What does a mathematician really mean when they describe something as beautiful? Is it the same type of beauty we perceive in art or music or landscapes - and is it something that the average member of the public can grasp?

Mathematician Vicky Neale has felt a deep emotional and aesthetic response to her subject since she was little. Now a Fellow of Balliol College, Oxford University, in this programme she presents her own personal take on what constitutes the idea of the beautiful in mathematics - drawing connections between other fields like art, music, literature and engineering.

Vicky talks to celebrated maths communicator Marcus du Sautoy about the connections between mathematics and literary narrative, and interviews the acclaimed structural engineer Roma Agrawal about how she strives to create beauty when she’s engineering skyscrapers, sculptures and bridges.

Meanwhile, pianist Nicholas Ross tells us how composers like Mozart have used mathematical ideas like the Golden Section and Fibonacci Sequence to structure their works. Does it really have an impact on a listener’s enjoyment of them?

Historian June Barrow-Green outlines the history of beauty in maths - from the Ancient Greeks, through a Sanskrit treatise on beauty, to the philosophy of GH Hardy whose Mathematician’s Apology of 1940 famously said “there is no permanent place in the world for ugly mathematics”.

Vicky also takes a stroll around a wet Blenheim Palace - or at least tries to - with philosopher Angie Hobbs, to explore what mathematicians and artists mean by aesthetic ideas like “elegance”, “economy” and “surprise” - and why they appeal.

Producer: Steven Rajam

A Whistledown production for BBC Radio 4