Mathemagics

Someone claimed quite grandiosely on Twitter that “mathematical sense is normal human sense” and that “fear of mathematics is always the teacher’s fault”. Is it though? I’ve always done well at math and had regular crises driven by an intense fear of mathematics; this has led me to believe for a long time that the trope of math being an “innate human subject” is probably overstated. I think, instead, math is a fairly counter-intuitive concept to a well-developed evolutionary way of thinking, and hence is one of humanity’s greatest creations.

The basis for this lies in how humans think. Close relatives such as chimpanzees are great at detail, solving memory tests at incredible speed and accuracy, presumably because they walk with their eyes on the ground and need to focus on individual aspects of the picture they see. Humans, however, are brilliant at heuristics and approximations. As we trudged in the prehistoric grasslands, an approximate overall grasp of the visuals trumped the ability to focus on one branch of one tree. Even when we count objects, we can always approximate to a good degree of precision very quickly.

Mathematics, however, requires an exact solution. There is one correct way (or a set of ways) of doing things, and all else are false, not approximately correct. It is important to consciously move from the heuristic mode of thinking of everyday life to one that is axiomatic, logical and structured. In contrast, subjects like the social sciences, and even sometimes the physical sciences, admit more wriggle space to think and argue approximately. This is probably why children that are not predisposed to this rigorous mode of thinking (which I believe is most children) have this dread of mathematics – juxtaposed with more “natural” subjects, it can feel alien and perplexing.

2 comments

  1. pranoy · July 27, 2020

    I do agree with general premise that mathematics allows less leeway than other sciences. I feel that this is in part to do with the lack of familiarity with language/culture of mathematics. It might also have something to do with the presentation style being influenced by the way mathematics developed(see for eg. the culture of Bourbaki). However, a lot of the nitty-gritty aspects are worked out with the same nature of intuition as used in the physical sciences(see for eg. https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/). Also, in the chronological development of an area, a lot of the axiomatization/structure does not happen as linearly as it is presented in books(For most of the branches of maths, the axiomatisation happened after a lot of the details were tried out).

    Liked by 1 person

    • Aroon Narayanan · August 14, 2020

      That’s an excellent point. The way we figure out results is often not the same way that things are presented after they are formalized.

      Like

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