Mathematicians are afraid of AI’s depressing thinking

It was recently reported that artificial intelligence would have helped to solve A problem related to the Navier-Stokes group of equations, which has challenged human intelligence for over a hundred years.

Worry has escalated into opposition from mathematicians in the United States.

One reason is that students at the California Institute of Technology organize math Marathonsevent with the artificial intelligence giants in October.

Current and former Caltech mathematicians published an open letter against the event. It has more than 2,000 signatories.

One hundred groups use artificial intelligence to solve unsolvable puzzles in mathematics and for new theories. For $20,000, teams get an AI credit for 40 hours.

According to the organizers, the goal is to investigate how artificial intelligence can be used responsibly in mathematics. Still, about AI waste, OpenAI announced that it is withdrawing from the Mathathon. Competitor Anthropic is involved.

One one of the signatories of the open letter is a doctoral researcher Sampo Paukkonen from the University of Helsinki.

“There hasn’t been a similar polemic in mathematical circles for years, when you listen to colleagues’ discussions about the changing job description and follow discussions around the world,” says Paukkonen.

“Back in the spring, artificial intelligence models were hallucinating and making mistakes. Now the mistakes have decreased. In some areas of mathematics, artificial intelligence has surpassed the level of human reason,” says the professor. Mikko Salo from the University of Jyväskylä.

Another one petition against the careless use of artificial intelligence has been signed by nearly thirty Fields Medalist mathematicians. The medal, awarded every four years, is regarded as the Nobel of the field.

The letters contain strong reflections on the use of artificial intelligence models.

First of all, an event like Mathathon mainly benefits big artificial intelligence companies, who can take credit for the thinking of sharp young mathematicians.

According to critics, the most important thing for artificial intelligence waste is not mathematics, but which of the models produces the best-selling solutions.

Mathematicians fear that the solutions found by artificial intelligence will bore young researchers.

“Quick answers do not increase understanding. The goal is to understand in depth what the methods are suitable for at any given time and to communicate with others how the methods could be used for different things,” says Salo.

According to mathematicians, pure mathematics matures thinking. The solution is not always the only important goal, but what is learned on the way to the solution is also important.

“Artificial intelligence may move from one mountain peak to another, but there can be something important in the valleys as well,” says Paukkonen.

“The publications are not yet easy for people to read. They are uniform text that does not always highlight which ideas are essential,” says Salo.

According to Paukkonen, human peer evaluation in mathematics is at the highest possible level among disciplines. It is also humbling:

“Pure mathematics is a harsh school of humility,” Paukkonen translates.

Some the human and creative achievements of mathematics have only proven vital over time.

For example, the Fourier transform works. It was presented by a French Joseph Fourier (1768–1830) more than two hundred years ago when he studied the propagation of heat. The transformation has since been developed by other mathematicians.

Now the Fourier transform is in a way used by everyone. It is used, for example, in sound and image processing. It breaks down a wave or signal into simple parts.

“When I was working at Nokia, I used the Fourier transform to process audio signals from mobile phones,” says Salo. The transformation has other uses in medical imaging, industry and technology and science in general.

During the Cold War, the Fourier transform was applied to the detection of underground nuclear weapons tests.

“It is still used today in maritime surveillance, where it helps detect and identify submarines based on their sounds,” says Paukkonen.

He is researching the chaos and quantum chaos theory connected to the Fourier transform.

The inversion mathematics studied by Salo also uses the Fourier transform. This math of inverse problems is helping to find groundwater reserves and produce better X-ray images of human teeth and the human body.

Could artificial intelligence models come up with a formula equivalent to the Fourier transform?

“They are not omnipotent, and they still do not work so well if there is no ready-made method for the problem in the literature. Human minds have produced ideas that artificial intelligence is not yet capable of,” says Salo.

Artificial intelligence can also be an opportunity and not a threat, as mathematicians have also stated. American Fields laureate Terence Tao characterizes artificial intelligence with reservations sometimes also practical as a tool.

“Artificial intelligence is a hugely powerful new tool in mathematics as well, but if used correctly, so that it would be good for humanity. We don’t need quick profits or advertising platforms,” ​​says Salo.

“It’s a tireless assistant that does a superhuman amount of raw reasoning, depending on computing resources,” says Salo.

On the other hand, artificial intelligence has already developed into a part of work practices, Paukkonen reflects.

“It works primarily as a secretary. You can ask it, for example, to find and compile source files, so that time does not pass for days. The hot thing in the world now is artificial intelligence agents.”

Artificial intelligence finds and combines information from a wider area than a human mathematician.

Although artificial intelligence can make mathematics more efficient, according to Paukkonen, efficiency and mathematical creativity are not the same thing.