Overview
In late December 2022, driven by my passion for mathematics, particularly category theory and homotopy type theory, I reached out to Professor Tom Leinster, a mathematician I deeply admire. As a 15-year-old high school student, I proudly shared my Chinese translation of his accessible article, "Rethinking Set Theory," which I had made available online. I sought his feedback on the translation and, more importantly, his guidance on structuring my advanced mathematical studies, having already delved into undergraduate topics like algebraic topology and abstract algebra. Professor Leinster replied in January 2023, expressing his admiration for my effort (though he noted he couldn't verify the Chinese) and recommending two insightful, unconventional books for further study: Saunders Mac Lane's "Mathematics: Form and Function" and Michio Kuga's "Galois's Dream." This exchange was an inspiring and unforgettable milestone in my early mathematical journey. From then on, I continued corresponding with Professor Leinster under my real identity, though those emails are private and will not be shared here.
Original Correspondence
Yuanjue Chou to Tom Leinster
Admiration for your work and request for guidance
Yuanjue Chou vsixadafahin5677@gmail.com
Fri, Dec 30, 2022, 6:30 PM
to Tom.Leinster
Dear Professor Leinster,
I am writing to express my utmost admiration and respect for your contributions to the field of mathematics. As a 15-year-old high school student from China with a deep passion for math, I hope to one day follow in your footsteps and engage in research, particularly in the areas of category theory and homotopy type theory.
I am thrilled to share that I have translated one of your articles, "Rethinking Set Theory," and made it available at the following website: https://chaoli.club/index.php/7082. I would be truly honored if you would consider reviewing my translation and providing feedback.
I am also writing to humbly request your guidance on how to best plan my studies to achieve my aspirations. While I have had the opportunity to study some undergraduate material in abstract algebra, set topology, algebraic topology, and a little bit of category theory, I feel as though I have only just begun to scratch the surface. I would be deeply grateful for any recommendations you have on how I can continue to learn and grow as a mathematician.
Additionally, I would be grateful for any recommendations you have for explanatory articles similar to "Rethinking Set Theory."
Finally, I wanted to express my warmest wishes for the new year!
Sincerely, Yuanjue Chou
Tom Leinster to Yuanjue Chou
Tom Leinster Tom.Leinster@ed.ac.uk
Wed, Jan 18, 2023, 5:17 AM
to me, Tom
Dear Yuanjue,
Thank you for your very kind email, and apologies for the delayed reply; I hope you got an automatic email saying I was away.
It's very nice that you've translated "Rethinking set theory". I'm impressed! Unfortunately I don't read Chinese, so I'm not able to give any feedback, but congratulations in any case - it's a great achievement.
I've been thinking about the best recommendations to make for materials to study with. I imagine you have already come across a few standard undergraduate textbooks, and there are thousands of those. So let me recommend two books that are not quite normal textbooks.
The first is a book by Saunders Mac Lane (one of the creators of category theory) called "Mathematics: Form and Function". Officially, this is an explanation of Mac Lane's philosophy of mathematics. However, what I like most about it is that it's filled with wonderful explanations of many different parts of mathematics. I read it when I was an undergraduate and found it very exciting, as it opened up new worlds to me and gave me tantalizing hints of how they were connected.
The second is "Galois's Dream" by Michio Kuga. This one I haven't actually read, but I've heard many good things about it. The subject is group theory and differential equations, but what's joyful about it is the unusual style it's written in. It's based on a lecture course that Kuga gave to first-year undergraduates, even though Galois theory is usually a rather more advanced course.
Those are just two random ideas! You may or may not like them. In any case, I wish you the best of luck in your studies.
Best wishes, Tom
On 30/12/2022 10:30, Yuanjue Chou wrote: This email was sent to you by someone outside the University. You should only click on links or attachments if you are certain that the email is genuine and the content is safe.
-- Professor Tom Leinster School of Mathematics, University of Edinburgh https://www.maths.ed.ac.uk/~tl The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. Is e buidheann carthannais a th’ ann an Oilthigh Dhùn Èideann, clàraichte an Alba, àireamh clàraidh SC005336.