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in 10,000 move now against the algorithm and you won’t get away with it. That’s the power of this sort of algorithm. It learns from its mistakes.

      That’s not to say it can’t make new mistakes. As game 5 proceeded, there was a moment quite early on when AlphaGo seemed to completely miss a standard set of moves in response to a particular configuration that was building. As Hassabis tweeted from backstage: ‘#AlphaGo made a bad mistake early in the game (it didn’t know a known tesuji) but now it is trying hard to claw it back … nail-biting.’

      Sedol was in the lead at this stage. It was game on. Gradually AlphaGo did claw back. But right up to the end the DeepMind team was not exactly sure whether it was winning. Finally, on move 281 – after five hours of play – Sedol resigned. This time there were cheers backstage. Hassabis punched the air. Hugs and high fives were shared across the team. The win that Sedol had pulled off in game 4 had suddenly re-engaged their competitive spirit. It was important for them not to lose this last game.

      Looking back at the match, many recognise what an extraordinary moment this was. Some immediately commented on its being an inflexion point for AI. Sure, all this machine could do was play a board game, and yet, for those looking on, its capability to learn and adapt was something quite new. Hassabis’s tweet after winning the first game summed up the achievement: ‘#AlphaGo WINS!!!! We landed it on the moon.’ It was a good comparison. Landing on the moon did not yield extraordinary new insights about the universe, but the technology that we developed to achieve such a feat has. Following the last game, AlphaGo was awarded an honorary professional 9 dan rank by the South Korean Go Association, the highest accolade for a Go player.

      From hilltop to mountain peak

      Move 37 of game 2 was a truly creative act. It was novel, certainly, it caused surprise, and as the game evolved it proved its value. This was exploratory creativity, pushing the limits of the game to the extreme.

      One of the important points about the game of Go is that there is an objective way to test whether a novel move has value. Anyone can come up with a new move that appears creative. The art and challenge are in making a novel move that has some sort of value. How should we assess value? It can be very subjective and time-dependent. Something that is panned critically at the time of its release can be recognised generations later as a transformative creative act. Nineteenth-century audiences didn’t know what to make of Beethoven’s Symphony no. 5, and yet it is central repertoire now. During his lifetime Van Gogh could barely sell his paintings, trading them for food or painting materials, but now they go for millions. In Go there is a more tangible and immediate test of value: does it help you win the game? Move 37 won AlphaGo game 2. There was an objective measure that we could use to value the novelty of this move.

      AlphaGo had taught the world a new way to play an ancient game. Analysis since the match has resulted in new tactics. The fifth line is now played early on, as we have come to understand that it can have big implications for the endgame. AlphaGo has gone on to discover still more innovative strategies. DeepMind revealed at the beginning of 2017 that its latest iteration had played online anonymously against a range of top-ranking professionals under two pseudonyms: Master and Magister. Human players were unaware that they were playing a machine. Over a few weeks it had played a total of sixty complete games. It won all sixty games.

      But it was the analysis of the games that was truly insightful. Those games are now regarded as a treasure trove of new ideas. In several games AlphaGo played moves that beginners would have their wrists slapped for by their Go master. Traditionally you do not play a stone in the intersection of the third column and third row. And yet AlphaGo showed how to use such a move to your advantage.

Hassabis describes how the game of Go had got stuck on what mathematicians like to call a local maximum. If you look at the landscape I’ve drawn here then you might be at the top of peak A. From this height there is nowhere higher to go. This is called a local maximum. If there were fog all around you, you’d think you were at the highest point in the land. But across the valley is a higher peak. To know this, you need the fog to clear. You need to descend from your peak, cross the valley and climb the higher peak.

      The trouble with modern Go is that conventions had built up about ways to play that had ensured players hit peak A. But by breaking those conventions AlphaGo had cleared the fog and revealed an even higher peak B. It’s even possible to measure the difference. In Go, a player using the conventions of peak A will in general lose by two stones to the player using the new strategies discovered by AlphaGo.

      This rewriting of the conventions of how to play Go has happened at a number of previous points in history. The most recent was the innovative game play introduced by the legendary Go Seigen in the 1930s. His experimentation with ways of playing the opening moves revolutionised the way the game is played. But Go players now recognise that AlphaGo might well have launched an even greater revolution.

      The Chinese Go champion Ke Jie recognises that we are in a new era: ‘Humanity has played Go for thousands of years, and yet, as AI has shown us, we have not yet even scratched the surface. The union of human and computer players will usher in a new era.’

      Ke Jie’s compatriot Gu Li, winner of the most Go world titles, added: ‘Together, humans and AI will soon uncover the deeper mysteries of Go.’ Hassabis compares the algorithm to the Hubble telescope. This illustrates the way many view this new AI. It is a tool for exploring deeper, further, wider than ever before. It is not meant to replace human creativity but to augment it.

      And yet there is something that I find quite depressing about this moment. It feels almost pointless to want to aspire to be the world champion at Go when you know there is a machine that you will never be able to beat. Professional Go players have tried to put a brave face on it, talking about the extra creativity that it has unleashed in their own play, but there is something quite soul-destroying about knowing that we are now second best to the machine. Sure, the machine was programmed by humans, but that doesn’t really seem to make it feel better.

      AlphaGo has since retired from competitive play. The Go team at DeepMind has been disbanded. Hassabis proved his Cambridge lecturer wrong. DeepMind has now set its sights on other goals: health care, climate change, energy efficiency, speech recognition and generation, computer vision. It’s all getting very serious.

      Given that Go was always my shield against computers doing mathematics, was my own subject next in DeepMind’s cross hairs? To truly judge the potential of this new AI we are going to need to look more closely at how it works and dig around inside. The crazy thing is that the tools DeepMind is using to create the programs that might put me out of a job are precisely the ones that mathematicians have created over the centuries. Is this mathematical Frankenstein’s monster about to turn on its creator?

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       ALGORITHMS, THE SECRET TO MODERN LIFE

       The Analytical Engine weaves algebraic patterns, just as the Jacquard loom weaves flowers and leaves.

      Ada Lovelace

      Our lives are completely run by algorithms. Every time we search for something on the internet, plan a journey with our GPS, choose a movie recommended by Netflix or pick a date online, we are being guided by an algorithm. Algorithms are steering us through the digital age, yet few people realise that they predate the computer by thousands of years and go to the heart of what mathematics is all about.

      The birth of mathematics in Ancient Greece coincides with the development of one of the very first algorithms. In Euclid’s Elements, alongside the proof that there are infinitely

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