This observed pattern can be described by personality typing. I like to think of it as 2 classifications of how our brain explores - depth-based vs breadth-based search. Problem solving vs random walk. Directed vs discovered. Convergent vs divergent, etc. Essentially, one type enjoys digger deeper (defined by getting closer towards a goal) into a topic, while another enjoys expanding outward (exploring a topic, no goal required).
The majority of people enjoy doing one type of thinking and hate doing the other, which causes this culture difference. Depending on the class of problems that a field has to tackle, the community may be dominant in one or the other. Mathematics is a field in which a random walk style of exploration can yield fascinating results, while an engineering field is much more likely to benefit from a focused approach. Usually, the type of thinking that yields more results becomes dominant in the community and gets the right to snub the other.
The difference and contention, I think, arises purely out of the dislike of doing the type of thinking that you're not naturally inclined to. This dislike is rooted in unfamiliarity and a strong sense of worth that parallels our inclinations. The contention is rarely settled by arguments of logic, efficiency or practicality - it is not that people don't believe in logic, but rather because the arguments don't address the core issue. The core issue is our natural inclinations, which at its roots, are innate or at least solidly ingrained in us by the end of childhood.
I know Tim. In additional to being a phenomenally good mathematician, his clarity and elegance of expression spills over into his writing and his lectures. Some people take a dislike to his style, but I can't see why.
He's also a really, really nice guy, and it's been a privilege on occasion to work with him. My contributions were miniscule, but he was fantastic to work with. I hope to do so again.
I don't think so, based on historical evidence. At least it doesn't seem to be like before- and after-45 or other midlife age. From all great theory builders, we rather see like this age being closer to late twenties. They start out by solving some minor problems, often ambitiously taking the labourous technical ones, and then boom, out of nowhere new stage-setting theory, not necessarily much related to previous work. These frameworks open new hard problems which then are becoming mainstream, while frameworks that emerge by accretion of facts and experience hardly make such impact. I give Alain Connes as an example; man steadily, for most of his academic life i.e. last 30 years, outlines theories at a rate of one per two or three years.
The majority of people enjoy doing one type of thinking and hate doing the other, which causes this culture difference. Depending on the class of problems that a field has to tackle, the community may be dominant in one or the other. Mathematics is a field in which a random walk style of exploration can yield fascinating results, while an engineering field is much more likely to benefit from a focused approach. Usually, the type of thinking that yields more results becomes dominant in the community and gets the right to snub the other.
The difference and contention, I think, arises purely out of the dislike of doing the type of thinking that you're not naturally inclined to. This dislike is rooted in unfamiliarity and a strong sense of worth that parallels our inclinations. The contention is rarely settled by arguments of logic, efficiency or practicality - it is not that people don't believe in logic, but rather because the arguments don't address the core issue. The core issue is our natural inclinations, which at its roots, are innate or at least solidly ingrained in us by the end of childhood.