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OK, so I said: The only way to learn mathematics is by doing exercises. To this, gone35 replied: This, in my experience, is utterly false. To me
by CarolineW 10y ago
OK, so I said:
The only way to learn mathematics
is by doing exercises.
To this, gone35 replied:
This, in my experience, is utterly false.
To me, that says that it's not true that the only way to learn mathematics is by doing only exercises. Logically, that means there is some way to learn mathematics by doing something other than exercise, possibly in addition to exercise, admittedly, but certainly something that is not exercises.
The word "utterly" seems additionally to imply that this extra something completely outweighs the exercises, perhaps even to the point of no longer requiring exercises at all. And so my question.
So I believe my question to have been completely reasonable. Rephrasing gone35:
In my experience, is utterly false that
the only way to learn mathematics is by
doing exercises.
So let me be very much more specific.
gone35: I would be very interested to
know what methods of learning
mathematics you espouse other
than, or perhaps in addition
to, doing exercises.
Is that better?
- gone35 10y agoI would be very interested to know what methods of learning mathematics you espouse other than, or perhaps in addition to, doing exercises. Read carefully, go to seminars, ask people, and think through stuff. I'm in lowly applied math/theoretical CS though, so it might be different in other, more abstract fields.
- johncolanduoni 10y ago> think through stuff Perhaps you are simply talking past each other? If "think through stuff" involved coming up with your own questions about the material and answering them, this would fall under what many mathematicians would call "exercise". In fact, I've found the belief that this is often more valuable than in-book excercises to be pretty pervasive in mathematics.
- jsprogrammer 10y agoI think the original proposition is just a tautology. What does it mean to "know" something? I think it is equivalent to being able to complete an "exercise". The fallacy here is thinking that the exercises in a book are special and must be completed and/or that you must have completed one before you could complete another outside the book.