Remarkable achievements indeed, but I would also note that there is always more to it than meets the eye. He lives a solitary life now, but he was an active mathematician up until 2004-05 at Steklov. We don’t know how his stay at Courant, Stony Brook, or UCB shaped his ideas. Additionally, his work builds upon Hamilton’s Ricci flow, which he had been working on, more or less, since 1992, which happens to coincide with his time at Courant and Stony brook. We don’t know the people with whom he was in regular correspondence. Also, the analogous results were proved by Smale and Freedman for dimensions higher than 3, now what did he borrow from their work, we don’t know. Also we know nothing about him other than that he is a recluse, who has withdrawn himself from the world, or that he espouses a ethical and moral philosophy that stands contra to what the global institutional mathematics espouses in terms of fame and recognition.
Please note that my point is not to refute the notion of a genius, but to show that the language we use undermines the shared understanding of the process of knowledge creation. I never said that you can’t work in complete seclusion, but that it misses the “middle”(think excluded middle) that we don’t usually convey. This can often lead to people talking past each other. Even in the case of Perelman, let’s strip him of his math education, his exposure to modern mathematical results, his correspondence with people involved in modern mathematics, could he have built everything by himself in order to prove Poincare conjecture? Now you might intuitively understand that this is not what we usually mean by a lone/solitary genius, but think about the numerous times you’ve spoken to people about a lone genius and people have found it difficult to understand. It’s because they feel you are undermining the fundamental nature of knowledge creation, that is, it is an iterative process that involves knowledge acquisition, conjecturing, formulation, correspondence, criticism, error correction, etc, which needs other people and processes. And when we speak in simplistic terms like lone genius and great founder, it is inevitable that we will end up getting entangled in the meta war and lose the sight of the object of communication.
My understanding is that the object of communication in our case is what leads to some people contributing significantly while others only do incrementally. Better questions would be how do they build on other’s work? What were the incremental components of their work that went unnoticed? How did the correspondence they had with other people in the field affect their trajectory? etc. Now see that all of these allows for a solitary life and work but not a ground up creation of new knowledge without any interaction whatsoever with other people or the processes in it.
Remarkable achievements indeed, but I would also note that there is always more to it than meets the eye. He lives a solitary life now, but he was an active mathematician up until 2004-05 at Steklov. We don’t know how his stay at Courant, Stony Brook, or UCB shaped his ideas. Additionally, his work builds upon Hamilton’s Ricci flow, which he had been working on, more or less, since 1992, which happens to coincide with his time at Courant and Stony brook. We don’t know the people with whom he was in regular correspondence. Also, the analogous results were proved by Smale and Freedman for dimensions higher than 3, now what did he borrow from their work, we don’t know. Also we know nothing about him other than that he is a recluse, who has withdrawn himself from the world, or that he espouses a ethical and moral philosophy that stands contra to what the global institutional mathematics espouses in terms of fame and recognition.
Please note that my point is not to refute the notion of a genius, but to show that the language we use undermines the shared understanding of the process of knowledge creation. I never said that you can’t work in complete seclusion, but that it misses the “middle”(think excluded middle) that we don’t usually convey. This can often lead to people talking past each other. Even in the case of Perelman, let’s strip him of his math education, his exposure to modern mathematical results, his correspondence with people involved in modern mathematics, could he have built everything by himself in order to prove Poincare conjecture? Now you might intuitively understand that this is not what we usually mean by a lone/solitary genius, but think about the numerous times you’ve spoken to people about a lone genius and people have found it difficult to understand. It’s because they feel you are undermining the fundamental nature of knowledge creation, that is, it is an iterative process that involves knowledge acquisition, conjecturing, formulation, correspondence, criticism, error correction, etc, which needs other people and processes. And when we speak in simplistic terms like lone genius and great founder, it is inevitable that we will end up getting entangled in the meta war and lose the sight of the object of communication.
My understanding is that the object of communication in our case is what leads to some people contributing significantly while others only do incrementally. Better questions would be how do they build on other’s work? What were the incremental components of their work that went unnoticed? How did the correspondence they had with other people in the field affect their trajectory? etc. Now see that all of these allows for a solitary life and work but not a ground up creation of new knowledge without any interaction whatsoever with other people or the processes in it.