96 I conceived the idea of having an annual sponsored public mathematics in my College, and I wrote innumerable letters to various companies seeking sponsorship. Since I had already lined up the eminent mathematician (and my former teacher; see my talk that I dedicated to him below) and cryptographer, Professor Fred Piper, as our first speaker, I expected that my only problem would be that two sponsors would materialise at the same time, and that I would have to disappoint one of them (I was very naive... )

(In January 2004, Fred Piper gave the annual Turing Lecture at the invitation of the British Computer Society. On May 6th 2004 I gave a talk on transcendental numbers, which I dedicated to Fred Piper - who taught me when I was an undergraduate at Royal Holloway College - marking his retirement.)

In September 1996 an event occurred which made me take the plunge and offer a public lecture myself: the announcement by Cray supercomputers of a new world record (which was broken shortly afterwards by George Woltman's GIMPS). While I was at it I also decided to offer a public lecture linking prime numbers with cryptography. Those two lectures, and some others, are available below.


In those far off days my college didn't have email or web facilities, but I did at home. It was from my home that I notified the Maple Users Group (which no longer exists) of my two initial lectures, and I offered the files to anyone who contacted me. I saved the early requests, and here they are (a pdf file).

Important note with regard to html versions of my lectures below. Maple, in converting active worksheets into html code, turns outputs (calculations, etc) into gif files, and so you may need to allow some time for downloading (at least years ago you did, but now - 2017 - perhaps not). 

  1. In October 1996 I gave a public lecture The recently discovered world record prime number. Unfortunately the original file is so corrupted that I have had to take it down.

  2. In November 1996 I gave a public lecture Prime Numbers and Public Key Cryptography (which, in 1999, when I first obtained a website, I put up here), but since I gave a better (I think!) and more expanded version of this lecture in September 1998 (the Clinton-Ahern lecture below) then I have removed that first version.

  3. In May 1998 I gave a three and a half hour talk (with a short coffee break!) to Mathematics and Computer staff in the Cork Institute of Technology. The title of my talk was On the use of MAPLE in the St. Patrick's College; a html version may be accessed here.

  4. In September 1998 the U.S. President, Bill Clinton, during a visit to Ireland, together with the Irish Prime Minister, Bertie Ahern, engaged in an 'historic, first digital signing of a treaty on e-commerce' between the U.S. and Irish governments. In November 1998 I gave a public lecture entitled Bill Clinton, Bertie Ahern, and digital signatures. Originally I linked my talk here, but it was in a much earlier Maple release (which I've now removed).

    Subsequently, having been invited to give that same talk in Chicago (Oct-Nov 2003), I made some alterations, and that altered, better version is available below.

    An article I wrote for the Irish Times of Mon. 16th. Nov. 1998, about the Clinton-Ahern lecture, may be viewed here.

    Early in 1999 Wiland Schmale of Oldenburg University asked if he could use my Clinton-Ahern lecture as the basis for a public lecture by himself, as one of a series to be given in Oldenberg, marking the 25th anniversary of its university, and I was happy to do so.

  5. In August 1999 I gave two talks (using Maple) in Plymouth, England, at the ICTMT4 (the 4th International Conference on the use of Technology in Mathematics Teaching):

    1. Using Maple to investigate L- and R-approximations to quadratic irrationalities (mws format, and in html format)

    2. The mathematical context of the recent (25thJuly 1999) discovery of the largest known composite Fermat number (mws format. A html version is available here.

  6. On Thursday 28th October 1999, I offered a public lecture entitled The history of Fermat numbers from August 1640. The background to that lecture was my discovery, with Yves Gallot, in July 1999 of the [then] largest known composite Fermat number. That record has now (February 2003, and - to everyone's surprise - October 2002) been surpassed by Yves Gallot, George Woltman, Paul Jobling and myself (see here).

    The mws file may be downloaded here, and a html format version may be downloaded here.

  7. In Chicago, October-November 2003, at the 16th International Conference on the use of Technology in Collegiate Mathematics I gave a Bill Clinton, Bertie Ahern, and digital signatures talk. A html version is available here.

  8. On Thursday 19th October 2006 I offered - as my contribution to the first ever Maths Week (Ireland) - a Number Theory and Cryptography talk to some secondary (high) school students and the general public. A html version is available here.

    My talk was a much modified version of my Chicago talk (above), and contained a much improved version of the Maple code for the technical to_number and from_number procedures.