# Dr Tony Gardiner (1947 – 2024)

Tony Gardiner was among a small group of mathematicians who founded the UK Maths Trust in 1996. Tony’s concern was that some school children were falling short in their maths education. He attributed the drop in UK performance in international maths attainment league tables to the UK government’s educational reforms in the 1980s.

UKMT would like to acknowledge Tony’s immeasurable contribution to the education of young people in mathematics.

We share memories of Tony from three of those who had the opportunity to work with him. Their words summarise the spirit and conviction he brought to what is now the most significant mathematics charity in the United Kingdom, and which is globally recognised as such. Our thoughts are with his family.

## Adam McBride

“I first worked closely with Tony in the early 1990s although I knew of him long before then. He was Leader of the UK IMO team on several occasions then.

If memory serves me correctly a crisis arose in 1992; the six questions for the competition had been chosen and preparations seemed to be complete when someone discovered that one of the questions was essentially in the public domain, having been used in some competition somewhere in the world. It had therefore to be scrapped and a replacement had to be found at the very last minute. It seems that Tony came to the rescue by composing a question related to expressing 169 as a sum of squares.

Another memory is of Tony leading crocodiles of Summer School students along the bank of a canal in Birmingham for a musical or theatrical performance and similar outdoor performances in the gardens of Oxford colleges.”

## Gerry Leversha

“In 2007, Tony organised a Summer School for newly-qualified mathematics teachers, and he asked me to deliver some of the lectures. I remember an episode from his own classes, on arithmetic, when he asked his audience how they defined a prime number. The standard reply, that a number was a prime if its only divisors were one and itself, prompted him to ask if that meant that one itself was a prime number.

Some of the teachers said it was, since its only divisor was 1, and others said it wasn’t, since the definition meant that there had to be two different factors.

Tony knew that he was being provocative. He asked whether this was just a conventional issue (which could be handled by making the definition more explicit) or whether it really mattered. Several teachers said it really didn’t matter at all and some started talking about negative prime numbers.

Tony quickly kicked this idea into touch. Somebody eventually mentioned prime factorisation. Tony said that this was crucial, but asked what was the really important fact about it. He then guided the discussion around to accepting that, if we allowed one to be prime, then factorisation was not unique. This had not, apparently, been emphasised during teacher training, but it is, of course, the most important property of numbers. Hence the best way to handle the definition would be to require that the number to be factorised was greater than 1.

This was absolutely typical of the way Tony worked. He would ask a fairly simple question, one that did not seem very important, about which there was a potential ambiguity. He then explored the consequences of resolving this, and made it quite clear that this resolution was not just a convention, not just a linguistic choice, and above all not a triviality, but one which was essential if arithmetic were to make any sense at all.

Little things matter, and you do not always realise what they are or why…”

## Chris Robson

“I got to know Tony Gardiner in the early 1990s after I joined and then chaired the London Mathematical Society’s Education Committee. Over many years, we were both involved in discussions about the school mathematics curriculum, both with fellow mathematics teachers and lecturers and with governmental bodies.

I soon recognised that Tony was a serious, deep-thinking man whose ideas should be listened to. He would speak earnestly and bluntly. Also he worked very hard on the different things he was involved in. Let me describe just one example:

In the later 1990s, there was controversy about the level of competence in mathematics of students entering Higher Education. Tony and I persuaded the LMS Council and through them the IMA and the RSS that it would be worthwhile to produce a report about this. A small group was set up under the chairmanship of Geoffrey Howson. A report was written by Tony, Geoffrey and myself. It was approved and so could be published.

It happened that a meeting about such issues was scheduled at the Royal Society involving speakers from amongst the Fellows of the RS, from governmental bodies and even a Minister of Education.

However there wasn’t time to publish the report in the normal fashion. So Tony organised speedy production using a local printer. He travelled down to London with a very heavy rucksack containing a large number of copies hot from the press. We met at the RS and distributed them to all the participants. Some speakers had been given informal copies a few days earlier and spoke in strong support of it, helping it to become very influential.

This illustrates Tony’s drive and hard work in action.”