[Creative Cultivation Program] The amazing Nobel Prize-winning experience originated from the love of mathematics in youth

Author: The Nutcracker Studio

The 2020 Nobel Prize in Physics was awarded to three scientists, one of whom, Roger Penrose, received half of the prize money. His award-winning results originated from a brilliant idea when he was crossing the road in 1964. At that time, Penrose and a friend were crossing an intersection, and an idea suddenly popped into his mind: the existence of black holes should be inferred from the general theory of relativity.

Penrose immediately ran back to the office, completed the verification and proof of the core theorem, and finished the entire paper in two days. The following year, the paper was published in Physical Review Letters. In 2020, this paper won Penrose the Nobel Prize in Physics.

Unlike our stereotype that "research projects take several years", Penrose's research project was completed in just a few days from the inspiration to the final draft. What made Penrose's manuscript so fast? In addition to his solid physics foundation, he also had unparalleled mathematical ability.

In fact, Penrose's common titles are mathematician and mathematical physicist. He invented the generalized inverse matrix when he was 24 years old. Today we will briefly talk about the story of Penrose's early journey into mathematics.

There is an urban legend about Einstein, which roughly says that he was dull and slow in childhood, and couldn't make handmade benches well, so he was discriminated against by his teachers and friends. This story has no source and is of course false. Interestingly, a similar thing actually happened to Penrose.

Penrose was 8 years old at the time, and an elementary school teacher gave the children an intelligence test. The so-called test questions were also very simple, which was to perform mixed operations on a number continuously, such as (7+8)x3-9. The children calculated the results in their minds and told the teacher. Penrose did not come up with an answer within the specified time, so the teacher at the time thought that he had an intellectual problem and demoted him to the third grade with disgust. Fortunately, the third-grade math teacher was very understanding. He found through careful observation that Penrose was not unable to calculate, but just had a slow speed in mental arithmetic. So during the math test, he specially allowed Penrose to answer questions overtime.

In 2020, Penrose won the Nobel Prize and was interviewed by a reporter. He recalled this experience and expressed his deep gratitude to the teacher.

A very common scene at that time was that when the math test time came, the students had handed in their answers one after another, but Penrose was still calculating slowly. Through the classroom window, he could see his classmates playing happily. When Penrose handed in his answer sheet, the teacher found that his score was surprisingly high after marking it. It turned out that the teacher was not wrong. Penrose was just slow in calculation, not bad at math, and there was no problem with his intelligence.

Penrose became fascinated with mathematics, especially geometry, and often had some fantastic ideas in his mind. Once he saw the pattern at the bottom of the sink, he suddenly asked his father: Can the whole world be covered with infinite hexagons?

His father clearly told him that it was not possible, but "pentagons were OK." His father then took Penrose to make a bunch of pentagonal paper models to understand the problem. Penrose and his father made geometric models and drew interesting geometric patterns, which was a lifelong hobby for both of them and lasted for a long time.

In the movie "Inception", the protagonists escaped the pursuit of the bad guys by using a magical staircase that can loop from beginning to end. That staircase is called the Penrose staircase. The Penrose staircase can be seen as a variation of the Penrose triangle. The common feature of these two strange geometric figures is that they can be drawn, but it is absolutely impossible to make them in our real world.

The two graphics were first created by Swedish artist Oscar Reutersvärd in 1934, and Penrose and his father further designed and promoted them, making them known to the world. The father and son called this type of graphics "impossibility in its purest form" in the February 1958 issue of the British Psychological Monthly.

In addition to taking his son to study the world of geometry, Penrose's father also took him into the broader world of science, such as using a simple astronomical telescope to observe the starry sky. After winning the Nobel Prize, Penrose said that it was his father's step-by-step guidance that made him extremely passionate about the universe and science.

Interestingly, Penrose's father's career expectation for his son was not to become a scientist, but to become a doctor when he grew up. When Penrose was interviewed by reporters after receiving the Nobel Prize, he said:

My parents were both doctors and I was one of three brothers. My parents had given up on my older brother, who was obviously going to be a physicist or something. My younger brother, who was a record ten-time British chess champion, was obviously going to beat him. So my parents decided that I would inherit the medical profession. I thought so too.

Penrose himself also thought that he should become a doctor when he grew up. The turning point happened when he was 16 years old. The principal talked to the students one by one, asked about the direction of study in the last two years of high school, and gave corresponding guidance. When Penrose came to him, he said that he wanted to focus on biology, chemistry and mathematics. The principal said that he could not make a combination, and could only choose one direction and then specialize in it.

"If you want to do math, you can't do biochemistry. If you want to do biochemistry, you can't do math. Your choice."

Penrose chose his favorite subject, mathematics, and gave up biochemistry, which also meant giving up the path of medicine. After returning home, Penrose told his parents about this decision. Although the two parents were very annoyed, they still respected Penrose's wishes.

At this point, the genius Penrose embarked on a career path that was most suitable for him and began his in-depth exploration of mathematics and physics.

After getting familiar with Penrose's early life experience in science, it is easy to realize that his future success in mathematics and physics was seemingly accidental but inevitable. Whether it is "covering the world with polygons" or "the purest form of impossibility", it is essentially the same thing. Thinking about the world in a fantastic way is what Penrose has been used to doing since he was a child. Many years later, he was walking on the street, thinking about profound cosmic problems, and still thinking about the world in a fantastic way.

Mathematics for a lifetime, thinking for a lifetime.

This article is produced by Science Popularization China-Starry Sky Project. Please indicate the source when reprinting.