Is math big or small?

> When Illustrating a mathematical idea, the first thing you need to decide is the scale.

I have spent much of my life illustrating mathematical ideas, and scale is never the first thing I decide. Most commonly it stays abstract and there is no scale; it's flexible and I can zoom in and out at will. Sometimes I will choose a scale partway through or towards the end of an explanation, if I want to use a specific analogy, but I can comfortably rescale it to something else - the scale is never fixed.

Interesting to see such a different view.

A first-year physics teacher once told the class something that stuck with me (paraphrasing): "Nothing is big or small by itself. I want you to always follow these words with 'compared to ...'".

It kinda seems like the point of the article was to talk about different mathematical illustrations, not to determine if math was big or small. Even in the article, the conclusion is that it's both. I suspect the only reason for choosing the title is to grab attention (and it worked on me).

Of course, I am extra cynical as a number theorist who can't visualize most of my field. I wrote my doctorate on Siegel modular forms, and I can honestly say I have no way to visualize them any further than numbers on a page.

I've always loved this recording of Thurston talking about branched coverings and knot complements using big knots: https://www.youtube.com/watch?v=IKSrBt2kFD4

Obviously a torus is the size of a doughnut.

Good article.

Math is smaller than the smallest and bigger than the biggest.

Doesn’t math come down to =

Yes.

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