In 2018, in late October, a distinctly odd painting appeared at the fine art auction house Christe's. At a distance, the painting looks like a 19th-century portrait of an austere gentleman dressed in black. Contained in a gilt frame, the portly gentleman appears middle-aged; his white-collar insinuates that he is a man of the church. The painting seems unassuming, something expected at an auction house that sells billions of dollars of painting each year. However, upon closer inspection, things get a bit odd.

What are the limits of human knowledge? Or is that something we cannot know? This is the question pondered by Professor of Public Understanding of Science at Oxford University, mathematician, broadcaster and author Marcus du Sautoy in his book, What We Cannot Know: Explorations at the Edge of Knowledge. I recently had the pleasure of speaking with Marcus about conscious artificial intelligence and other mind-blowing things that science can't answer. Can We Have Conscious Artificial Intelligence and Other Mind-blowing Things Science Can't Answer It's Amazing What We Know, But There's Still a Lot Unknown In his book, de Sautoy takes us to the edge of knowledge or more precisely to seven "edges" of human knowledge that contemplate what we do and can possibly know about things as diverse as nature, the ingredients that make up the universe, and human and AI consciousness.

I expect to suffer some degree of writer's block pretty much every day for the rest of my life. I'm a journalist and a novelist; it comes with the territory. But I have a feeling I'm going to suffer less from now on, thanks to my new best friend, GPT-2. Let me back up a bit: Six months ago, the research lab OpenAI created an AI system that generates text -- from fake news to poetry -- that in some cases actually sounds like it's written by a human being. The OpenAI team has been rolling it out in stages, each time giving us a more powerful version of the language model they dubbed GPT-2, and carefully watching to see how we use it.

Standing in a wood-paneled room at the University of Oxford, surrounded by her artwork, Ai-Da looks out at her creations. "I want people to know that our times are powerful times," she says slowly, pausing between sentences. Like many artists, she wants her work to promote discussion. And yet unlike other artists, Ai-Da tells us with a blank expression and glassy eyes that only blink occasionally, she does not have consciousness, thoughts and feelings. Ai-Da's creators bill her as the world's first robot artist, and she's the latest AI innovation to blur the boundary between machine and artist; a vision of the future suddenly becoming part of our present.

Artificial intelligence (AI) pioneer Alan Turing infamously asked many years ago, "Can machines think?" Today, Oxford mathematician Marcus du Sautoy poses an equally provocative question: Can machines create? In his new book, "The Creativity Code: Art and Innovation in the Age of AI," du Sautoy explores the structural nature of creativity in human endeavors, and looks at areas where AI can have the most influence. "Creativity is a code that evolution across millions of years has honed inside our brains," du Sautoy writes. "Is our creativity in fact more algorithmic and rule-based than we might want to acknowledge? Can we hope to crack the creativity code?"

The game of Go played between a DeepMind computer program and a human champion created an existential crisis of sorts for Marcus du Sautoy, a mathematician and professor at Oxford University. "I've always compared doing mathematics to playing the game of Go," he says, and Go is not supposed to be a game that a computer can easily play because it requires intuition and creativity. So when du Sautoy saw DeepMind's AlphaGo beat Lee Sedol, he thought that there had been a sea change in artificial intelligence that would impact other creative realms. He set out to investigate the role that AI can play in helping us understand creativity, and ended up writing The Creativity Code: Art and Innovation in the Age of AI (Harvard University Press). The Verge spoke to du Sautoy about different types of creativity, AI helping humans become more creative (instead of replacing them), and the creative fields where artificial intelligence struggles most.

Marcus du Sautoy is the kind of science writer who cares more about questions than answers. In his books he tackles "unsolved problems", "number mysteries" and "the great unknown", topics at the edge of human understanding. They are subtitled with words such as "odyssey", "exploration" and "journey". But Du Sautoy is a flaneur: his trips are not motivated by destinations. This is both the main strength and flaw of The Creativity Code, a wide-ranging and fact-packed tour d'horizon of current applications of artificial intelligence in mathematics and the arts.

Marcus is the Simonyi Professor for the Public Understanding of Science at Oxford University, quite a mouthful.

Do androids dream of electric beats? In 2012, Iamus released a CD of classical music performed by the London Symphony Orchestra. Music critic Tom Service was somewhat dismissive, calling Iamus's composition Hello World! "so unmemorable, and the way it's elaborated so workaday, that the piece leaves no distinctive impression." But it wasn't a bad debut really--when you consider that Iamus is not a composer but a computer algorithm, developed by researchers at the University of Málaga in Spain. Marcus du Sautoy, mathematician and Simonyi Professor for the Public Understanding of Science at Oxford, doesn't talk about Iamus in his new book The Creativity Code, but the question he poses about such efforts amounts to this: can we call Iamus a composer? When Iamus's compositions were played to musically informed listeners, they were unable to distinguish them from music in a similar (modernist) style composed by humans.

As Marcus du Sautoy greets me at the entrance to New College, Oxford, his appearance is a quiet riot of colour. His clothes rather suggest someone who ran into White Stuff or Fat Face and frantically grabbed anything he could find – in this case, a salmon zip-up top, multihued check trousers and shoes that are a headache-inducing shade of turquoise. When we settle down to talk in a nearby meeting room, he repeatedly glances at a notepad – whose pages, just to add to all the garishness, are a bold shade of yellow. They are full of what look like scrawled equations, mixed with odd-looking shapes: the raw material, he explains, of a project involving very complicated geometry. "There's an infinite symmetrical structure that I'm looking at," he says, "and I think the top bit of it will tell me everything that's going on inside it. It's almost like an infinite lake, and I should be able to know everything that's happening in it by looking at the first centimetre."