Samuel Salomi, who achieved a grade B in A-level maths this year at the age of nine, has been accepted for an Open University degree course, and the university has agreed to waive his fees. Now 10, he will be the youngest student ever to enrol. He has chosen the OU because he wants to carry on studying other subjects at home - where his mother has taught him since he was 18 months old. Samuel has now eased back from working 12 hours a day to eight.
Another maths ace, Sarah Flannery, 17, from Cork, has won the European Young Scientists competition in Greece, for inventing a computer code which is 30 times faster than the current one for sending secret messages via the Internet and e-mail. She devised it while on a work placement in a Dublin cryptography office.
Otherwise teenagers appear to be behaving badly, as usual. The nanny state in the form of Tessa Jowell, the public health minister, wants teenage girls to be taught by GPs and family planning clinics to say no to sex. She laid some blame for youngsters' promiscuity on a media that bombards children with images of sex from a young age.
In Sheffield, which made the headlines last month for a 12-year-old's pregnancy by her 14-year-old boyfriend, a health centre has taken a more pragmatic line: it is offering boys free condoms via a mobile clinic.
The BBC is getting in on the act: a new "morality-free" series, in defiance of the Government, called Learning to Be You, will feature teenagers talking frankly about sex. The Beeb claims the programme is needed because of inadequate sex education.
In contrast, Sindy, the British answer to Barbie, is projecting a revamped wholesome, caring image by losing her Baywatch tan, donning a sunhat and wearing a T-shirt with an Imperial Cancer Fund logo. She is modelled on a 15- or 16-year-old girl who loves her friends and animals but is also pretty cool,said Vivid Imaginations, her manufacturers. Just what Ms Jowell would wish.