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It's amazing how math can require so much work for what appears to be a single result, but I spend an entire semester proving a single mathematical theorem and

It's amazing how math can require so much work for what appears to be a single result, but I spend an entire semester proving a single mathematical theorem and to do that I had to work through an entire textbook, so I don't think it's that unusual.

PartiallyTyped 5y ago
I am not a mathematician, though I do very applied math (ML), I took a course this semester that is intended for Pure Math MSc, called Advanced Vector spaces, having only done some linear algebra and calculus at the undergraduate level, some abstract algebra and some geometric algebra. I am consistently in awe of how well mathematicians have stacked layers of abstraction one on top of the other, and how many different ideas end up being very related to one another. Maybe I am romanticised it and the fact that I regret not going for pure math, but there is beauty in all those abstractions that fit together so nicely.
- kevinventullo 5y ago
  As a former mathematician, I would say the stacked layers get a lot messier closer to the cutting edge.
  - PartiallyTyped 5y ago
    May I ask why former? Defining better abstractions is part of the process that got us so far. Even in ML, we are starting to define some very good abstractions for Neural Networks through the perspective of symmetries and geometry.
    - kevinventullo 5y ago
      The academic job market is brutal compared to tech, especially the “two-body problem”: https://slate.com/human-interest/2013/10/academia-s-confounding-two-body-problem.html https://slate.com/human-interest/2013/10/academia-s-confound... I completely agree we should be defining better abstractions! I more meant it gets a lot harder to do so near the cutting edge.
      - PartiallyTyped 5y ago
        I meant that it takes time to figure out the correct ones, modern algebra is the outcome of nearly 300 years of 'modern' mathematics! It's unfortunate that such issues exist! But considering the issues within academia, you are most likely in a better situation now that otherwise with respect to free time and salary.

PartiallyTyped 5y ago

I am not a mathematician, though I do very applied math (ML), I took a course this semester that is intended for Pure Math MSc, called Advanced Vector spaces, having only done some linear algebra and calculus at the undergraduate level, some abstract algebra and some geometric algebra. I am consistently in awe of how well mathematicians have stacked layers of abstraction one on top of the other, and how many different ideas end up being very related to one another. Maybe I am romanticised it and the fact that I regret not going for pure math, but there is beauty in all those abstractions that fit together so nicely.

kevinventullo 5y ago
As a former mathematician, I would say the stacked layers get a lot messier closer to the cutting edge.
- PartiallyTyped 5y ago
  May I ask why former? Defining better abstractions is part of the process that got us so far. Even in ML, we are starting to define some very good abstractions for Neural Networks through the perspective of symmetries and geometry.
  - kevinventullo 5y ago
    The academic job market is brutal compared to tech, especially the “two-body problem”: https://slate.com/human-interest/2013/10/academia-s-confounding-two-body-problem.html https://slate.com/human-interest/2013/10/academia-s-confound... I completely agree we should be defining better abstractions! I more meant it gets a lot harder to do so near the cutting edge.
    - PartiallyTyped 5y ago
      I meant that it takes time to figure out the correct ones, modern algebra is the outcome of nearly 300 years of 'modern' mathematics! It's unfortunate that such issues exist! But considering the issues within academia, you are most likely in a better situation now that otherwise with respect to free time and salary.