Tony Gardiner, mathematician whose annual schools challenge thrilled competitive children

Gardiner wrote problem-solving books which enabled bright pupils in varied schools around the globe to find a home in mathematics

Tony Gardiner, who has died aged 76, was the crusading mathematician behind the UK Schools Mathematics Challenge, an annual brain-racking competition for children aged between 11 and 14, aimed at stirring up enthusiasm for maths.
Concerned that British schoolchildren were falling behind in mathematics attainment in international league tables, Gardiner, then a lecturer at Birmingham University, founded Junior and Intermediate Mathematical Challenges under the name of the UK Mathematics Foundation Challenge in 1987, along lines that owed nothing to government educational reforms or progressive teaching methods (of which he was highly critical). Calculators were banned.
The idea of the “challenge” tapped into children’s natural competitiveness with questions designed to stretch them and encourage them to develop formal arguments and proofs. Forty per cent received certificates – six per cent gold, 14 per cent silver, 20 per cent bronze.
The best performers were then invited to try the Junior Mathematics Olympiad, a three-hour written paper which, as Gardiner explained, gave them “a glimpse of what there is still to learn”. “Tea and a cake cost £4.50. Tea and an éclair cost £4. A cake and an éclair cost £6.50. What is the cost of tea, a cake and an éclair?” ran a question from one recent paper.
“They are not like the questions you get in the book. There are different types of maths mixed in one puzzle,” observed one pupil interviewed by The Independent in 1993. Operating on a shoestring budget (entry: 30p a head), within five years the Mathematics Challenge had spread to about 1,600 schools, from independents to inner-city comprehensives.
Though entry was voluntary and none of the certificates would do schoolchildren the slightest good in terms of attainment targets or Key Stage 3 tests, anecdotal evidence suggests that it has encouraged many to go on to specialise in mathematics.
Gardiner continued to run the Junior and Intermediate Challenges until 1996 when, with the numbers of entrants reaching 105,000 and 115,000 respectively, he founded the UK Mathematics Trust (UKMT) to run both the challenges and the separate National Mathematics Contest (now the Senior Mathematical Challenge), established in 1961 by F R Watson. 
Thanks largely to Gardiner’s leadership and energy, the UKMT is now one of the UK’s largest mathematics enrichment programmes. In 2002-03 he designed and ran the first national year 12 Team Maths competition which is now one of 14 events run by UKMT.
He was scathing about education reforms and in a 2000 article in The Independent attacked the Blair government’s new “world-class” maths tests for school children as failing to provide any solution to the problem of how to encourage the most able.
“Setting good problems to test the top 5 to 10 per cent is hard,” he wrote. “Setting problems that can be marked reliably… is harder still. Those who have been doing both for many years… suggest that one should start by using short, closed questions of a relatively traditional kind and stick, initially, to paper and pencil tests…
“Instead, the Department for Education and Employment insisted that the test be delivered by computer; and the test developers preferred open problems of a kind better suited to exploratory classwork than to reliable assessment…
“Then there was the critical flaw that most of the problems could be solved by trial and error. Yet maths is the science of exact calculation. So our best pupils are condemned to sit lousy tests, with no obvious purpose, at an inappropriate age.”
Anthony Gardiner was born at Bracknell, Berkshire, on May 17 1947 to Lt Col David Gardiner, an officer in the Royal Signals, and his wife Mary, a nurse in Queen Alexandra’s Royal Army Nursing Corps.
Owing to his father’s Army career, Tony’s childhood was spent in Hong Kong and Singapore, and at the age of nine he was sent to the Duke of York’s Royal Military School in Kent. He took his A-levels aged 15 and, with his parents still overseas, remained at the school for three more years.
He read mathematics at Southampton and did an MSc at Warwick University. He spent the next five years working on a PhD, affiliated to Warwick but based at other locations including Dar es Salaam, where he lectured at the university, and, in Germany, Bielefeld University, where he also lectured.
In the early 1970s he completed a postdoc at Royal Holloway College. From 1974 to 2000, he was a reader in mathematics and maths education at Birmingham University, where, in the early 1980s, he established a series of “Take Home” competitions called the Birmingham University Mid Term Mathematical Problem Solving Journal.
By the mid-1980s, 3,500 11-15 year-olds and 1,200 16-18-year-olds were taking part. He set and marked all the problems himself. Out of this came the idea for National Maths Challenges. In 1994 he set up the National Maths Summer School for the most able 14 to 17-year-olds and ran them annually until 2000. He also established a Teachers’ Summer School, intensive six-day events for 60-90 teachers, which ran from 2007-09.
He had the gift of inspiring others with the beauty of maths and many of his students went on to become maths teachers. Around the globe, at varied types of school, his problem-solving books enabled budding mathematicians to find a home in maths.
As a mathematician, Gardiner made contributions in areas including finite and infinite groups, algebraic graph theory and number theory. He wrote some 15 books and in 2003 created the Problem Solving Journal, a termly problems booklet for secondary school students.
In 1995, he was awarded the Paul Erdős Award for his contributions to UK and international mathematical challenges and Olympiads and, in 2016, he was presented with an award from Texas A&M University for Excellence in Mathematics Education.
Gardiner liked to say: “Failure is far more important and far more creative than success.” Outside mathematics, he was a great fan of classical music and gardening. He gave his lawn, vegetables and plants as much love as he did maths.
He married, in 1971, Gwyneth George, who survives him with three sons and two daughters.
Tony Gardiner, born May 17 1947, died January 22 2024