When Monsters Came for Mathematics

My past is in mathematics that has a reputation because it is a solid, solid subject. After something is proved, it usually remains towards forever. But when I was investigating my book, I realized that even in mathematics, certainty could be a dangerous thing. In the 19th century, several important mathematical theorem began to be solved. For two thousand years, European mathematicians were inspired by the natural world. As a result, they concluded that some things were intuitively open: the geometric shapes followed the rules such as “larger than the whole part ve and followed the proper movement of an object whose change rates decreased. However, while dealing with eternity or abstract dimensions, these assumptions are no longer made. In the 1870s, the mathematicians had discovered strange theoretical counterclockwise examples, such as a piece of the same size as the whole and a movement known as “anywhere.

While writing my book, I wonder whether it is so intense to real life geometry inspired by the natural world when I descend to the deepest, while developing the mathematical real concepts of other cultures. China adopted concepts such as negative numbers that were much earlier than Europe – an easy -to -visual abstract concept, because their first text focused on problems that contain dey and debt. It turned out that his confidence in geometric intuition was an effective Trojan horse for European mathematicians, and he missed the defective assumptions to his work. In the 19th century, some settled researchers have emerged against the emerging examples.monsters”And an anger against common sense”; they were discomfort to escape. However Over time, these monsters became inevitable and even beneficial. Modern research is now based on applicable ideas: astrophysics require non -standard geometric rules, while probability theory has been built on infinitely unpredictable changes.

In the last decade, about AI algorithms – and in some cases I have spent a lot of time to build. Something that often disturbs me is that it seems that the AI ​​can make such basic mistakes from time to time. Recognize the image. FamousAdding a light digital waterfield may cause a AI classification to mix a panda image for a Gibbon.

I interviewed while writing my book Tony WangAn AI researcher who is interested in two special hypotheses to explain these errors. First, algorithms may be indirectly imitating fast, instinctive mental processing that can lead people to a bad judgment. This suggests that an algorithm, which reflects its decisions a little more, can avoid such errors. The second possibility was that AI was not yet good enough, and a really “superhuman yer version exceeds these mistakes.

Modern research is now based on sustainable ideas.

To test these hypotheses, Wang and his colleagues have focused on the complex Go game managed by AI in the last decade. They started with a “rival” algorithm training looking for defects in the best -playing AI software. In the end, they found two ridiculous strategies that could defeat the software – strategies that even an amateur person will not be deceived. Nevertheless, the “superhuman” player was more sure of the victory until he lost.

This showed that no hypothesis was right. Even the reflective artificial intelligence, who could play a complicated game as GO, was not safe, and seemingly “superhuman” software still fell for ridiculous tricks. No matter how smart a AI is, unexpected weaknesses can be inevitable.

When I start writing EvidenceThe effect of false information-especially in the worst months of Covid-19 pandema-was very in my mind. In January 2021, the rebels stood up the United States Capitol, while Covid denials harassed medical officers outside the hospitals. Why do so many people believe in things that are not right?

Today, the wrong information and the so -called flood of inaccuracies are very careful as online. In contrast, researchers and policy makers sought ways to reduce false beliefs. But the more I look at it, the more this simple story has been solved. A vocal minority consumes excessive amounts of false information and conspiracy theories online, but wider picture still shows most people. engage It is much more than suspected with reliable news sources.

“Doubt everything or believing that everything is equally suitable for two equally suitable solutions.”

This imbalance leads to a problem: If a study only measures the belief in the wrong content, an intervention that reduces faith All It will look like information successful. It can protect them from lies, but may also have the harmful side effects of weakening their trust in reality.

At the beginning of the 20th century, the mathematician Henri Poincaré said, ör Doubt everything or believing that everything is two equally suitable solutions, ”he said. In recent years, there was a lot of risk of believing in the dominant focus, but I realized that the threat of excessive doubt was not enough attention. We should look at the deeper reasons where people leave the real information and the valid evidence and experts ignore them.

As science becomes more complex, the relationship between reality and trust will become more difficult. Poincaré was once described as the “last universalist ;; Since then, no mathematician has never been perfect in all areas of the area as it existed. Simply put it, there are many mathematical issues that can be mastered. The same applies to other scientific fields. Even experts from climate analysis to AI should specialize. Now, more than ever, science and technology are based on creating and maintaining confidence in experts, institutions and machines.

Tasnuva Elahi’s head image; Picture Wickerwood / Shutterstock

• Man kucharski

  Published 13 June 2025

  Adam Kucarski is a professor at the London School of Hygiene and Tropical Medicine, where he works on the analysis of infectious disease epidemics, and the work that won the 2023 Adams Mathematics Award. It is regularly printed and appeared in the broadcast media and is the author of those who have been published recently.Evidence: Art and Science. Hertfordshire lives in England