The Isaac Newton Institute celebrates its 20th birthday this year, having opened in July 1992. To join in the celebrations we bring you a selection of articles exploring some of the research programmes that have been held there. The Institute asked us to produce these articles in 2010 and we were honoured by being afforded this rare glimpse behind its venerable doors. And as you'll see, what started out as abstract mathematics scribbled on the back of a napkin can have major impact in the real world.

In 1694, a famous discussion between two of the leading scientists of the day - Isaac Newton and David Gregory - took place on the campus of Cambridge University. The discussion concerned the kissing problem, but it was to be another 260 years before the problem was finally solved.