[HN Gopher] The dirty secret of mathematics: We make it up as we... ___________________________________________________________________ The dirty secret of mathematics: We make it up as we go along (2018) Author : yamrzou Score : 18 points Date : 2022-09-14 05:25 UTC (1 days ago) (HTM) web link (medium.com) (TXT) w3m dump (medium.com) | morpheos137 wrote: | Mathematics may be made up in the sense of what we use for | notation or symbology but the underlying relations are timeless | and superuniversal. | | In any universe or species pi defined as the ratio of the path | length traced by a set of coplanar points equidistant to a common | point to the path traced by a set of points in a different plane | intersecting exactly two points in the first path and the | aforementioned common point will be the same as our pi. | whycombinetor wrote: | Is this still true in hyperbolic geometry, where the | circumference of a circle of radius r is greater than 2.pi.r? | ska wrote: | I think you are oversimplifying in a way that eludes the point | OP was trying to make. | | Or rather two points. First that the process of actually | creating mathematics is messy and largely made up as it goes | along. I can create a new mathematical structure that turns out | to not be very useful, etc. Secondly that the way math is | taught typically hides this, and creates a very linear | "greatest hits" approach which is misleading. | | You are correct that one of the things that has come out of | centuries of studying mathematics are clear definitions of | abstract objects that almost _have_ to have been found; but the | day-to-day isn 't that. | | On the other hand, how something is taught and how it is | practised often aren't that close to each other. Part of the | reason the pedagogy looks the way it does is to distill | centuries of thought and argument into a few credit hours. | robot_no_419 wrote: | Math is presented in a way that's supposed to be organized, | compact, and categorical. If we taught math the same way math was | proven and discovered, it would be so slow and inefficient that | we would still be covering linear algebra in post grad. | | As an analogy: The 1,000th person to climb Mt. Everest takes a | well defined path that has already been mapped out as the most | efficient path to the top. If every single person had to go | through the treachery of finding the dead ends, cliffs, crevices, | and death traps that the first few climbers endured, it would be | a journey only a few could accomplish. | | Most people (computer scientists, engineers, chemists, | physicists) using math only need to reach the top and see the | view from the peak. The few climbers that are really dedicated to | climbing (ie, the math researchers who reach the frontier of | math) will naturally learn about the rest of the jagged, unmapped | landscape as they climb harder and unconquered mountains. ___________________________________________________________________ (page generated 2022-09-15 23:00 UTC)