(2003). I have a simple theory. Math is not a young man's game, but math at these levels is extremely demanding and all consuming of one's mind. As you get older life gets more complicated, you get a wife, kids, dog, etc. Your mind is no longer focused on one thing and one thing only. So it's exceptionally rare to see someone with a normal life do extraordinary discovery in mathematics past a certain age. Paul Erdős is often mentioned as a counterexample to the young mathematician. Yet, Erdős pretty much lived for mathematics and didn't really have a set place let alone a normal life with wife and kids. I'm not saying that this is the only contributing factor, but I'm willing to bet it's a big one.
The thing I find fascinating about both this article and now your comment is that regardless of who's game it is, it seems to be taken as fact that it's a MANS game. You said "you get a wife"...I suppose history isn't littered with too many breakthrough female mathematicians.
I believe the article followed Hardy's quote, and I followed the article lead. I realized after posting that it might be seen as male oriented but I believe the same is true for female mathematicians.
I'll happily look down on applied mathematics, but classifying Emmy Noether as only a physicist would be ridiculous, as a large part of her life's work was indeed pure mathematics. I can't imagine the abuse of history needed to assert otherwise.
And remember, even Hardy, most famous of the Purists, often slummed it with (hold your nose) physicists and on a few occasions even with (the horror) biologists.
I don't believe it's not about "not caring". I think it's more about having a finite number of productive brain-cycles per day, and what you spend them on (opportunity cost).
If you spend all day thinking about others, you won't get any math done. If you spend all day thinking about math, you won't be in tune with others. If you can balance things out properly, you can do both.
Sometimes it's necessary to go to one extreme for a long period of time. If you're working on a really hard problem, it might be best to isolate yourself from society for days/weeks/months at a time to figure it out. If a close family member is stricken with a major illness like cancer, it might be best to focus and spend your thoughts, time, and emotions entirely with them.
In reality it's usually a balancing act between different things. But you can understand why it's sometimes necessary to go to extremes.
I also think that in the adult life you search positive feedback in other critical things like life standard. When you are young it is enough to receive positive and easy feedback in your family or school. I recommend to read the Kasparov's book: how life imitates chess (not the best title) where he mention different chess player personalities and ages.
But we can't forget that there are huge brain changes when you are young.
In the same vein as Kasparov's book, there is this interview of Kramnik where he talks about the world champions before him [0]. It's interesting how he explains how different qualities can offset each other, for example, discipline and creativity.
I agree. Math seems to be a one man or two man show, so you need to be absolutely focused on what you are doing.
Businessmen can delegate and use the system set up in their young adult years to continue their trajectory. Franchising is an example that comes to mind.
I have always admired Paul Erdős, a really interesting life doing something he loved.
