BBC Inside Science

Tom Whipple investigates one of the biggest days in the 10,000 year history of maths. This week, overnight, OpenAI dropped hundreds of mathematical papers onto the internet. From the Margulis-Platonov conjecture to the Gaussian Propeller conjecture to Banach’s simple Lebesgue-spectrum problem. Decades of maths progress overnight. PhDs of work done in hours. This week saw the Nobel Prizes awarded for Chemistry, Physics and Physiology or Medicine. From mice with blue lights in their brain to massive ice cubes with blue lights underground, science journalists Kit Chapman and Caroline Steel tell us what we need to know.In 2016, President Obama reflected on the moon landings and on the delicate and dangerous task of putting humans there. He commented, when giving a former MIT programmer the Presidential Medal of Freedom: “Our astronauts didn’t have much time...but thankfully they had Margaret Hamilton.” Margaret led the programming team for the Apollo missions and was a pioneer, in every sense of the word, until her death this week. Between Cape Horn and the Cape of Good Hope, there is a volcano inhabited by Chinstrap penguins. People don’t visit Zavodvski island much, but if you had been there in 2011 you would have been outnumbered by chinstraps 600,000 to one. Today, almost half a million have gone missing. Professor Norman Ratcliffe from the British Antarctic Survey tells us what he thinks is going on. Presenter: Tom Whipple Producers: Ben Mitchell, Clare Salisbury, Katie Tomsett Editor: Martin Smith Production Co-ordinator: Jana Bennett-Holesworth

In October members of the General Conference on Weights and Measurements are voting to change how we keep time on Earth accurate. Currently an additional second, known as a Leap Second, can be added to make sure modern atomic clocks stay in sync with solar time. However, all of this might be about to change as the rotation of the Earth speeds up and interferes with our measurements. Tom takes a trip to meet Principal Scientist Setnam Shemar at the National Physics Laboratory to learn how our time lords keep us all on schedule. Plus, Associate Professor Claire Nichols from Oxford University helps us understand why the Earth's rotation puts our timekeeping in jeopardy.Also on the show, professor of Mathematical Biology, Kit Yates, has scoured the news to bring us two of the hottest science stories this week. We find out how scientists can tell the body temperature of the Tyrannosaurus rex from fossils, and whether the record has been broken for the warmest temperature complex life – eukariotic cells – can tolerate on Earth. Our coverage of the Royal Society Trivedi book prize is also heating up as the winner is announced next week. Ahead of the ceremony author, former winner and judge Bill Bryson shares with Tom why he holds the prize in such affection. We also hear from shortlisted author Lise Barnéoud whose book, Hidden Guests, uncovers the surprising science of microchimerism and how some of your cells are not your own. To discover more fascinating science content, head to bbc.co.uk, search for BBC Inside Science and follow the links to The Open University.Presenter: Tom Whipple Producer: Alex Mansfield, Katie Tomsett, and Tabitha Taylor Buck Production co-ordinator: Jana Bennett-Holesworth Editor: Ilan Goodman

Is AI really plotting against us? In a week where an Anthropic researcher believes there is more than a 10% chance AI 'could kill all humans' we're delving deeper into the capabilities of AI agents. Tom Whipple is joined by Alex Mallen, from Redwood Research, the team whose recent investigation exposed the surprising, weird, and worrying scale of a website hack conducted by OpenAI agents.Is this the most important story we will ever cover on Inside Science? Or is this all just credulous sci fi hype? Professor Stuart Russell helps us unpick how we might align AI with humanity’s hopes. Plus, science journalist Caroline Steel has trawled the news to bring us the science stories you might have missed. This week Caroline discusses how AI has allegedly helped solve a Millennium Prize maths problem and why planetary scientists are turning their attention to a shrinking Mercury. To discover more fascinating science content, head to bbc.co.uk, search for BBC Inside Science and follow the links to The Open University.Presenter: Tom Whipple Producers: Alex Mansfield, Katie Tomsett, Tabitha Taylor-Buck Editor: Ilan Goodman Production Co-ordinator: Jana Bennett-Holesworth