Others have adequately addressed your question about learning new things (SarahC and multifoliaterose are doing math in academia, listen to them), but brushed off your question about “feeling dumb”. Why ignore this issue when you can solve it? Whenever I need to get sharper and more “toned” for tomorrow, I work through some math problems or some Project Euler tasks. The effect is quite noticeable, and the more I practice the longer it stays afterward. I’ve found that it’s more helpful to solve problems that are slightly below my current limit of ability, but try to do them quickly, switching to the next problem immediately when I finish the last. Getting ’em done makes me feel much more confident about my intelligence. It also carries over to mental agility in conversations, etc.
Reading stuff, on the other hand, doesn’t seem to help my mental agility at all, even if it’s clever stuff like the Sequences or HP:MoR.
Whenever I need to get sharper and more “toned” for tomorrow, I work through some math problems or some Project Euler tasks. The effect is quite noticeable, and the more I practice the longer it stays afterward. I’ve found that it’s more helpful to solve problems that are slightly below my absolute limit of ability, but try to do them quickly, switching to the next problem immediately when I finish the last. Getting ’em done makes me feel much more confident about my intelligence. It also carries over to mental agility in conversations, etc.
I think this is a good suggestion. When I first got interested in math late in high school I did a lot of problems from old math contests and this made me feel sharper, boosting my confidence. Some things that may be useful to johnbgone here:
I think your post was very appropriate.
Others have adequately addressed your question about learning new things (SarahC and multifoliaterose are doing math in academia, listen to them), but brushed off your question about “feeling dumb”. Why ignore this issue when you can solve it? Whenever I need to get sharper and more “toned” for tomorrow, I work through some math problems or some Project Euler tasks. The effect is quite noticeable, and the more I practice the longer it stays afterward. I’ve found that it’s more helpful to solve problems that are slightly below my current limit of ability, but try to do them quickly, switching to the next problem immediately when I finish the last. Getting ’em done makes me feel much more confident about my intelligence. It also carries over to mental agility in conversations, etc.
Reading stuff, on the other hand, doesn’t seem to help my mental agility at all, even if it’s clever stuff like the Sequences or HP:MoR.
I think this is a good suggestion. When I first got interested in math late in high school I did a lot of problems from old math contests and this made me feel sharper, boosting my confidence. Some things that may be useful to johnbgone here:
The Art of Problem Solving materials. They have a free archive of old AMC problems on their website.
There’s a good and accessible book called Mathematical Circles: Russian Experience
I remember having a favorable impression of Alfred Posamentier’s Challenging Problems in Algebra.
The Art and Craft of Problem Solving by Paul Zeitz is great (but much of it requires more prerequisites than the aforementioned materials).