There is an interesting tension at the Sarajevo Film Festival which, though this was my first time, I suspect exists as a matter of course. And this is a tension between the spirit of the people I meet here – ebullient, good-humoured and indefatigable (they really know how to party) – and the films themselves, which suggest a country and a region still reeling from the turmoil of its recent past. It’s a strange experience, then, poised between light and gloom.

Can Marcus du Sautoy do for maths what Brian Cox did for physics? Can he convince us of the beauty of numbers and help us fall in love with pi? It’s a tall order, but not only does Professor du Sautoy have an unstoppable passion for ratios, he’s also a natural communicator, which clearly helps if you’re the Simonyi Professor for the Public Understanding for Science, which he is. And so du Sautoy guided us through some basic mathematical principles which underpin the workings of the universe. He introduced us to The Code.

For 35 years, contemporary art in Iraq was a no-no unless it was grimly, dully figurative or a gaudy mural glorifying Saddam Hussein. But this year, six Iraqi artists were invited to the most prestigious annual contemporary art event in the world; the Venice Biennale. It may be of little significance that Alan Yentob’s parents came from Iraq, but last night’s Imagine was probably the best of the series so far. Its focus may have been these artists and their art, but its reach was somehow much greater.

Dan, a tall ginger streak of entitlement, had an issue with the hygiene. Channel 4 were about to lift him out of a five-star hotel in the Gambia and send him off to see how the other half lives. “They’re not going to be as clean as us,” he predicted nervously. Dan worried that he might have to survive sans moisturiser and hair gel. He hadn’t been warned about the lack of cutlery. And of loo roll. Nor that you approached each problem with the same manual solution.

I was once shown around Anglia TV’s studios by the bloke who used to say, "And now, from Norwich - the quiz of the week!” by way of introduction to the immortal Sale of the Century. A tremendous thrill, as you can imagine.

If I'm being honest, I never saw the charm of Alan Bennett's Talking Heads. Too many quiet disappointments, too much capital-A Acting. They lacked naturalism in presentation and content, whereas Double Lesson, from Channel 4's First Cut series of quirky documentaries and quasi-documentaries, had naturalism to spare last night.

Programmes about Italian organised crime made by the foreign media are always hampered by the finnicky nature of the beast itself: there is so much background detail that needs to be staked out at the outset that your head is whirling from information overload. Like its mainstream political parties, high-street banks and national daily newspapers, Italy has three, four or five times as many of each as any other European country of similar size.

Chess grand masters have a reputation for possessing the kind of brilliance that’s inclined to tip into madness. Victor Korchnoi claimed he'd played against a dead man, while Wilhelm Steinitz insisted he'd played chess against God by wireless. As for Bobby Fischer, his momentous duel against Boris Spassky for the World Chess Championship in Iceland in 1972 earned him the accolade of being perhaps the most brilliant chess player of all time, but by the time of his death in 2008 he had become an embittered, ranting maniac.

This is the one DVD of all the recent issues of dance on film that will show you simply and honestly the rigour and the beguilement of how people are drawn to dance, and what dance draws out of them. A straight documentary about the dance-theatre of Pina Bausch, it's really about teenagers and their extraordinary ability to soak up opportunities, innocently perform complex things and wipe them clean of old associations - and make all us feel more human and restored.

You might say that the grand hotels brought this on themselves. Time Shift: Hotel DeLuxe on BBC Four last night saw beneath the shine of their marble atria and heard the uncomfortable murmurs under the joyful gossip of their chic bars. What started out as an apparent paean to the luxury hotel - the Savoy, the Ritz, the Dorchester - with an emphasis on the glamour, energy, buzz and innovation they created soon turned into a documentary with a social conscience.