The year 2023 marks the 102th anniversary of Noether’s ring theory, a branch of theoretical mathematics that is still fascinating and challenging numerous mathematicians today.

Neother was born in 1882 in Germany, whose father was a math professor, but it must have seemed unlikely to a young Neother that she would follow in his footsteps because women were banned from academia and few took classes at universities. After Neother graduated from a high school for girls, Erlangen University started to let women enroll. She signed up and earned her doctorate in mathematics, which should have been the end of her mathematical journey. Teaching at a university for women was still out of the question. But Neother stuck with mathematics anyway, staying in Erlangen and unofficially guiding doctoral students without pay.

In 1915, she applied for a position at the University of Gottingen. Bill Nicholl, the dean at the university, also a mathematician, was in favor of hiring Neother, although his argument was far from feminist (女权主义). “The female brain is unsuitable for mathematical production,” he wrote, “but Neother stood out as one of the rare exceptions.”

Unfortunately for Neother,the Ministry of Education would not give the university permission to have a woman as their teacher. Neother stayed in Gottingen and taught courses listed under the name of a male faculty teacher. During those years, she kept doing research and made important contributions to theoretical physics and Einstein’s theory of relativity. The university finally granted her lecturer status. Two years later, Neother published revolutionary discoveries in ring theory, which is the study of mathematical objects called rings. Neotherian rings show up all the time in modern mathematics. Mathematicians still use Neother’s map today,not just in ring theory,but in other area such as number theory and algebraic geometry.

When you ask people to judge others by their speech, a trend emerges: Listeners dislike disfluency. Slow talkers producing loads of ums and pauses(停顿)are generally perceived as less charming. But science tells us there may be even more to disfluency.

Disfluencies do not occur in arbitrary positions in sentences. Ums typically occur right before more difficult or low-frequency words. Imagine you’re having dinner with a friend at a restaurant,and there’re three items on the table: a knife, a glass, and a wine decanter(醒酒器). Your friend turns to you and says, “Could you hand me the...um...” What would you assume they want? Since it’s unlikely that they will hesitate before such common words as knife, and glass, chances are you’ll pick up the decanter and ask, “You mean this?”

This is exactly what we demonstrated through controlled eye-tracking studies in our lab. Apparently, listeners hear the um and predict that an uncommon word is most likely to follow.Such predictions, though, reflect more than just simple association between disfluencies and difficult words; listeners are actively considering from the speaker’s point of view. For example, when hearing a non-native speaker say the same sentence but with a thick foreign accent, listeners don’t show a preference for looking at low-frequency objects. This is probably because listeners assume non-native speakers may have as much trouble coming up with the English word for a common object, like a knife, as for unusual ones and can’t guess their intention.

In another experiment, listeners were presented with an atypical speaker who produced disfluencies before simple words and never before difficult words. Initially, participants displayed the natural predictive strategy: looking at uncommon objects. However, as more time went by, and they gained experience with this atypical distribution of disfluencies, listeners started to demonstrate the contrary predictive behavior: They tended to look at simple objects when hearing the speaker say um.

These findings represent further evidence that the human brain is a prediction machine: We continuously try to predict what will happen next, even though not all disfluencies are created equal.

We are living in a world where technology is never a neutral tool for achieving human ends. Technological innovations reshape people as they use these innovations to control their environment. Artificial intelligence, for example, is altering humanity.

While the term AI arouses anxieties about killer robots or catastrophic levels of unemployment, there are other deeper implications. As AI increasingly shapes the human experience, how does this change what it means to be human? Central to the problem is a person’s capacity to make choices, particularly judgments that have moral implications. Aristotle argued that the capacity for making practical judgments depends on regularly making them—on habit and practice. We see the emergence of machines as substitute judges in a variety of everyday contexts as a potential threat to people learning how to effectively exercise judgment themselves.

In the workplace, managers routinely make decisions about who to hire or fire and which loan to approve. These are areas where algorithm (算法) is replacing human judgment, and so people who might have had the chance to develop practical judgment in these areas no longer will.

Recommendation engines, which are increasingly popular in people’s consumption of culture, may serve to restrict choice and minimize luck. By presenting consumers with algorithmically selected choices of what to watch, read, stream and visit next, companies are replacing human taste with machine taste. In one sense, this is helpful. After all, machines can survey a wider range of choices than any individual is likely to have the time or energy to do on their own.

Algorithms could soon—if they don’t already-have a better idea about which show you’d like to watch next and which job candidate you should hire than you do. One day,humans may even find a way for machines to make these decisions without some of the prejudices that humans typically display.

But unpredictability is part of how people understand themselves and part of what people like about themselves. From this aspect, humanity is in the process of losing something significant. As they become more and more predictable, the creatures living in the AI world will become less and less like us.