This is cute, but I would much rather see this history written out as a serious non-tweety article. There is a ton of fascinating and useful information hiding underneath the humor.
Math textbooks are really bad at giving a high-level overview of a whole lineage of ideas like this. I would love to read the long-form article on this subject for a mathematically-competent reader, but have no desire to actually study the subject in detail.
You may not be facetious, but you are being condescending by implying that I have never read a math textbook, or that I have made no attempt to find this information. In fact, I have read fairly extensively about elliptic curves and I have never seen any source that describes the history. To the contrary, many sources say that elliptic curves have nothing to do with ellipses, but this series of tweets seems to imply that this isn't true. So if you want to point me to an actual source, that would be much appreciated. But all you have to say is RTFM then my response is STFU.
You're meant to pick up the history as you learn the techniques. You're supposed to learn about Galois when you study groups, Cardano when studying complex numbers, etc. We explicitly invoke the names of mathematicians not to try to summon some saintly Great Men, but to imagine their mindsets and how their various discoveries fit together. Directly examining your textual argument, it's not possible to learn about elliptic curves without learning at least a tiny fragment of the history, where one of Weierstrauss, Montgomery, or Edwards has had their name directly associated with the concrete representation of the equation defining a curve.
I'd like to think that I'm pretty good with elliptic curves, given that I explain them to other folks. However, this tweet-thread still showed me things that I didn't know about the history of maths. Some of these tweets directly led to minutes (hours) on Wikipedia and chasing down various PDFs to read.
Honestly, you could stand to be less self-aggrandizing. It's okay if you don't get every joke immediately; you don't have to know every bit of historical background.
Elliptic curves aren't interesting because of the answers that we have. They're interesting because of the questions. One open question [0] is on the Millennium Prize list. Another open question is almost never written down because it's so simple; "why 1728?" [1] Coming to understand these questions is the goal of our entire process, so there's not much that I can really do other than to ask you to join the process of exploration.
To answer your specific question: "Elliptic curves
have almost nothing to do with ellipses at all. Why then are they called elliptic curves?
The answer lies in the word almost. There is a connection between ellipses and
elliptic curves, but it’s not at all obvious and is the result of a connected but distinctly
nonlinear sequence of mathematical events."
[1] https://www.maa.org/sites/default/files/pdf/upload_library/2...
[2] https://www.maa.org/sites/default/files/pdf/upload_library/2...