It isn't every day you get to tell one of the world's leading researchers that he has got it wrong. Especially when you are still at school. But that is what Jason Long, now in sixth-year at The Glasgow Academy, did this summer, while working on a Nuffield bursary project - on the cryptography mathematics that makes modern commerce possible.
"It wasn't a fundamental mistake," says Jason, as he stands beside his poster, fielding questions. "But it was a mistake. Carl Pomerance (well-known number theorist) in the States was really nice about it when I emailed him. He said I was very good at number theory."
Jason is one of 81 young people displaying their summer research on posters in two sumptuously furnished rooms at the Royal College of Physicians, Edinburgh. With its coffered ceilings, Corinthian columns and dark paintings of dead but distinguished fellows, it's an imposing setting. But these are confident youngsters, unintimidated now, as good scientists must be, by the trappings of adult authority.
"It gave me confidence," says North Berwick High's Joseph Turner of his summer project investigating the invertebrates - worms, beetles, molluscs and leeches - that live in freshwater lakes. "It was a shock at first, a steep learning curve, going from school to doing research with real scientists. I had to focus in a way I've never had to at school, where you just do the work and sit the exams.
"I learnt so much when I was at the Centre for Ecology and Hydrology that I plan to stay there as a volunteer this year and continue with the research, before going to university. This is the field of science I want to pursue, and it's experience I couldn't get staying on at school."
While the relevance of the research to the real world presents a challenge to Nuffield students, who have to complete a solid piece of work in four to six weeks, it's also part of the appeal. By far the majority of projects on display are in biosciences or medicine, with chemistry, physics, maths and engineering in much smaller numbers.
Sarah McDonald, now in S6 at Linlithgow Academy, has been investigating miscarriages, which occur in an astonishing 30 per cent or more of human pregnancies. She has been testing the hypothesis that bacteria are to blame. "Listeria is the main one, but I've been doing research at Napier University with a salmonella model. We've been looking to see if progesterone has an inhibitory effect on the white blood cells that fight bacteria."
Her results are fascinating, suggestive and a little surprising. The female hormones produced during pregnancy do indeed seem to create an environment that lets bacteria thrive. But only for a time. "We found that a low dose of the hormone affected the ability of white blood cells to attack infection more than a high dose did."
Sarah is cautious and says more research is needed to learn exactly what is going on. But her results are consistent with the idea that bacteria do cause miscarriages, and that most happen in the first few weeks, before the hormones have built up to the higher levels that seem to inhibit bacterial growth.
The effect on Sarah of the work she put into the project is less surprising. "Before I did the project I was interested in either medicine or scientific research," she says. "I'm more interested in the research now than I was."
While most Scottish students taking part in Nuffield science projects do so at the end of their fifth-year, there are advantages to tackling one a year later, says Ross Aitchison from Biggar High, Lanarkshire: "It gives you a little more time. You don't have to go back to school right away."
Ross's research was aimed at understanding how our brains process moving images, says Dr Uma Shahani, one of several project supervisors who have accompanied their students to the event. "We were lucky to get Ross. He is very able and will be on a paper about the research that we are going to present at a conference in the US in October."
Ross himself will not be there, he says ruefully. "I'll be in my first year at Strathclyde University, studying optometry. But it's very satisfying to know they will be talking about my work, and that it will be looked into further. I enjoyed the project and will likely go on to do research after my degree. I was surprised by just how much new information at a high level I was able to take in. I didn't realise I could do that in such a short time."
Showing bright youngsters what they are capable of is an educational task too often neglected, says Strathclyde University's Professor Adam McBride - who, besides supervising Jason Long and two other Nuffield students this year, also delivers maths masterclasses around the country and mentors students in international competitions.
"They need as many enrichment activities like these as they can get," he says. "Our school system does not stretch the most able. We have to get away from the idea that the teacher knows it all.
"Not only are all the answers not at the back of the book, but we sometimes don't even know the question. That is the excitement."
The Nuffield bursary scheme and showcase events are managed throughout Scotland by TechFest-SetPoint: www.techfestsetpoint.org.uk