Elliptic Curves: The Great Mystery

> (and motivated)

Look, that's the important part, right? If I wanted to learn the material, I could. But I'm not really interested in learning the material right now, or following the arguments exactly. It's a great article when you're in that mindset.

Quanta, I don't have to be ready to learn the material. I can get a little awareness of what's going on, I don't have to follow specific arguments over a series of paragraphs -- it's news, not lecture. Sometimes that's what I need, to keep aware of what's going on without having to learn it straight up.

I'm a fan of channels like Mathologer and 3B1B, so I'm no stranger to sitting down and following a lovely argument all the way through. I just object to the idea that Quanta is serving the same need as this article and doing a worse job. I just think it's serving a different need altogether.

There are literally hundreds of introductory level analysis textbooks. Some are very terse with challenging exercises presenting things in a definition-theorem-lemma-proof example style (baby Rudin, Lang, Kolmogorov & Fomin, Zorich). Others are pretty chatty, and give lots and lots of examples and motivating discussion (Carothers, Abbott, Pugh). Still others focus more on building (correct) intuition, have few detailed proofs, but give lots of high level vistas of the landscape. These explain how analysts think, and give more historical context (Bressoud, both of Bryant's books, WW Sawyer's introduction to numerical functional analysis). There are even some that take a somewhat more Socratic approach and relegate most of the material to the exercises (Moore & Cloud).

I claim that this diversity of math writing on a single topic is fantastic. I love Baby Rudin, and found Abbott and even Carothers to be so chatty as to be confusing, where others find both of those texts to be a breath of fresh air. Later I came to appreciate Carothers more, and by extension the higher level texts by Bryant and Sawyer.

If you don't like a particular piece of math writing, just consider that there might be others out there who benefit from it. For instance, my partner who has intense math anxiety and barely passed high school algebra can often follow them, and I've found them nice for getting a quick description of a field in math I know nothing about and the problems and methods of that field.

Anyway to be clear, this isn't to say you shouldn't be critical, just that we need more math writing, not less, and if something isn't landing for you, maybe it's landing for others.

I could have made my argument without that line. Thanks for checking me.