Dana Mackenzie, a mathematics and science writer and chess master, is the author of “Master Sun’s Problem.”
For the past few years, mathematicians have been in uneasy denial about artificial intelligence. At first, models started conquering high-school-level, competition-style problems, which purists dismissed as not real math research. Then they started proving genuinely new theorems that purists waved away as particularly well-suited to computation.
Finally, this month, OpenAI claimed its unreleased model solved one of the seven Millennium Prize problems, which are considered so important or difficult that their solutions have million-dollar bounties.
That has made denial difficult. Indeed, some academics have moved to the other extreme, catastrophizing about the “end of mathematics” — a future where machines lead the way in solving the most difficult problems and humans are left to tidy up after them. If history is any guide, this will turn out to be a slight exaggeration.
This AI steamroller has been seen before. It arrived in 1997 when world chess champion Garry Kasparov unexpectedly lost a match to Deep Blue, a chess computer built by IBM.
His loss was (in my opinion) slightly premature and partly self-inflicted. His massive self-confidence was shattered in the second game when the computer beat him with a move that looked so sophisticated that Kasparov suspected it must have received human aid. In the final, decisive game, Kasparov played like a shell of his normal self. He was beaten psychologically before he even arrived at the chessboard.
Nevertheless, that moment put an end to the denial among chess fans that computers would never beat humans. By the early 2000s, there was simply no question about where things were headed. The best computers were consistently beating the best humans, apparently fulfilling former world champion Bobby Fischer’s prediction that “computers will make us all obsolete.”
But guess what? Chess didn’t die. Humans still enjoy playing an ancient and challenging game, even if some other entity plays it better. It didn’t really matter whether that entity was Kasparov or Deep Blue.
Far from dying, chess prospered. Interestingly, Deep Blue never played again after beating Kasparov, since IBM saw no intrinsic value in chess. But a flood of smaller companies used similar technology to bring chess to the masses with programs like Fritz, Crafty, Rybka and Stockfish.
This revolution had a democratizing effect, giving chess players the equivalent of a grandmaster (or just an infinitely patient tutor) in their living room. Old conventional wisdoms were shattered. The internet brought chess to millions of people who were entranced by newer, faster versions of the game and by streaming videos that turned grandmasters into media stars.
The computer was an essential part of this revolution. Instant computer analysis made it possible for even amateurs to follow the action — they could see grandmasters’ mistakes and brilliance in real time, and have the illusion of understanding.
Another sea change happened in the 2010s, when a Google subsidiary, DeepMind, released AlphaZero, the first chess-playing software based on machine learning, which taught itself the game without human input.
Chess players were stunned when AlphaZero overwhelmed Stockfish, the best conventional chess program. Again, doomsday seemed to be upon us. Again, it wasn’t.
AlphaZero had the most startlingly humanlike style any computer had displayed, only better. The best humans play combinations that look five or six moves ahead, but AlphaZero was playing moves whose point only became clear 20 or more moves later. It was a shot in the arm for creative chess.
Like IBM, Google quickly retired AlphaZero, seeing it as a benchmark for its technology rather than a practical achievement. It was again smaller companies that stuck around to change the chess world, assimilating AlphaZero’s neural net technology. That, too, only made chess more popular.
I suspect mathematics will experience a similar evolution. Top-line AI companies will probably lose interest and start pursuing their next white whale. Then we will move to the democratization phase, when second-wave AI companies, devoted only to math and science, start offering almost-as-good services for less money. An example of this might be Axiom Math, a small AI company recently founded by a mathematician, which attempts to bridge the divide between superhuman reasoning and human understanding.
I realize the chess analogy may fail. One particular concern of the present AI boom is the fabulous expense of humongous data centers. Deep Blue and AlphaZero were surely expensive, but not that expensive.
For my optimistic view of AI to come true, the second wave of AI has to be dramatically more affordable, and I believe that it will be. Ego-driven businesses and governments will always seek expensive frontier models to keep ahead of their competitors, but scientists will not need the most expensive tech to solve science problems.
Of course, mathematics must also confront the pitfalls of AI that chess faced. The technology makes cheating easy, especially in online games. Mathematicians will similarly be able to misattribute AI’s work for their own, or more insidiously, the field might see a gradual erosion of scientific mettle as researchers resort to AI too often and too readily.
The math community, and other sciences, will need to figure out how to detect AI use, how to use it responsibly and how to give proper credit when a machine is involved. None of these problems are dealbreakers, but they will require a steady hand to navigate between the Scylla of denial and the Charybdis of catastrophizing.
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