"Olympiad gold medals and Fields medals are two different things", it seems to be the correct nonsense.
Ivan Fesenko's exact words are: "Whether or not you can do a good job in mathematics has nothing to do with your performance in the Olympiad. ”
When he was in secondary school, he competed in almost every level of the Mathematics Olympiad and won the All-Russian High School Mathematics Olympiad. Sometimes it was a sense of achievement, more often it was interest, step by step, taking him from the Olympiad to the study of mathematics - a beautiful and very different world.
Ivan Fesenko's mathematical research, including explicit reciprocal formulas, explicit class field theory and higher class field theory, advanced ADELIC structures, advanced Zeta integrals, and extensions of IUT theory and applications, has contributed to the pioneering development of many fields of modern number theory. From 2015 to 2021, he devoted a lot of time and energy to the study of Far Abelian geometry and the IUT theory of Japanese mathematician Shinichi Mochizuki, and co-organized 4 IUT international conferences with him. In July 2022, he collaborated with Japanese mathematician Shinichi Mochizuki and three other young mathematicians to publish the first proof of the effective ABC inequality and the new proof of Fermat's theorem.
He has served as an assistant professor and associate professor at St. Petersburg State University and a professor in the Department of Mathematics at the University of Nottingham. Recently, across 8 time zones, Ivan Fesenko joined Westlake University full-time as a distinguished professor in the School of Science, Institute of Theoretical Science, and established the Advanced Number Theory Research Group.
He has been teaching for nearly 40 years, and has about 60 doctoral students and postdoctoral students from his research group, including a Fields Medal winner. After moving to China, the mathematics professor was particularly passionate about nurturing people. Chinese children have long been world-renowned for their performance in the International Mathematics Olympiad, but in mathematics research, especially in establishing a school that can lead academic development, more efforts are needed to achieve more good results in some internationally recognized awards for mathematical research.
Why study math?Become a person who understands AI.
AI may be able to assist in many things, including mathematical research;But mathematicians are the ones who really have the potential to read AI. ”
Many people talk about the necessity of learning mathematics, often going back thousands of years to this ancient discipline, and Ivan chooses to never talk about it.
If we simply divide the objects of mathematical research into two categories: figures and numbers, the former is the study of the geometry of continuous objects, which originated from the measurement of the needs of agricultural land;The latter is the study of number theory of discrete objects and is essential for business development. Ivan's research is to bridge the gap between these two different frameworks of thinking, using new algebraic, geometric, and analytical tools to carry out advanced research based on new developments in advanced number theory. In the field of algebra, his research interests cover algebraic k theory, infinite group theory;In the field of analysis, he includes advanced Haar's measures, integral and harmonic analysis, and the interaction of model theory and quantum theory.
He used to think that it was a wonderful thing to get the left and right brains to think together through this "bridge". Now, something even more amazing has happened.
For the first time in the history of human civilization, mathematicians have had the opportunity to complete research in collaboration with another kind of intelligence – artificial intelligence, rather than with real human collaborators. It's a wonderful combination!Ivan is looking forward to this, "The function of the human brain and the function of the machine brain will combine to have unlimited potential, and I believe that we will see a lot of results from this collaboration in the next five years." ”
In the past year, ChatGPT has been the most "out of the circle" technological breakthrough in the field of artificial intelligence. Excited, shocked, vigilant, positive or negative, the emotions that have swept the internet are because "no one knows what's going on, no one knows why it's so powerful, no one knows what we're celebrating, and what we need to be wary of......The person who can help with the explanation is most likely a mathematician, Ivan said.
He is extremely interested in such interdisciplinary problems, such as ChatGPT as the representative of the AI large model, and the other is quantum physics.
A few years ago, he was approached by a unicorn company in Boston, USA, where a group of PhD students from Harvard and MIT attempted to build the world's largest quantum computer. It was this group of young people who told him that the cutting-edge research in number theory he shared could come in handy in the development of quantum computers. Not long ago, he attended an academic conference on quantum physics, a conference that at first glance had little to do with number theory, and he heard a lot of new connections between modern mathematics and quantum theory.
It struck me to wonder how much of a very abstract piece of knowledge could be so helpful to another field far away. Ivan said. However, as soon as the words fell, he found that this kind of unbelievability had already been traced.
In fact, the modern life we take for granted, or the digital economy, is thanks to the widespread application of mathematics. Even number theory, which seems far from any practical application, is already the part of mathematics with the most potential for application. "Smartphones, electronic payments, and online communication all rely on the work of number theory over the past 40 years, and when these achievements were first discovered, no one could have predicted that they would become so important in future applications. Ivan said.
Whether it is cutting-edge science or a new round of industrial revolution, isn't it a good reason to learn mathematics to have the "right to speak" throughout all this?
Who is suitable for math?Be the one who pushes the envelope.
Or you can ask the other way around: who is not suitable for math?
Ivan Fesenko observes a phenomenon of interest in China: "Some of the children who won the gold medal in the Olympiad did not have much ambition to do mathematical research, and they saw the Olympiad as a kind of 'sport' to some extentHowever, some children who are interested in mathematics majors feel that they are not as smart as their peers who have outstanding competition results, and they have little confidence in learning mathematics. ”
He's been through both. Whenever he heard such stories, he would tell them that Olympiad skills and mathematical research are two completely different things.
Solving an advanced math problem can take hours, or even daysBut real mathematical research requires a completely different kind of ability. "You need to solve problems, study for years, try to take what you've learned to a whole new level, or burst out with a whole new idea, which is completely different from Olympiad training." ”
Of course, there is also a common denominator: you must be brave and persistent.
He identified two examples from his former students:
Ivan Fesenko (left) with Caucher Birkar (right).
A gifted teenager named Caucher Birkar, born into a peasant family in the Kurdish region of western Iran, a childhood with farming as the theme did not seem like a typical environment in which an interest in mathematics could develop. Unlike Ivan Fesenko, his father was a university professor of astronomy, and since he was a child, he was "fed" a lot of physics and astronomy popular science picture books, and the exquisite formulas in the books turned on his "mathematics" switch.
However, Caucher Birkar showed an extraordinary talent for mathematics and excelled in international mathematics competitions. In 2000, he applied for political asylum in the UK to do a PhD at Ivan Fesenko's group at the University of Nottingham. "When I first came here, I didn't speak much English, but he was obviously a very smart guy, and I gave him a math problem, the kind of problem that if you solve it, you can get a Ph.D., which normally takes three or four years, and it only took him three months to solve it. ”
Later, Caircher Birkar became a professor of mathematics at the University of Cambridge, where he won the Fields Medal, the highest award in mathematics, in 2018, and is now a professor at Tsinghua University, also in China.
If you are also a young person with a great talent for mathematics, no external environment – family, language, or even the international situation – should be a stumbling block to your studies and research.
Another student's project was far less smooth than Caucher Birkar's at the beginning. "When I was having a hard time researching, this classmate approached me and said he wanted to give up. "The first time he came to me, I had a long talk with him and convinced him to try again, and maybe it would be done."A few months later, he came again, still not work, still wanting to give up. What to do?I can only continue to talk and persuade him, reminding him how much he liked mathematics and how beautiful mathematics ......”
Ivan knew that this brave young man in front of him would never really give up because of a little difficulty. Outside of mathematics, this student enjoys horseback riding and gliding, and mathematics is just another portrayal of his courage to push the limits.
Until one day, the cycle of conversation finally stopped.
He succeeded, with a beautiful result, and it seems that I am very good at encouraging students who are in adversity. Ivan laughs and says that this situation is very common in the process of mathematical research, and you not only have to learn how to do research, but you also need to know how to continue to get up and grope forward after dozens of falls.
How to learn math?Be the one who jumps out of the box.
First, get to know a mathematician and listen to his guidance or advice.
Ivan Fesenko has met some of these people in his research career. At the age of 17, when he had just entered college, he met the mathematician Alexander Merkurjev.
alexander merkurjev
Image source: its LinkedIn homepage.
He was 27 years old, only 10 years older than me, and he was already a full professor. He was an incredibly brilliant mathematician, and I admired him a lot, and his advice was crucial to my growth, both in terms of his teaching style and academic lectures. Ivan says that he chose the direction of his research and has produced a number of key results that are inseparable from Alexander Merkurjev's guidance.
Therefore, he plans to organize a summer or winter camp on the theme of mathematics at Westlake University, which is open to outstanding high school students in China, hoping that they will have the opportunity to get in touch with the mathematics classes in the university before entering the university, meet one or two mathematics tutors, and have a preliminary impression of mathematics research.
They are all very good seedlings, and they may be stretched thin because of the pressure of preparing for exams and studying styles in high school. Ivan notes that this kind of short-term math school, which is common in Europe and the United States, seems to be difficult to find in China, but he believes that such opportunities are necessary. "These children should develop the habit of thinking outside the box and innovatively in addition to 'cramming' learning. The future of cutting-edge science is more than innovation, not following, and innovation requires a leap in the way of thinking, just like jumping from the ground to 10,000 meters in the air, we need to provide such support to young scholars, give them the majestic power to soar into the sky. ”
Another piece of advice from Ivan Fesenko: open up your world, absorb and think.
Because of their insistence on chalk, mathematicians are often labeled "old-school". In fact, compared to their peers thousands of years ago, mathematicians have perhaps changed the most.
Today's mathematicians are active globetrotters, who may finish their undergraduate studies in one country, go to another for a PhD, and then go to a new country for a teaching ......During their research work, they are not bound by experimental cycles and equipment, and they can bring their own minds and go, at most a computer. Everywhere I went, there were almost all peers who could learn from each other, sometimes purely talking about mathematics, and sometimes colliding with different disciplines to create interesting ideas.
Ivan Fesenko is a visiting student in Japan.
Mathematics is no longer a one's thought experiment.
At the age of 33, Ivan left his familiar St. Petersburg for England, and 27 years later decided to move to Hangzhou, China. "I heard that there is a Westlake University in China that uses a new system to conduct cutting-edge scientific research, and I discussed it with scholars from China, Japan, and some other countries, and the attitude towards this school is very positive, which makes me more and more interested in becoming a part of it. He said.
Opening up his own world is also another attempt he wants to advance at Westlake University. He hopes that by designing some short-term visiting programs, mathematics scholars in the university can leap into "another culture", absorb different mathematical ideas, and experience a different world of science.
Ivan Fesenko spent 27 years in England, only 12 years in Nottingham, before moving to Warwickshire, the home of Shakespeare and George Eliot. "People there seem to have been less affected by the Industrial Revolution than in the big cities, retaining some centuries of style and customs. ”
After coming to China, he went to see the Temple of Confucius and listened to the truth of "those who know are happy with water, and those who are benevolent are happy with mountains";He also ** the Chinese song "Baikal" in his mobile phone, because someone recommended to him that the melody came from his hometown and the singer was from China.
This openness to leapfrogging from one culture to another has been a part of Ivan's innovative research career.
Just like the WeChat avatar he chose for himself - a calligraphy character "Xu".
Xu, glyphically like if in English, that's my initials. Ivan Fesenko said that both the English word if and the Chinese character "Xu" contain the meaning of "if", representing the infinite possibilities of the future.
This article is **from WeChat***ScienceWestlake, School of Science, Westlake University", and the original title is "Former University of Nottingham Professor Ivan Fesenko Joins Westlake University Full-time|The gold medal in the Olympiad and the Fields medal are two different things.
Start planning for my 2024