The revelation of von Karman’s growth: Why did he become a once-in-a-century scientific genius?

Why did von Karman become a once-in-a-century scientific genius? His natural talent is important, but it is even more inseparable from his upbringing. By reviewing von Karman's autobiography and examining his early educational background, the author of this article found that von Karman's father's educational philosophy, the educational methods of his high school alma mater, and the influence of wise mentors and friends he met later had a particularly important influence on him - contributing to his lifelong curiosity and exploration spirit, and his pursuit of the realm of "knowing why" in science. Understanding von Karman's growth path has important implications for our current education and teaching, and student growth.

Written by Ding Jiu (Professor of Mathematics at the University of Southern Mississippi)

2023 marks the 60th anniversary of the death of Theodore von Kármán (Kármán Tódor in Hungarian, surname first), an American applied mathematician, physicist and engineer. He was born in an educational home in Hungary, grew up in the academic holy land of Germany, the University of Göttingen, became famous at the Aachen University of Technology, and shone at the California Institute of Technology in the United States. He eventually became the most famous aerodynamicist and aeronautical engineer in the world at that time. He won numerous awards throughout his life. In the last year of his life, in addition to being the only winner to receive the first National Medal of Science from the President of the United States, he was also selected as the International Teacher of the Year.

When I first read von Karman's autobiography The Wind and Beyond nearly thirty years ago, I couldn't put it down and read it from beginning to end. I gained a lot and read it again a few years later. Last month, in order to write an article in his memory, "A Scientific Genius Dancing in the Wind - Commemorating the 60th Anniversary of von Karman's Death", I borrowed The Wind and Beyond from the school library. His wise words, like the strong winds output by the high-efficiency wind tunnel he innovatively developed for the California Institute of Technology, blew into my mind and heart again.

Why did von Karman become a once-in-a-century scientific genius? There are many different answers, such as his extraordinary talent and intelligence, which are innate "gifts from God". These innate factors are certainly very important, but the acquired growth environment, such as the educational philosophy of parents, the teaching methods of the school, the subtle influence of teachers and friends, the ideological penetration of books, and the invisible influence of mentors, all play a key role.

Von Karman's autobiography, which he dictated, not only records his rich experiences and interesting stories in his nearly 80 years of life since he was a "child prodigy", but more importantly, he occasionally combines vivid memories with his personal thoughts on "education", an eternal topic for mankind, as well as his experience of the relationship between science and engineering, theory and practice. In my eyes, the latter part of the "narration and discussion" on the concept of science and education is the biggest highlight of von Karman's autobiography, which is completely different from other autobiographies or biographies of others, and also gave me the most profound wisdom summary after reading this book.

Von Karman considered his father a major influence on his life, and this gratitude often emerges in his autobiography. So, to understand how von Karman laid the foundation for his brilliant achievements, we need to move back in history by another thirty years, into Hungary in the mid-nineteenth century.

Father's influence

Von Karman's father, Mór Kármán (December 25, 1843 - October 14, 1915), was a famous educator and cultural policy maker in the Austro-Hungarian Empire. When he was young, he was influenced by Rabbi Lipót Löw (1811-1875), a pioneer of Hungarian neo-Judaism. As a rabbi, Löw once fired Morr because of his love of learning a wide range of knowledge other than religion, and tried to make him a rabbi. But Morr Kármán preferred school to church, so he went to the University of Vienna in Switzerland to study philosophy, education and linguistics, and in 1866 he received a doctorate from the Faculty of Humanities of the Royal University of Pest, the flagship institution of higher learning in his homeland. The school was renamed the University of Budapest in 1873, and changed its name again in 1921 to the Royal Hungarian Pázmány University in memory of its founder three hundred years ago, the philosopher Péter Pázmány (1570-1637). Finally, in 1950 it was changed to its current name, Eötvös Loránd University, in memory of the outstanding Hungarian physicist Loránd Eötvös (1848-1919).

In 1868, on the recommendation of Loew, Moll Kamen taught religion courses at a high school in Pest. The following year, shortly after Hungary gained independence from Austria, he went to the University of Leipzig, commissioned by Baron József Eötvös (1813-1871), the Minister of Religion and Education, to study for two years under the German educational reformer Tuiskon Ziller (1817-1882), specializing in the German gymnasium system. The baron was the father of Roland Eötvös mentioned above. Ziller firmly supported the belief in the "moral purpose of education" emphasized by German philosopher and founder of modern psychology and educational theory Johann Friedrich Herbart (1776-1884), and he tried to show how every part of basic education contributes to the formation of a strong character. Moll Kamen was greatly influenced by this doctrine throughout his life.

After returning to Hungary in 1872, Mohr Kamen became a private lecturer in pedagogy, ethics and psychology at the University of Pest, and was hired by the Ministry of Education to establish a model school for teacher training in Budapest, where he served as a tutor until he resigned due to illness in 1897. This school was the Minta Gymnasium, which later produced many outstanding people. This public boys' school was established according to the German model and focused on training school teachers. "Minta (model)" is not an official name, but is called this because "in order to obtain a teacher's qualification, students must learn how to teach, not just what to teach." Minta students practice teaching, and school teachers work in parallel with university students.

From 1873, Mohr Kamen served as secretary of the Hungarian Board of Education for ten years, playing an important role in the design of the high school curriculum. During this period, he edited the journal "Hungarian Education" first with others and then alone. From 1907, he became an official in charge of theoretical teaching methods at the Hungarian Ministry of Religion and Education. In 1908, he was appointed full professor at the University of Pest. The year before, he had been ennobled by Emperor Franz Joseph (1830-1916). The process was quite interesting. The emperor summoned him to the palace and said that he wanted to reward his excellent work and proposed to ennoble him as "Excellency". Mohr Kamen bowed in thanks, but made another suggestion: "Your Majesty, I am flattered. But I prefer something that I can pass on to my children." The emperor agreed and gave him the hereditary noble title "von Szolloskislak". When this hereditary noble status was passed to von Karman, he could not even pronounce the longest word in the full name clearly, so he used the method of "simplifying the complex" that he was good at in his scientific career and simply deleted it. This is why the world only knows the shortened noble surname "von Kármán".

Like his respected German educator predecessor Herbart, Mohr Kamen believed that teaching methods were primarily the science of knowledge, but in contrast to Herbart's teacher-centered view, he emphasized the importance of student activities. His theoretical contributions and practical work at the Minta Gymnasium contributed to the modernization of Hungarian teaching methods, especially at the high school level. In addition to his own books in the field, he also translated teaching method literature from English and German into Hungarian for publication.

The courses offered at the Minta High School founded by Mohr Kamen include Hungarian, German and literature, Latin and Greek, religion and ethics, philosophy, geography, natural history, representative geometry, mathematics and physics, art and sports. This shows that the humanities occupy an important position. Géza Schay (1900-1991), a Hungarian chemist, studied at the Minta High School from 1913 to 1918. He believed that the school was "the first school where students not only learn the subject content, but also learn to think."

Von Karman, who was sent to this school by his father at the age of nine, also thought so. Before that, he had never been to other schools, even though he showed the ability to multiply two multi-digit numbers mentally at the age of six. Old Karman did not strike while the iron was hot and train him in "Olympiad math skills" to solve difficult math problems, but taught him a wide range of knowledge at home, allowing him to experience the "joy of thinking" and "happiness of discovery" as early as possible.

At the age of 80, von Karman still clearly remembers a story from when he was 6 years old. At a salon party held at home that day, his brother pushed him to the center of the salon. An older relative knew his multi-digit multiplication skills, so he asked everyone present to be quiet, and then shouted to him: "Okay, Todor. Multiply these two numbers in your mind: 144567 times 19765." Then the salon was silent, and all eyes turned to the child expectantly. Like a performer on stage, little Karman hesitated for a moment, then announced the result, and someone checked with pen and paper and announced that his answer was correct.

The boy repeated the performance several times without fail, and the guests applauded and laughed, as if they were all a little surprised. But old Karman was the exception. He stood away from the guests that day, watching his son's performance closely, but his face was full of worry. After the guests left, the father called his son into the study and said, "Todor, this is a clever demonstration, but I want you to promise me that you will never think about mathematics again. Do you understand?" The six-year-old son did not understand his father's good intentions at the time, and thought that his father would praise his talent. A few years later, von Karman finally understood his father. In fact, old Karman was afraid of his son's quick thinking. He didn't like magical children. He thought it was abnormal for his son to calculate long numbers in his head. He would eventually become some kind of freak.

In the next three years until he entered school, as a substitute for mathematics, Karman let his son read geography, history and poetry. Looking back on his life, von Karman in his later years was deeply grateful to his father, "I believe that my lifelong interest in the humanities of civilization began with my father's attempt to keep my childhood mind away from arithmetic tricks." Moll Karman was not only von Karman's father in the biological sense, but also in the educational sense. Have each of us who are fathers ever thought about how we used to be fathers?

In 1897, on the occasion of his twenty-fifth year of teaching, More Kammen's former students and colleagues at home and abroad held a celebration banquet for him, edited a 300-page memorial volume, and presented him with poems:

Kind Master, in order to give our school an ideal,

What is your compensation?

Always have a strong spirit, but often

Weakness,

You never tire of preaching your principles.

You have accomplished everything God has given you.

Your words are heard even by your enemies,

And not unheard of in the desert,

This is your joyful awareness of this.

The Light of Ming Pagoda

In 1890, at the age of nine, von Karman left home and entered the Minta Gymnasium founded by his father, where he studied until 1899. His father's strong influence on him continued during this period of youth, and this school, the first in Hungary to be permeated with modern educational ideas, and its founder shaped him in all aspects.

Minta Middle School was the first school in the Austro-Hungarian Empire to break the rigid relationship between teachers and students. Unlike other middle schools, students in the school could communicate freely with teachers after class, and their teachers would occasionally appear in the group of students walking in the school corridor. The school charter stipulated in written form for the first time in Hungary that teachers could shake hands with students when they met them outside of class. This threw the deeply rooted tradition of "teacher's dignity" into the dustbin of history.

Minta Middle School was a great educational experience for von Karman. His father firmly held the idea that schools should "teach everything" - Latin, mathematics, history, etc., and show how they are related to daily life. Teachers never encourage students to just remember rules from books, but let them try to develop them themselves. (In my article "Scientific Prodigy Dancing in the Wind - Commemorating the 60th Anniversary of von Karman's Death", I quoted several paragraphs of von Karman's description of the specific teaching methods of his alma mater, which will not be repeated here.) In his later years, when von Karman recalled this period of youth study history, he concluded: "This is a good education system, because in my opinion, how a person learns the elements of reasoning in primary school will determine his ability to pursue intellectual pursuits in the future." Does this heartfelt remark from personal experience have any inspiration for the current primary and secondary education methods in our country? For example, Qian Xuesen (1911-2009), a student of von Karman, once asked: "Why can't our schools produce outstanding talents?" Perhaps a major reason is that the rigid indoctrination-based primary and secondary education fundamentally weakens the educated's "ability to pursue intellectual pursuits in the future."

Von Karman believed that his father's greatest contribution was the invaluable gift of curiosity that he carried with him throughout his life. In their conversations, the question of "why something has a certain property" was a frequent topic. His father often told him: "Humans not only try to observe, but also try to understand. This is the great difference between humans and animals." For example, why are raindrops big and small? Why are they not the same size? Why can't you see the air? As early as the young age of eight, von Karman could reconstruct the movement of the planets. When the wireless telegraph was invented, his father once brought home a device called a coherent device, which consisted of a primitive spark transmitter and receiver. Despite his wife's surprise, old Karman took it apart and made the whole family understand why it worked.

Thirty years later, this scientific education method with the purpose of "understanding" was also used by the father of young Richard Feynman (1918-1988) to cultivate good habits in his son in the United States across the Atlantic. Feynman's father tried to guide his son to think in a "scientific way" very early on, and let him understand the fundamental difference between just knowing the name of things and fully understanding the essence of things. For example, a certain bird has different names in different languages, and it is useless to know these names without knowing its characteristics. This scientific way of learning and thinking is completely contrary to the mechanical memorization definition recitation method, and it is particularly worthy of attention from domestic teachers and students. In his best-selling book "What do You Care What Other People Think?", Feynman vividly recalled the anecdotes of his father's early inspirational education. Another of his best-selling storytelling books, Surely You're Joking, Mr. Feynman!, records an inspiring story: When he was a teenager, he was asked by his neighbor to check a radio problem. Under the puzzled gaze of the adult, he paced back and forth, thinking constantly with his brain, trying to figure out the crux of the problem. Eventually, he became "famous" in the town for helping his neighbor fix the noise in the radio.

In my practice of popular science writing and reading about mathematical knowledge or the life of mathematicians in recent years, I have discovered an interesting phenomenon, that is, the number of readers of Chinese articles that only tell stories about people far exceeds the number of readers of articles that popularize the mathematical ideas created by mathematicians. This shows that many people, many of whom should be young people who are curious about scientific knowledge, are often only satisfied with the primary stage of simple understanding of scientific concepts, "knowing what it is but not why it is." This has a lot to do with our educational tradition and current situation. Listening to stories can easily help you know "celebrity anecdotes" without thinking, and then you can "convey" them to others, and by the way show how "learned and talented" you are. In fact, knowing only the stories of people and knowing nothing about the scientific connotation is like knowing only the name of a bird but knowing nothing about its habits. It is a "dragonfly-like" reading method that lacks a thorough understanding of the essence, and the understanding of science is almost a "self-deception" act.

In Western civilization, religion occupies a considerable dominant position. After his son entered Minta High School, Mor Karman often discussed philosophical issues with him, including religious beliefs. Karman Jr. once asked Karman Sr.: "If we really believe that God knows everything and therefore knows all the laws of physics, why does he hide them?" To this thorny question, his father replied: "This contradicts God's idea. We don't always know why he does something, but we believe that he will do the best for us." In this way, he guided his son to look at the relationship between science and religion rationally and helped him learn how to distinguish between thinking and feeling, two areas related to the mind and the heart. In his scientific career, von Karman asserted that he had never seen a conflict between science and religion.

Von Karman was fully confident in his development very early on and established the ideal of devoting himself to science and engineering in the future. In order to have a broader vision, he also read books on the philosophy of science in middle school, such as the famous book Science and Hypothesis by French mathematician Henri Poincaré (1854-1912). The ideas of this book influenced his scientific thinking for a lifetime. In this beautiful book, Poincaré used the cognition of dimensions by humans and insects as examples to explain the "limitations of science." Therefore, once the current laws of nature cannot explain the phenomenon, new laws need to be sought. Von Karman even believed that "without the ideas of Poincaré, the revolutionary concepts of Einstein and Planck would not have been accepted by the scientific community so quickly."

The influence of the wise

At the age of eighteen, von Karman graduated from Minta Gymnasium with the Etfos Prize, the best Hungarian student in mathematics and science. The prize was named after Roland Etfos, a physics professor at the University of Budapest known for his research on gravity.

From 1899 to 1902, von Karman studied at the Royal Joseph University for three years and received a bachelor's degree in mechanical engineering. The earliest predecessor of this university was founded in the 1630s and became the first engineering university in Europe in the 18th century. It has changed its name many times in its nearly 400-year history and was renamed the Budapest University of Technology and Economics in 2020. There, von Karman took the mathematics courses of the famous mathematician Gyula König (1849-1913), and enjoyed the unique challenges that mathematics brought to the brain more eagerly, immersing himself in the logical reasoning of mathematics as he did in middle school. At the same time, he also took humanities courses such as history and literature, rediscovered the joy of reading Goethe (Johann Wolfgang von Goethe, 1749-1832), and sometimes even felt the need to write poetry.

After entering college, von Karman was proud of his high IQ, memory, and comprehension. When his father discovered that his son was a bit "slippery" and tried to outsmart others, he warned von Karman very sternly that real thinking requires more than just cleverness. "You have to increase your thinking," said the elder Karman, "rather than just using it, otherwise you will reach a plateau and end up accomplishing nothing." What timely advice for a smart young man.

With his father's correct guidance and personal experience, von Karman realized that great scientific discoveries are the result of a combination of sufficient knowledge reserves and explosive creativity. He shared the same characteristics with David Hilbert (1862-1943), the leading mathematician of his time: he thought slowly but deeply, which is often lacking in smart people. He opposed the use of IQ tests to classify people. These tests do not measure a person at his own pace, but only test speed. However, von Karman always believed that for true intellectual success, speed is not important, but the ability to think deeply, solidly and creatively is important.

The engineering professor at the university who had the greatest influence on von Karman in terms of creative thinking was Donát Bánki (1859-1922), a mechanical engineer and inventor who taught hydraulics. He opposed the use of purely empirical rules in engineering and tried to explain to his students, in part, why things in nature happen the way they do. Von Karman learned many good principles from him, especially in terms of innovative ideas about solving engineering problems with a scientific eye. In fact, his first recognized theoretical achievement was made under Bánki's supervision. It was related to engines, trying to answer the question "Why do valves sometimes vibrate and make noises?" The solution of this first theoretical problem he encountered in his life left him with the following exclamation:

"I have found that I have a great ability to isolate myself from others and think about a problem. At such times, the richness of scientific ideas fascinates me and allows me to exclude any other considerations. I believe that if you have a scientific problem in your mind and work on it seriously, you will carry it day and night like a woman with a child. You will not get up from your chair until you are sure whether the idea is right or wrong."

Unlike other engineers, von Karman turned the above engineering problem into a mathematical problem. The quality of the article he wrote under his own name was greatly appreciated by Professor Banky, who included it in a book he edited. Inspired by this, this outstanding student set himself a more ambitious goal, especially in his interactions with mathematics professors such as Felix Klein (1849-1925) and Hilbert in the golden age of Göttingen a few years later:

“To be happy in my career, I had to focus on fundamental theory. I had to be a real scientist, a scientist in the sense of a scholar, not someone who just uses science, but someone who makes new contributions to our knowledge and our understanding of nature.”

Von Karman learned German and French in middle school because his parents always emphasized the importance of foreign languages. When he went to college, his father communicated with him in a mixture of his native language and these two foreign languages, which made him fluent in speaking and writing German and French. However, he did not pay attention to learning English until he was about to graduate from college. Not only was it too late, but his pronunciation was also inaccurate, so much so that decades later an American general said in an interview: "In the years I worked with von Karman, I knew he did a good job, but I never really understood what he was saying." After graduation, he served as an artilleryman for a year, and then returned to his alma mater as an assistant professor for three years, accumulating useful engineering practice experience. At this time, he was well-trained in mathematics, science, engineering, humanities and even foreign languages. What he needed was a leap to "the next level."

Von Karman's new start in his academic career began in 1906, when he entered the University of Göttingen in Germany and studied under Ludwig Prandtl (1875-1953), one of the founders of modern fluid mechanics. He received his doctorate in 1908, which truly opened up his academic model of using mathematics to arm engineering and guiding engineering research with scientific laws. During his seven years in Göttingen, he not only made rapid progress in mechanics research, but was also deeply influenced by the frontier seminars on mathematics and physics organized by great mathematicians such as Hilbert and Minkowski (1864-1909). He also actively communicated with physicists of similar age such as Albert Einstein (1879-1955) and Max Born (1882-1970), and even cooperated with the latter in the field of solid-state physics, achieving two new concepts.

Klein, the architect and leader of the Göttingen School of Mathematics, had a profound influence on von Karman. At that time, full professorships in German universities were scarce, and it is said that this has not changed much now, unlike the abundance of full professors in contemporary China and the United States. Even the outstanding Hilbert worked as a lecturer and associate professor at his hometown University of Königsberg for nine years before he succeeded someone else as a full professor. Two years later, due to Klein's efforts, he became a full professor in Göttingen. From then on, the two of them brought mathematics and even physics there to glory. Another major contribution of Klein was the establishment of full professorships in applied mathematics and applied mechanics in German universities for the first time. Carl Runge (1856-1927), in the "Runge-Coutt method" of numerical integration, became the first professor of applied mathematics in history. Runge's "mathematical contributions" also include: one of his daughters is a mathematician, and another daughter married the mathematician Richard Courant (1888-1972).

Klein strengthened the young lecturer von Karman's understanding of the relationship between science and engineering. Klein advocated the combination of mathematical theory and practical engineering. He liked to claim that the greatest mathematicians, such as Archimedes (c. 287-212 BC) and Isaac Newton (1643-1727), knew how to apply mathematics to solve practical problems. He believed that engineering graduates should have a solid theoretical foundation and a clear understanding of the scientific method. The initiative of "marriage of science and engineering" he advocated in Göttingen was later carried forward by von Karman and used in scientific research and teaching practice at Aachen University of Technology and California Institute of Technology.

As a pure mathematician, Hilbert was somewhat contemptuous of applied mathematics. He even looked down on physicists and left a famous saying: "Physics is too difficult for physicists; he needs the help of honest, well-founded mathematics." Once he listened to a report by von Karman, who asked him how he felt, and he replied: "I still don't like applied mathematics, but it's always good to listen to smart people." The more abstract theorist Ernst Zermelo (1871-1953) said a little more "complimentary": "Karman, among all the applied idiots, I think you are the only one who may be educated."

In von Karman's eyes, Hilbert's interests were purely scientific, and he was only concerned with basic theories. His vision made von Karman praise him: "He is a rare figure among scientists - a great teacher who can grasp the core of the problem and illuminate people's minds with a flash of understanding." Hilbert's ideas made von Karman understand that the imprecise qualitative description of natural phenomena that was popular in the previous century should be strengthened or even replaced by mathematical quantitative methods. Von Karman concluded in his autobiography: "This had a strong impact on my belief that 'nature is mathematical' and made me spend my life looking for mathematical solutions in areas where ordinary people only see insurmountable chaos."

Von Karman felt lucky to have been influenced by these masters: "I believe that my later interest in contributing to many different aspects of space technology, rather than focusing on just one field, was established in the environment of Göttingen, where a lot of new mathematics and physics were born, creating today's atomic and space scientists."

After immersing himself in Göttingen, the stronghold of modern mathematics and physics, for seven years and making a name for himself in the international mechanics community, the Technical University of Aachen offered von Karman a full professorship. In the twenty years before and after this, his main research areas gradually focused on aeronautical engineering, which was the call of the era of "flying to the sky" represented by the Wright brothers in the United States. As the director of the Institute of Aeronautics, he built this famous German engineering school into an aeronautical science base with global influence. His own pioneering research was also fruitful, the most famous of which may be his discovery of the vortex theory, named "Kármán Vortex Street", which has a wide range of uses. In 1930, he was already well-known in the aeronautical engineering community in Europe. Faced with the strong anti-Semitism of the German Nazis, he decided to cross the Atlantic Ocean and land in the United States to serve as the director of the Guggenheim Aeronautical Laboratory at the California Institute of Technology.

This laboratory was established four years ago because the investor, New York mining tycoon and philanthropist Daniel Guggenheim (1856-1930), asked the principal to find a "pilot" from Europe. The necessary condition was quickly met. Aeronautical research requires wind tunnels, which are indispensable equipment, otherwise it is easy to talk about it on paper. The pilot von Karman gave the new school a "welcome gift" by designing a large wind tunnel with record efficiency for it.

The story begins with his first trip to the United States in 1926. The visit was invited by telegram from the president of Caltech in order to gain the favor of the Guggenheim Foundation. Von Karman also helped the eager school to improve the preliminary design of the wind tunnel, overturning the previous "Eiffel model" and adopting an improvement plan similar to Prandtl and his own design ideas in Aachen. This "Eiffel" is Gustave Eiffel (1832-1923) in the iconic building "Eiffel Tower" in Paris. He was a civil engineer who focused on meteorology and aerodynamics after retirement. As a result, in the first test after the Caltech wind tunnel was built in 1930, its "energy ratio" not only far exceeded the data of the Eiffel wind tunnel by 3:1, but also matched the world record claimed by the Soviet wind tunnel of 5:1-6:1, reaching 5.6:1. As soon as he arrived in the new country, von Karman showed his innovative scientific ability in engineering design to his American colleagues.

When his family first moved to the United States, where English is the common language, von Karman, who was often able to "simplify" in scientific research, seriously considered dropping the accent mark above the two letters a in his last name von Kármán, because he felt that these two "small strokes" were a burden for Americans. However, one day on the campus of Caltech, a conversation between two faculty members caught his ears: "Who is the new professor?" one asked. "I don't know," the colleague replied, "but he must be a foreigner, he has that thing above the a." Von Karman was annoyed by this comment, so he decided to keep "that thing" above the letter a. (Of course, he did not predict that I, who wrote two articles to commemorate and discuss him ninety-three years later, spent a little more time typing his original Spanish name on the computer.)

Von Karman taught and contributed his talents for thirty-three years in the United States. He made creative contributions in several fields of applied mechanics and aeronautical engineering, which he attributed to two things, in addition to his natural talent, a "gift from God" (Tódor, the name his mother gave him, from Greek etymology), and his own dedication to science (including never marrying): first, his father, an outstanding educator, taught him for a long time, and second, he met good teachers at two universities in his youth, especially in Göttingen. When someone asked him how he rated himself among the great scientists of that century, he answered not very "modestly" like this: "If you define a great scientist as someone with great ideas, then you have to put Einstein first. He had four great ideas. In the history of science, perhaps only Sir Isaac Newton was ahead of Einstein, because he had five or six ideas. All the major scientists of our time are associated with only one or at most two great ideas. For my part, I have three great ideas. Maybe more. Yes, maybe three and a half great ideas."

There are many scientists, but few have "great ideas". Their becoming great scientists who go down in history is the result of multiple nourishments. Tracing the growth of von Karman as a teenager and young adult, and witnessing the current youth education environment in my country from families to schools at all levels, will we feel "a special feeling in our hearts"?

Written on August 17, 2023

Hattiesburg Summer House

This article is supported by the Science Popularization China Starry Sky Project

Produced by: China Association for Science and Technology Department of Science Popularization

Producer: China Science and Technology Press Co., Ltd., Beijing Zhongke Xinghe Culture Media Co., Ltd.

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