WHEN 18-time international Go champion Lee Sedol , mathematicians everywhere will have shared a moment of quiet introspection. Three years earlier, Lee had been beaten 4-1 by an artificial intelligence, DeepMind鈥檚 AlphaGo. Having observed the machine鈥檚 rapid pace of progress since then, Lee concluded that AI is an 鈥渆ntity that cannot be defeated鈥� 鈥� at least by human Go players 鈥� a verdict that prompted his retirement.
AI鈥檚 triumph in a game as complex as Go might signal that mathematics, a subject that it has had in its cross hairs from its beginnings, is also ripe for automation. As , it is prudent to ask if mathematicians, too, should be concerned by the rise of machine intelligence.
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Mathematicians must reckon with the fact that computers are smarter than the calculators of previous generations. But they should enjoy a more optimistic outlook than Lee. For one thing, mathematics is far more vast in scope than Go. It is precisely because it demands more creative intellect, that mathematics leaves room for us .
Human-machine collaboration in mathematics isn鈥檛 new. Its watershed moment came in 1976, when Kenneth Appel and Wolfgang Haken delivered their proof of the four colour theorem with the help of a computer. The theorem states that any map can be filled in with four colours in such a way that no neighbouring regions share the same colour: a simple-sounding claim, the proof of which eluded mathematicians for over a century. Appel and Haken reduced infinitely many cases down to about 2000 highly complex configurations, which a computer could crunch through to solve the problem. The division of cognitive labour was clear: the ingenious stroke came from the humans, with the menial task of computation left to the machine.
This dynamic is still at play today. The pattern-recognition skills displayed by DeepMind鈥檚 machine-learning programs have helped researchers to usher in breakthroughs in abstract areas of mathematics, such as knot theory and algebra. Computers are no longer restricted to just churning out routine calculations, now they can mine enormous data sets to detect incredibly subtle patterns that evade even professional mathematicians.
But this is no cause for humans to raise the white flag. On the contrary, mathematicians are seizing upon these tools to refine their intuitions. The more creative mathematical acts of asking meaningful questions, interpreting computer-generated patterns and constructing well- reasoned arguments remain the preserve of humans. AI may be the spaceship that will ferry us to new mathematical vistas, but we must captain it.
Mathematicians have always welcomed the latest tools and technologies as thinking aids to which we can outsource the aspects of cognition that come least naturally to us. The abacus alleviated the manual burden of tracking large quantities; hits a perceptual limit at just five objects. The slide rule, a device inspired by John Napier鈥檚 logarithm tables, relieved the notorious burden of multi-step calculation 鈥� reducing the task of multiplication down to one of addition, for example.
Lee鈥檚 adversarial framing of AI doesn鈥檛 apply to mathematics, which is a tale of ever-evolving collaboration between humans and machines. Today鈥檚 computers are smarter than their ancestors; our thinking partners rather than mere aids. Tomorrow鈥檚 will be smarter still. But these technologies were created to serve as cognitive allies to humans. It is time we embraced them as such.
Junaid Mubeen is a mathematician turned educator, and author of Mathematical Intelligence
