We spoke to philosophers Philip Goff and Keith Frankish about their popular new online show, Mind Chat, in which they interview scientists and philosophers on the mystery of consciousness.

Andrew Wiles gave a series of lectures cryptically titled “Modular Forms, Elliptic Curves, and Galois Representations” at a mathematics conference in Cambridge, England, in June 0f 1993. His argument was long and technical. Finally, 20 minutes into the third talk, he came to the end.

Honeycreepers, small birds inhabiting the Hawaiian Islands, have a rich assortment of beak shapes. Some species have long, thin beaks suited to plucking insects from leaves. Others possess thick beaks good for cracking open tough seeds. According to the classic view of evolution, natural selection drove the development of these different species. Each variant adapted to suit a different ecological niche. But Blair Hedges, a biologist at Temple University in Philadelphia, has proposed a...

A PhD student in the Netherlands has demonstrated a technique that could cut the cost of producing graphene by a factor of a thousand, opening up the real-world potential of the so-called "wonder material". Shou-En Zhu from the Delft University of Technology described in his thesis how chemical vapour deposition of methane on a copper sheet can create graphene crystals that align together to form an "endless sheet" of pure graphene.

Summing up years of work in one sentence.