Historian of science Simon Schaffer is interested in the purpose of beauty within evolutionary explanations. Taking the ideas of Charles Darwin as his starting point, he wants to know how and why the capacity to see beauty evolved and whether this powerful, fleeting and apparently most useless of attributes can really have an evolutionary explanation. Simon talks to neuroscientist and biologist Stephen Rose and film-maker and anthropologist Chris Wright about whether Darwin really can explain why he finds Mahler's 5th Symphony beautiful.

This programme is part of a week of programmes looking at the history of ideas around Freedom.

Mathematician Vicky Neale is keen to explain why mathematics is beautiful but also to work out whether beauty can itself be explained mathematically. There is a rich tradition of thought here going all the way back to the Greek philosopher Pythagoras, whose understanding of mathematical relationships sits at the origins of western music. Vicky talks to guitar technician Eltham Jones and to Prof Thomas Johansen from the philosophy faculty in Oxford.

This programme is part of a week of programmes looking at the history of ideas around Freedom.

Philosopher and wine enthusiast Barry Smith samples David Hume's theory of good taste. The 18th century Scottish philosopher argued that the appreciation of beauty was not easily arrived at - it required dedication, knowledge, expertise. In that sense he is the godfather of the critic and the patron saint of the connoisseur. As he delves into our sense of 'good taste' Barry recounts a wine laden tale from Don Quixote, talks to Neuroscientist Semir Zeki and to Art Historian Liz Prettejohn.

This programme is part of a week of programmes looking at the history of ideas around Freedom.

Producer: Jolyon Jenkins.

A new history of ideas presented by Melvyn Bragg but told in many voices.

Melvyn is joined by four guests with different backgrounds to discuss a really big question. This week he's asking 'Why are things beautiful?'

Helping him answer it are Mathematician Vicky Neale, historian of science Simon Schaffer and philosophers Barry Smith and Angie Hobbs.

For the rest of the week Vicky, Simon, Barry and Angie will take us further into the history of ideas about beauty with programmes of their own.

Between them they will examine the mathematics of beauty, whether beauty has moral force, whether beauty can be explained in evolutionary terms and how David Hume developed a theory of good taste.

Paul Broks tackles an age-old philosophical argument over whether humans have free will or whether all events are pre-determined. As a neuroscientist he is interested in the latest info on how our brains work. He also goes back to the 18th century French thinker Henry Poincare who argued that the universe was entirely mechanistic and that therefore all events in it are pre-ordained. Paul talks to researchers in the field including Professor Patrick Haggard of University College London to establish whether there is any place for human free will in a determined universe.

This programme is part of a week of programmes looking at the history of ideas around Freedom.

Producer: Jolyon Jenkins.

Theologian Giles Fraser thinks freedom is overrated. It has become a kind of tyranny or obsession. He is interested in the tradition of religious thinking that understands true liberation sometimes comes from accepting boundaries on life. His key thinker is the medieval philosopher and Franciscan monk William of Ockham whom he blames for this turn of events. Giles talks to Brother Sam, a contemporary Franciscan Monk, about the way his life of constraint has led him to feel free. Giles also talks to Phillip Blond, theologian and political adviser.

This programme is part of a week of programmes looking at the history of ideas around Freedom.

Harry Potter is a criminal barrister and watches people being let off and locked up for a living. He is interested in the ways the state can curtail our liberty. His key thinker is John Stuart Mill, the 19th century British philosopher who argued that the state should take a minimal role in the lives of its citizens.

Harry talks to Mark Dempster, ex-drug addict, dealer and now counsellor about the limits of individual liberty and to Prof. Philip Schofield of University College London about JS Mill and his ideas.

This programme is part of a week of programmes looking at the history of ideas around Freedom.

Angie Hobbs wants to tell you about two kinds of freedom - Negative and Positive. This influential philosophical distinction was made in the 20th century by Isaiah Berlin but it's rooted in the ideas of the hugely influential Greek Philosopher Plato.

Negative freedom involves getting things out of your way - be it the state, the police or your parents. Positive freedom is the ability to take command of your own self and make decisions that are in your own interest.

Berlin used the metaphor of doors: Negative freedom concerns the number of doors open to you. Positive Freedom is about how you choose between them.

Angie talks to conservative MP and ex-banker Jessie Norman and to environmental activist and ex-Jain monk Satish Kumar to see how these two ideas of freedom can co-exist.

This programme is part of a week of programmes looking at the history of ideas around Freedom.

A new history of ideas presented by Melvyn Bragg but told in many voices.

Melvyn is joined by four guests with different backgrounds to discuss a really big question. This week he's asking what does it mean to be Free?

Helping him answer it are philosopher Angie Hobbs, criminal barrister Harry Potter, neuropsychologist Paul Broks and theologian Giles Fraser.

For the rest of the week Angie, Giles, Harry and Paul take us further into the history of ideas with programmes of their own.

Between them they'll talk about Isaiah Berlin's distinction between positive and negative freedom, JS Mill's thoughts on individual liberty and the state; what neuroscience has to say about the age-old philosophical debate about free will and whether freedom is overrated as a political, moral and psychological concept.