The Universe Speaks in Numbers: Douglas Stanford and Pedro Vieira interviewed by Graham Farmelo

Phil Anderson was one of the most creative theoretical physicists of the past century. Among dozens of key contributions, he pioneered our understanding of symmetry breaking and paved the way to our modern understanding of weak and electromagnetic interactions, and the prediction of what became known as the Higgs boson. He did all this without state-of-the-art mathematics and was wary of mathematics-led approaches to our understanding of Nature. In this interview, recorded on 31 July 2014, he talks about his early career and his suspicions of string theory. He also tells me what topics he would advise bright young scientists to study.

The second part of leading theoretical physicist Nima Arkani-Hamed's inspiring interview with Graham about the mysterious harmony between pure mathematics and fundamental physics.

Cosmologist Martin Rees, a pioneer of multiverse concept, is one of the most productive and respected thinkers about the origins and development of the universe. A former president of the Royal Society, he is also famous for his wise and thoughtful commentary on the state of science, and his thinking about the future. In this interview, he ranges widely over many themes, including the question of whether the pursuit of fundamental physics will one day run out of steam, become too expensive and perhaps too difficult to pursue.

The interplay between fundamental physics and pure mathematics has led to many remarkable mathematical insights over the past fifty years. Karen Uhlenbeck is one of the mathematicians who made pioneering insights into geometry when studying the physicists' gauge theory of particle interactions. In this podcast, she talks candidly about how many mathematicians came only grudgingly to accept in the 1960s and 1970s that they could do first-class work by focusing on topics whose importance had first been emphasised by physicists, in connection with understanding the real world.

Steven Weinberg is perhaps the most accomplished living theoretical physicist. Now based at the University of Texas at Austin, he has made substantial contributions to our understanding of all the fundamental forces of Nature. In this podcast, he reflects on his career in physics, the 'golden years' in which he and others put the finishing touches to the Standard Model of particle physics, and his views about the future of theoretical physics.