What does it feel like to invent math?

What people said

skadamat · 2017-12 · Strong recommendation

So many things I could say about this, but I"ll let Alan Kay speak for me - [LINK] Alan talks about how ideas in Calculus could be manifested from an early age and a richness in understanding built up as they aged up: - at very young ages, kids really respond well through "doing" / the enactive channel. When asked to draw a circle, kids in Papert's group would first emulate what a LOGO turtle would do by rotating their body in a circle (making tiny increments in x and y). - as they got a bit older, the visual / iconic channel was more developed and they could understand the abstraction of a circle on pencil/paper and how the concepts carried over there - closer to early teens, symbols were much easier to grasp and relate to, etc. With this context in mind, there have been some cool efforts to mix the second and third channels I just mentioned to communicate advanced math concepts. Vi Hart and Grant Sanderson's youtube channels come to mind. Here are my favorite videos by Grant: - "What does it feel like to invent math": [VIDEO] - On the visual intuition behind a hard problem on the Putnam exam - "The hardest problem on the hardest test": [LINK] - From vectors to matrices to vector spaces to higher-level ideas like the link between linear algebra and calculus: "Essence of linear algebra" series: [LINK] What I especially like about Grant's videos, is that he often walks through what a mathematician would do, the questions she would ask, etc.

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JoeCamel · 2016-07 · Strong recommendation

I loved this video [VIDEO] "An exploration of infinite sums, from convergent to divergent, including a brief introduction to the 2-adic metric, all themed on that cycle between discovery and invention in math."

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8minfromsol · 2024-10 · Recommendation

3blue1brown has an earlier, kind of meta, video about “What does it feel like to invent math?” where Grant tries to show how one might invent, and so by define, p-adics. Complete with the customarily excellent visual aides. [VIDEO]

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