I’m skeptical that the relevance of the two modes of thinking in question has much to do with the mathematical field in which they are being applied. Some of grothendiek’s most formative years were spent reconstructing parts of measure theory, specifically he wanted a rigorous definition of the concept of volume and ended up reinventing the Lebesgue measure, if memory serves, in other words, he was doing analysis and, less directly, probability theory...
I do think it’s plausible that more abstract thinkers tend towards things like algebra, but in my limited mathematical education, I was much more comfortable with geometry, and I avoid examples like the plague...
Maybe the two approaches are not all that different. When you zoom out on a growing body of concrete examples you may see something similar to the “image emerging from the mist”, that grothendiek describes.
I’m skeptical that the relevance of the two modes of thinking in question has much to do with the mathematical field in which they are being applied. Some of grothendiek’s most formative years were spent reconstructing parts of measure theory, specifically he wanted a rigorous definition of the concept of volume and ended up reinventing the Lebesgue measure, if memory serves, in other words, he was doing analysis and, less directly, probability theory...
I do think it’s plausible that more abstract thinkers tend towards things like algebra, but in my limited mathematical education, I was much more comfortable with geometry, and I avoid examples like the plague...
Maybe the two approaches are not all that different. When you zoom out on a growing body of concrete examples you may see something similar to the “image emerging from the mist”, that grothendiek describes.