wow, I loved this! thank you. I have a masters degree in math and always enjoyed studying it, so I understand the sacredness you're talking about. though reading this reconfirmed that I had some bad teachers in university and I always felt like some.level of understanding was missing because of it.
After my studies, I had to focus on health issues which required becoming waay more emotionally mature and increase consciousness, asking deeper questions, looking for truth. I always felt like my studies of math prepared me for that. my abstract thinking skills helped me observe myself and the patterns of my mind and behavior. This article made the connection that much more clear, thank you!
Thank you. I'm glad it resonated with you so much! And yeah, I very much relate about math offering a clarity of thinking and functioning even in emotional stuff. It's been a HUGE boon in integrating intense emotional experiences.
You might appreciate this: the Twitter rant I linked to was inspired by my rage when rereading one of Rudin's books (Papa Rudin if I remember right). It's a really precise laying out of answers with barely any hint about what the questions were! And the proofs gave no sense of what the ingenuity behind them were. It would have been so simple to say things like "Riemann integrals can't deal with things like characteristic functions, which we care about because <reason>. So we need a different way of dealing with those. Here's the basic intuition behind a Lebesgue integral. But to make that intuition precise, we need to know how 'big' a set is. So we're going to talk about measure theory as a way of figuring out a sane way of talking about set 'size'."
There was a related rant by Bill Thurston many years ago about how papers and presentations in conferences or colloquia offer the math. I haven't been able to find it in over a decade. If I remember right, he pointed out how it's all definition/theorem/proof when that's just not the interesting bit. What I want to see is more like "We thought X should be true. We were basically right, but we tried to prove it in these two other ways, which ran us into these difficulties. We were able to fix it when we realized thus-and-such. That mostly worked, but we slammed into a problem with weird consideration Q, which had us wrestling for a few months developing this subsection of theory to handle. That's why this basic definition is so quirky: calling it yada-yada wouldn't have worked because of Q."
In other words, most of the value of a mathematical result comes from the friends you make along the way! Or the insights rather. Mathematicians have to work backwards from papers anyway to figure out why the authors made the definitions or proof moves they did. Why not just share those details? Offer the narrative arc?
That said, there IS some benefit to wrestling with the insights and rederiving them for yourself. That part is quite good. But I think that could be better designed. I doubt that's carefully thought through when folk are writing math papers. My guess is they're just trying to write down the correct formal end product of their effort.
wow, I loved this! thank you. I have a masters degree in math and always enjoyed studying it, so I understand the sacredness you're talking about. though reading this reconfirmed that I had some bad teachers in university and I always felt like some.level of understanding was missing because of it.
After my studies, I had to focus on health issues which required becoming waay more emotionally mature and increase consciousness, asking deeper questions, looking for truth. I always felt like my studies of math prepared me for that. my abstract thinking skills helped me observe myself and the patterns of my mind and behavior. This article made the connection that much more clear, thank you!
Thank you. I'm glad it resonated with you so much! And yeah, I very much relate about math offering a clarity of thinking and functioning even in emotional stuff. It's been a HUGE boon in integrating intense emotional experiences.
You might appreciate this: the Twitter rant I linked to was inspired by my rage when rereading one of Rudin's books (Papa Rudin if I remember right). It's a really precise laying out of answers with barely any hint about what the questions were! And the proofs gave no sense of what the ingenuity behind them were. It would have been so simple to say things like "Riemann integrals can't deal with things like characteristic functions, which we care about because <reason>. So we need a different way of dealing with those. Here's the basic intuition behind a Lebesgue integral. But to make that intuition precise, we need to know how 'big' a set is. So we're going to talk about measure theory as a way of figuring out a sane way of talking about set 'size'."
There was a related rant by Bill Thurston many years ago about how papers and presentations in conferences or colloquia offer the math. I haven't been able to find it in over a decade. If I remember right, he pointed out how it's all definition/theorem/proof when that's just not the interesting bit. What I want to see is more like "We thought X should be true. We were basically right, but we tried to prove it in these two other ways, which ran us into these difficulties. We were able to fix it when we realized thus-and-such. That mostly worked, but we slammed into a problem with weird consideration Q, which had us wrestling for a few months developing this subsection of theory to handle. That's why this basic definition is so quirky: calling it yada-yada wouldn't have worked because of Q."
In other words, most of the value of a mathematical result comes from the friends you make along the way! Or the insights rather. Mathematicians have to work backwards from papers anyway to figure out why the authors made the definitions or proof moves they did. Why not just share those details? Offer the narrative arc?
That said, there IS some benefit to wrestling with the insights and rederiving them for yourself. That part is quite good. But I think that could be better designed. I doubt that's carefully thought through when folk are writing math papers. My guess is they're just trying to write down the correct formal end product of their effort.
Thanks for your comment!
Love you bro. You get it. 😉