Having been a geometer that migrated to computer science via formal logic, I can testify to this division—to some extent.
When I first learnt formal logic and then machine learning, I had the same plodding, ‘algebra’ approach. But now that I’ve grasped it better, I’ve started to develop an intuition in these areas, that can shortcut most of the plodding approach (and it’s so much more fun).
I think the difference might be more in the way the ideas are communicated. You can communicate semi-rigorous geometric ideas in a (somewhat) intuitive way, and have other geometers grasp them, at least enough that they can re-create them rigorously if needed. But algebraic ideas have to be more explicit if you want anyone beyond your immediate circle to get them.
See for instance Bourbaki, where the internal discussions were filled with intuition and imagery, but where the written outputs were famously tedious and rigorous.
I’m a math/econ undergrad, I’ve found that using geometry and imagery to contextualize all my classes is the easiest way for me to really understand a subject.
To use a small example: Learning things like the chain rule or the product rule in calculus became trivial once I learned via this method. However, that is not a way of teaching that is present where I’m learning. I’ve had little (but not zero) success in finding resources on my own that choose to communicate ideas in this way. Or help me hone my visual-math reasoning skills (12). I feel like learning other ways just require too much memorization and doesn’t easily slot into my intuition. As a result whenever something doesn’t intuitively translate to imagery, I feel like I’m plodding along. Are there books, lectures, sequences, or anything out there that I could use? Anything you could send my way would be really appreciated.
Having been a geometer that migrated to computer science via formal logic, I can testify to this division—to some extent.
When I first learnt formal logic and then machine learning, I had the same plodding, ‘algebra’ approach. But now that I’ve grasped it better, I’ve started to develop an intuition in these areas, that can shortcut most of the plodding approach (and it’s so much more fun).
I think the difference might be more in the way the ideas are communicated. You can communicate semi-rigorous geometric ideas in a (somewhat) intuitive way, and have other geometers grasp them, at least enough that they can re-create them rigorously if needed. But algebraic ideas have to be more explicit if you want anyone beyond your immediate circle to get them.
See for instance Bourbaki, where the internal discussions were filled with intuition and imagery, but where the written outputs were famously tedious and rigorous.
I’m a math/econ undergrad, I’ve found that using geometry and imagery to contextualize all my classes is the easiest way for me to really understand a subject.
To use a small example: Learning things like the chain rule or the product rule in calculus became trivial once I learned via this method. However, that is not a way of teaching that is present where I’m learning. I’ve had little (but not zero) success in finding resources on my own that choose to communicate ideas in this way. Or help me hone my visual-math reasoning skills (1 2). I feel like learning other ways just require too much memorization and doesn’t easily slot into my intuition. As a result whenever something doesn’t intuitively translate to imagery, I feel like I’m plodding along. Are there books, lectures, sequences, or anything out there that I could use? Anything you could send my way would be really appreciated.