Out of the blue appears a very young (he was 21) but very straight-looking fellow carrying an attaché case and wearing a jacket who comes and sits down without talking to anyone. I approach him after the talk to try to socialise, but cutting short he says he came from Brussels to talk with the speaker. I play the go-between; of course Stegall agrees and off they go to his office to discuss one on one. After what was surely more than an hour, they come out. Jean leaves immediately and Stegall looks exhausted. Feeling a sense of responsibility as host to the visitor, I worry that he might have been bombarded with too many questions and to my surprise, he says, no, no, more like bombarded with answers. He then tells me solemnly (much to his credit, as I distinctly remember): "I am absolutely sure that I just met someone exceptional." Of course I was a priori sceptical but gradually the whole Banach space community (including myself) discovered, before many other communities, that Jean Bourgain was indeed an exceptional mathematician, head and shoulders above anyone else in the field.
This account was reported by Jean Georges Gilles Pisier and can be found at https://mathshistory.st-andrews.ac.uk/Biographies/Bourgain/
Some mathematicians have described their encounters with Jean Bourgain in https://www.ams.org/notices/202106/rnoti-p942.pdf
Additionally, Terence Tao also recounts his encounter with Bourgain and highlights his own difficulty in understanding one of Jean’s papers here https://terrytao.wordpress.com/2018/12/29/jean-bourgain/
I read about Jean Bourgain’s life and was deeply fascinated. His extraordinary productivity and brilliance truly make him one of the greatest mathematicians of the 20th and 21st centuries.