why is that the case? in the many years since maths has existed - have educators...or just...people in general not thought that folks may want to learn this for themselves? it boggles my mind how much of this stuff is locked away and gate kept.
Learning to write proofs is really learning a new kind of thinking, and that is not easy to do alone. For sure you can learn from books or other resources alone, but as with everything, when you are stuck in some way, good guidance can be very beneficial. I’ve thought proofs and logic at multiple levels and even though people struggle with similar issues, there is almost never a one-size-fits-all way to help an individual progress. It all depends on your context, way of learning, temperament etc etc.
It isn’t that it’s locked away. It’s just that it’s much, much easier to learn some skills with a teacher than on your own.
Imagine, e.g. trying to learn to play piano without a teacher. You could technically maybe do it but it would be 100x harder and you’d end up with a bunch of bad habits. But once you have the basics down you can learn new music on your own.
Proof-based mathematics is similar. There’s just a lot of technical, non-obvious stuff that you have to learn before you go off on your own.
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why is that the case? in the many years since maths has existed - have educators...or just...people in general not thought that folks may want to learn this for themselves? it boggles my mind how much of this stuff is locked away and gate kept.
Learning to write proofs is really learning a new kind of thinking, and that is not easy to do alone. For sure you can learn from books or other resources alone, but as with everything, when you are stuck in some way, good guidance can be very beneficial. I’ve thought proofs and logic at multiple levels and even though people struggle with similar issues, there is almost never a one-size-fits-all way to help an individual progress. It all depends on your context, way of learning, temperament etc etc.
It isn’t that it’s locked away. It’s just that it’s much, much easier to learn some skills with a teacher than on your own.
Imagine, e.g. trying to learn to play piano without a teacher. You could technically maybe do it but it would be 100x harder and you’d end up with a bunch of bad habits. But once you have the basics down you can learn new music on your own.
Proof-based mathematics is similar. There’s just a lot of technical, non-obvious stuff that you have to learn before you go off on your own.