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A Dialogue Between a Struggling Student and his Advisor, Eugenio Calabi

By Xiuxiong Chen, Professor of Mathematics, Stony Brook University  

I met Professor Eugenio Calabi in the Fall of 1989, a couple of months after I arrived on the University of Pennsylvania campus. We hit it off quite nicely, as he was a zealous lecturer and loved to go to the blackboard, while I was an eager listener and loathed to go in front of people, for fear that they might find out that I was not as good as my transcripts might have indicated. In retrospect, he must have found out early on, in his infinite wisdom, that I didn’t understand much of what he was talking about, but that apparently didn’t dampen an iota of his enthusiasm for talking to me. In my recollection, we spent 4-5 hours each day “talking” mathematics to each other—be it in his office, in the mailroom, or in our tea room. This is extraordinary luck for any graduate student to be blessed with. I endured growing pains for a long period of time after my graduation and Professor Calabi was with me during the whole process. His wit, humor and focus on the fundamentals have helped me regain balance in shaky times, and keep cool in sunny times. I cherish his invaluable teachings and wish to share these with the community. What follows are a few dialogues we have had over the years which hopefully will help elucidate the lasting wisdom of Eugenio Calabi. 

Like any ambitious young person, I was
curious about how to be famous:
 

XC: How many papers do I need to write in order to be famous? 

EC: One.

Eugenio Calabi stresses the importance of
being original and doing what you love: 

XC: It seems to be relatively easy to write papers on a trendy subject? 

EC: Be original and follow your own heart and
intuition. 

XC: How do I be original? 

EC: Read classical papers which have withstood the test of time. Like a dog, smell the smell miles away before anyone else has noticed. 

I often complained about the hardship
of getting my papers published: 

XC: Will being in a famous university help publish my papers? 

EC: Maybe. Do you want your address to become famous because of you, or you to become famous
because of your address? 

XC: A mediocre paper gets published in a top journal, what should I do? 

EC: Nothing. If your paper is of fundamental importance, people would find it even if it were published in the corner of earth; if your paper is of mediocre quality, you are better off to be published in an obscure journal so no one will notice it. 

When I was relatively young, I was shocked to find out that a friend had “cheated” on me. It was a tough pill to swallow, but Calabi steered me away from bitterness: 

XC: A friend has stolen my idea. What should I do? 

EC: Congratulations, now your idea is worth stealing!

XC: ??? 

EC: Will you have new ideas? 

XC: Yes. 

EC: Will you allow him to steal again? 

XC: No. 

EC: Then you win since you continue to have new ideas and he cannot continue to steal from you. 

For many, including myself, going to ICM is an ego trip. Calabi helped put it into perspective: 

XC: I was invited to ICM 2002. 

EC: Congratulations, it is important to you personally! 

XC: Just personally? 

EC: Yes. We will know if it is important to geometry in 10 years. Think about who you remember among ICM speakers in differential geometry in 1994 or earlier. 

Ever since my student years, Eugenio Calabi has stressed to me over and over again that it is mathematical problems, not he, that is my teacher. I didn’t quite understand initially, but I have gradually gained an appreciation and become a faithful follower of his philosophy. Indeed, with limited talent myself, I was blessed with many extremely gifted students and hence opportunities to put his philosophy into practice. We find good problems together and learn mathematics from the problems we work on. As a side benefit, I have learned, though with some struggles, quite a bit from my students over the years. Calabi is correct that problems and gifted students are my teachers. This is the biggest secret of my moderately successful career and I wish to share it with future generations.