> But many people feel the same way about, for example, physical exercise: they don’t enjoy doing it and find it to be very hard work when they try. But it would be strange indeed to say that you can’t “do” exercise. You may not want to do it. You may be unwilling to invest the time and effort into doing it. But you aren’t incapable of doing it. And the same is true, in my experience, in mathematics.
I think a more apt comparison might be to sports, rather than to exercise. Everyone can get reasonably good at "exercise" i.e. be able to run a mile in a reasonable time, but I think we can all agree that there are certainly many people who simply "can't do" a sport.
For example, I am pretty bad at baseball. I was a terrible batter and an even worse fielder. I "persevered" and played Little League Baseball for several years, eventually realized I didn't have much if any aptitude for it, and stopped playing altogether. Does this mean I'm lazy or that the Little League coaching system is broken? No, it just means I'm not that good at baseball and probably never will be, and I don't think any amount of great coaching would have changed that.
Are there some people who could have been good at a given sport but "slip through the cracks" due to laziness or bad teaching? Maybe, but I doubt it's a significant number.
It's easy to take mathematics ability for granted on a focused forum like HN, but perhaps being good at math is no different from being a great sports athlete - Some people are really good at it, but most aren't and it's pretty unrealistic to expect everyone to change their expectations and opinions on the matter.
I think a more apt comparison might be to sports, rather than to exercise. Everyone can get reasonably good at "exercise" i.e. be able to run a mile in a reasonable time, but I think we can all agree that there are certainly many people who simply "can't do" a sport.
For example, I am pretty bad at baseball. I was a terrible batter and an even worse fielder. I "persevered" and played Little League Baseball for several years, eventually realized I didn't have much if any aptitude for it, and stopped playing altogether. Does this mean I'm lazy or that the Little League coaching system is broken? No, it just means I'm not that good at baseball and probably never will be, and I don't think any amount of great coaching would have changed that.
Are there some people who could have been good at a given sport but "slip through the cracks" due to laziness or bad teaching? Maybe, but I doubt it's a significant number.
It's easy to take mathematics ability for granted on a focused forum like HN, but perhaps being good at math is no different from being a great sports athlete - Some people are really good at it, but most aren't and it's pretty unrealistic to expect everyone to change their expectations and opinions on the matter.