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I'm a math professor, and my students find it revelatory to understand math as I talk and draw. Math notation is not math, any more than music notation is musi

I'm a math professor, and my students find it revelatory to understand math as I talk and draw. Math notation is not math, any more than music notation is music. Notably, the Beatles couldn't read sheet music, and it didn't hold them back. The best comparison would be is reading someone else's computer code. At its best computer code is poetry, and the most gifted programmers learn quickly by reading code. Still, let's be honest: Reading other people's code is generally a wretched "Please! Just kill me now!" experience. Once you realize math is the same, it's not about you, you can pick your way forward with realistic expectations.

eointierney 5y ago
Super answer! I wish you were one of my professors, and I had excellent professors. If I may humbly add, try making your own notation and playing around with it. Very rapidly one realizes just how hard a problem good notation is.
- BSOhealth 5y ago
  Richard Feynman did just this and described it at least in his great autobiography, “Surely you must be joking, Mr. Feynman!”
- Syzygies 5y ago
  Actually, making my own notation is how I start puzzling out any problem. When one reformulates a problem, the appearance keeps changing but the problem is still there. It often takes multiple reformulations to "see" a problem, unencumbered by artifacts of birth. The other day an EE grad student came to my office to show me his lab's research. After changing notation a couple of times, I was able to recognize that their novel combinatorial problem was an instance of graph coloring.
  - eointierney 5y ago
    Can your lectures be shared online? I would love to watch you create notation.
j7ake 5y ago
Great insight! I’ve definitely encountered mathematically inclined people but who cannot read or write math. Now it makes sense to me. Also I’ve found the converse true. There are people who can manipulate mathematical symbols very well but actually don’t understand the big picture or general direction. The analogy would be that there are people who can write and read music notes (even transpose to different keys) without hearing it in their head (I was one of them).

eointierney 5y ago

Super answer! I wish you were one of my professors, and I had excellent professors. If I may humbly add, try making your own notation and playing around with it. Very rapidly one realizes just how hard a problem good notation is.

BSOhealth 5y ago
Richard Feynman did just this and described it at least in his great autobiography, “Surely you must be joking, Mr. Feynman!”
Syzygies 5y ago
Actually, making my own notation is how I start puzzling out any problem. When one reformulates a problem, the appearance keeps changing but the problem is still there. It often takes multiple reformulations to "see" a problem, unencumbered by artifacts of birth. The other day an EE grad student came to my office to show me his lab's research. After changing notation a couple of times, I was able to recognize that their novel combinatorial problem was an instance of graph coloring.
- eointierney 5y ago
  Can your lectures be shared online? I would love to watch you create notation.

j7ake 5y ago

Great insight! I’ve definitely encountered mathematically inclined people but who cannot read or write math. Now it makes sense to me. Also I’ve found the converse true. There are people who can manipulate mathematical symbols very well but actually don’t understand the big picture or general direction. The analogy would be that there are people who can write and read music notes (even transpose to different keys) without hearing it in their head (I was one of them).