European heatwave and climate change, Eugenia Cheng, Next generation batteries for electric cars, Joseph Hooker exhibition.

The current heat wave in Europe is proving deadly. High day and night temperatures, coupled with high humidity, can be a very dangerous combination. A new study has calculated the risk of deadly heat on a global basis, and shown that between 48% and 74% of the world's population will be subjected to life-threatening heat and humidity for at least 20 days a year. Ed Hawkins, Professor of Climate Science at the University of Reading, discusses the findings. Gareth also asks BBC weatherman, Darren Betts, whether the recent wave of climate trend animations, or gifs, doing the rounds on social media, are a helpful tool in communicating climate change risks.

Professor of Mathematics, Eugenia Cheng, is one of the shortlisted authors for the Royal Society Insight Investment Science Book Prize 2017. She talks Gareth through the inspiration for her book "Beyond Infinity: An expedition to the Outer Limits of the Mathematical Universe".

The UK Government announced last week that it was aspiring to remove all petrol and diesel vehicles from roads by 2040. Current battery technology relies on lithium-ion batteries. Are lithium, and the other metals required for batteries, sustainable for a totally electric transport system? And do they have the charge capacity to make them a reliable alternative to fossil fuels? Dr Billy Wu, of the Dyson School of Design Engineering at Imperial College London, goes through the alternatives and the next generation of battery technology.

To mark the 200th anniversary of the birth of one of Victorian Britain's most important scientists, Joseph Hooker (1817-1911), Kew Royal Botanic Gardens is holding an exhibition titled Joseph Dalton Hooker: Putting plants in their place. It's a fascinating selection of his photographs, journals and paintings. Gareth is taken on a tour by the curators - historian Professor Jim Endersby of the University of Sussex and Galleries and Exhibitions Leader at RBG Kew, Maria Devaney. They explain how as a tireless traveller and plant collector, Hooker was the founder of modern botanical classification and a close friend of Charles Darwin.

Produced by Fiona Roberts Presented by Gareth Mitchell.