Teachers and pupils should each get a pound;250 bonus every time a student gets a top grade at A-level maths, a major science conference was told this week.
Frances Cairncross, president of the British Association for the Advancement of Science, believes the move could help to increase the number of state-school pupils opting for maths.
Ten thousand fewer young people took maths A-level this year than in 2001.
Ms Cairncross, who is also chair of Britain's Economic and Social Research Council, said paying teachers and pupils a "bounty" would ultimately help the country.
"An innumerate population is less likely to devise good solutions to climate change and a host of other environmental problems than one at home with mathematical and scientific concepts," she said.
"Perhaps we need to experiment with a bounty for every grade A maths A-level taken in a maintained school - divided equally between the student and class teacher - or a couple of extra UCAS points."
She said ministers should pilot levels of reward for staff and students to see what level of payment would make a difference. She said payment was needed in state schools to stop them falling further behind private schools in maths and science teaching.
Almost half of A-level A grades in maths, physics, chemistry and biology and more than half of those in economics are won by private school students.
"It is a scandal that such a high proportion of the best A-levels in these key subjects are coming from fee-paying schools," Ms Cairncross said.
About 30,000 people, including 5,000 pupils, joined more than 300 of the UK's top scientists at the BA Festival of Science in Norwich to discuss topics ranging from food safety to how the universe began.
Efforts to boost the interest of pupils of all ages in science was a theme of the festival. A pound;500,000 scheme use puppets in primary science lessons was launched on Wednesday.
The funding, from GlaxoSmithKline, will be used to train 9,000 teachers in how to use Jasmin and Benny, two large, hand-held puppets, to boost pupils' understanding of scientific concepts.
A two-year research project funded by the Nuffield Foundation showed pupils spent almost three times as long involved in scientific reasoning when puppets were used in lessons.
It found that children treat the puppets as if they are real characters in class in a similar way to how adults relate to soap-opera characters. The puppets were particularly effective with pupils who are normally reluctant to speak in class and with those who have learning difficulties.
Brenda Keogh, one of the puppets' creators, said: "The puppets each have their own character and bring science problems to life making the subject-matter more relevant for children."
* firstname.lastname@example.org Details of "Puppets: Talking Science - Engaging Science" are available from www.puppetsproject.com