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Do you believe someone needs to understand the history of math to effectively use math? I don't think anyone is claiming historical context isn't helpful, but

Do you believe someone needs to understand the history of math to effectively use math? I don't think anyone is claiming historical context isn't helpful, but these are tools for thinking. This doesn't go anywhere near the 'history repeating itself' mantra. The only way it could get close to that is for someone who is attempting to discover new math (or philosophy), but that's a very small subset of those who benefit from these tools.

jhbadger 4y ago
Yes. So many things in math, in science, in programming, only make sense if you understand where they came from and in what context. Otherwise things just seem weird and arbitrary and hard to understand.
- P5fRxh5kUvp2th 4y ago
  I don't need to understand how a fence post evolved in order to successfully use fence posts.
  - jhbadger 4y ago
    To use them well I think you would. People who haven't been exposed to a history of a method or technology often say "I think this is silly; I can think of a better way to do this". Sometimes, extremely rarely, they are right. But more often, what they are thinking of is something that was tried and was found not to work well. Knowing the history of what you are doing, and what things worked and failed prevents you from making the same mistakes your forerunners did.
    - P5fRxh5kUvp2th 4y ago
      There's always an odd dichotomy between those who do, and those who do not. No farmer in existence would ever agree they need to understand the historical context to successfully use a fence post, or that they need it to be able to critically evaluate their specific needs and adjust their usage of fence posts to meet those needs. I find this attitude amongst software architects a lot as well. The stereotype of the hapless academic didn't come about because there's no truth to it.
- _Algernon_ 4y ago
  In math everything can be derived directly from the underlying axioms given enough time. You don't need historical context. You may want the set of previously proven things to save some time, but you don't need it.
igorkraw 4y ago
Use? No, math is a tool. Extend? Yes. Math is a tool that came from a context, so there might be implicit assumptions made on choosing that particular notation and definition that might or might not be justified. Appreciating where and idea comes from lets you work with the idea. I also think it helps learning and generalising. A competent programmer with no knowledge of history can deal with things like e.g. non-monotonicity in time by just writing robust code. But it helps to know where it comes from: clock drift, user modification, error, leap seconds etc. If you know one of these, you can leverage different assumptions.
- P5fRxh5kUvp2th 4y ago
  You don't need to understand the history of monotonicity to understand and effectively use the concept. Will it make you better? yes, of course, but that isn't what's being discussed here.

jhbadger 4y ago

Yes. So many things in math, in science, in programming, only make sense if you understand where they came from and in what context. Otherwise things just seem weird and arbitrary and hard to understand.

P5fRxh5kUvp2th 4y ago
I don't need to understand how a fence post evolved in order to successfully use fence posts.
- jhbadger 4y ago
  To use them well I think you would. People who haven't been exposed to a history of a method or technology often say "I think this is silly; I can think of a better way to do this". Sometimes, extremely rarely, they are right. But more often, what they are thinking of is something that was tried and was found not to work well. Knowing the history of what you are doing, and what things worked and failed prevents you from making the same mistakes your forerunners did.
  - P5fRxh5kUvp2th 4y ago
    There's always an odd dichotomy between those who do, and those who do not. No farmer in existence would ever agree they need to understand the historical context to successfully use a fence post, or that they need it to be able to critically evaluate their specific needs and adjust their usage of fence posts to meet those needs. I find this attitude amongst software architects a lot as well. The stereotype of the hapless academic didn't come about because there's no truth to it.
_Algernon_ 4y ago
In math everything can be derived directly from the underlying axioms given enough time. You don't need historical context. You may want the set of previously proven things to save some time, but you don't need it.

igorkraw 4y ago

Use? No, math is a tool. Extend? Yes. Math is a tool that came from a context, so there might be implicit assumptions made on choosing that particular notation and definition that might or might not be justified. Appreciating where and idea comes from lets you work with the idea. I also think it helps learning and generalising. A competent programmer with no knowledge of history can deal with things like e.g. non-monotonicity in time by just writing robust code. But it helps to know where it comes from: clock drift, user modification, error, leap seconds etc. If you know one of these, you can leverage different assumptions.

P5fRxh5kUvp2th 4y ago
You don't need to understand the history of monotonicity to understand and effectively use the concept. Will it make you better? yes, of course, but that isn't what's being discussed here.