The life of Erdős: A genius mathematician and a “weirdo”: “The Man Who Loved Only Numbers” (Paul Hoffman)

I wrote this article in Japanese and translated it into English using ChatGPT. I also used ChatGPT to create the English article title. I did my best to correct any translation mistakes, but please let me know if you find any errors. By the way, I did not use ChatGPT when writing the Japanese article. The entire article was written from scratch by me, Saikawa Goto.

Introduction

Movies and books covered in this article

I will write an article about this movie/book

Three takeaways from this article

Such an incredible “unrestrained way of life” where even if he gets money, he gives it away to others and rejects extraordinary employment conditions offered by universities.

Self-introduction article

Please refer to the self-introduction article above to learn about the person writing this article. Be sure to check out the Kindle book linked below as well.

The quotes in the article were translated using ChatGPT from Japanese books, and are not direct quotes from the foreign language original books, even if they exist.

I had Never Heard of the Mathematical Genius Erdős until I Read this Book. His “Eccentricity” and Love for Mathematics

Before reading this book, I had never heard of a genius mathematician named Erdős who was so eccentric and passionate about mathematics that it’s surprising. I love math and science, and I read quite a few books in those fields, but I had no idea that such an amazing mathematician existed.

Erdős’ Greatness as a Mathematician

First of all, let’s talk about Erdős’ greatness as a mathematician.

He wrote about 1,500 papers during his lifetime, collaborating with over 500 people, and each of his published papers is said to be excellent. In terms of the number of publications, he is second only to the genius Gauss among all mathematicians in history.

Furthermore, he devoted himself to mathematical research until the age of 83, just before his death. It is said that mathematicians’ talent dries up when they are young, and as evidence, the “Fields Medal,” known as the “Nobel Prize of mathematics,” has a restriction that the recipient must be 40 years old or younger at the time of receiving the award. However, Erdős was even thinking about mathematics for 19 hours a day in his later years. His life was truly amazing.

One of his most impressive achievements is said to be that he nurtured many young mathematicians.

Compared to other academic fields, mathematics tends to be particularly solitary. While there may be opportunities to discuss and collaborate with other mathematicians, the main work is typically done by “developing thoughts in the mathematician’s own head.” This inevitably becomes a lonely pursuit.

Of course, there are those who have passed their peak and go on to educate and train the next generation as professors and educators. However, it is rare to find a mathematician who can both immerse themselves in the inherently solitary pursuit of research while also nurturing young talent.

It seems that Erdős was able to perform such a feat thanks to his exceptional insight. He had the talent to instantly see what kind of problems were suitable for the mathematician in front of him. So, in his interactions with various mathematicians, Erdős continued to contribute by accurately presenting the problems that his colleagues should work on and raising their level.

What’s amazing is that he continued to do the same thing even in fields he wasn’t particularly familiar with. Even with problems in areas he didn’t know well, he was able to provide suggestions that hit the heart of the matter, and sometimes even prove things in fields he knew nothing about on first sight. If we were to put this episode in a more general context, it would be like “winning against a fairly advanced player in a game you’ve just learned the rules and mechanics of.” That’s how his astonishing insight was applied to all areas of “mathematics.”

The book also features a story of a mathematician who was saved by meeting Erdős. In the world of mathematics, which often gives the impression of “solitude,” Erdős stood out as a mathematician who was truly unparalleled in his dedication to nurturing the next generation.

The Overwhelming Greatness of the Eccentric Erdős

So far, I have written about Erdős’ greatness as a mathematician. From here on out, I will touch upon his incredible uniqueness as a human being.

He spent his whole life wandering. It’s said that he didn’t have a permanent residence. He would fly around the world, stay at the home of mathematicians he knew, and continue talking about mathematics without regard for the other mathematician or their family’s daily life. Then, when the time was right, he would leave their home and head towards another mathematician’s home.

Of course, by doing this, he established relationships with other mathematicians and sometimes collaborated with them, publishing co-authored papers. He achieved the impressive feat of writing over 500 co-authored papers in this way.

Additionally, due to Erdős’s large number of co-authored papers, a concept called the “Erdős number” has been created with affection. To explain the specific reasoning behind it would be a bit complicated, so in brief, it is an index that measures the “closeness” to Erdős based on whether or not one has co-authored a paper with him. Individuals who have co-authored with Erdős (A), individuals who have not co-authored with Erdős but have co-authored with A (B), individuals who have not co-authored with Erdős but have co-authored with B (C), etc., are assigned different numbers. This creates a system where individuals with smaller Erdős numbers are considered to be closer to Erdős.

The idea of “Erdős number” was born because Erdős published an abnormal number of co-authored papers. And it can be said that it was precisely his way of life, “wandering,” that produced this.

Erdős only had one dirty bag as his possession. Today, it would still be easy to understand. This is because we have become a world where it is possible to live from place to place, such as “a couch surfer”, by completing everything with a smartphone. Erdős could be said to have pioneered “a couch surfer” in the days before smartphones.

His daily life is tough. He often gets mistaken for a homeless person because of his shabby appearance and his extreme lack of direction sense makes him get lost even on straight roads. Moreover, as he was only interested in mathematics, everyone who has ever lived with Erdős has been inconvenienced in some way.

However, Erdős continued to be loved. Some people may have been fascinated by his mathematical talent, but I think what drew people to him was a kind of “purity.”

Erdős didn’t have an obsession with anything. When he got money, he kept only what he needed to live and gave the rest away to someone else. He donated money and also gave it to widows and homeless people.

Naturally, job offers poured in from universities all over the world, but he turned them all down. He was even offered a lifetime job with an unprecedented package, but he refused because he didn’t want to be tied down.

Honestly, it’s not easy for someone like him to live a genuinely life in society. Erdős was able to do so because of his exceptional mathematical talent. However, there is still a sense of admiration for living a life that thoroughly embraces such “purity”. Those who were associated with Erdős probably felt the same way. I think the respect for him being able to establish such a “heretical” way of life that cannot be achieved normally was also a factor in his acceptance.

Conclusion

I have read various autobiographies and biographies of mathematicians. Based on the information I’ve gathered so far, my impression is that there are many weirdos among mathematicians. It’s just my personal impression, but I think the very fact that mathematics requires thinking that is detached from “reality” is what attracts weirdos or creates weirdos. Although there are certainly opportunities for mathematics to be applied in the real world, mathematicians are not studying mathematics with the intention of applying it. They are simply thinking about the “questions that can exist only within the world of mathematics” that they feel they should pursue without any awareness of connection to reality. In a sense, it’s like “creating novels, movies, and works of art without thinking about publishing or selling them.” There is definitely a certain kind of “madness” inherent in that.

This book is about a mathematician named Erdős, but there is almost no mathematical description, so even people who are not good at math can enjoy reading it. You can enjoy just the fact that “such a mathematician existed”, and some people may feel like they want to step into the world of math after reading this book.

I thought it was an interesting book about mathematicians after all.