Euler's textbooks were such a gift to Europe. I'm always a bit perplexed he doesn't get more credit for this given he wrote some of the first calculus books people could read, because Newton had not cared or tried to. So in many ways Euler was also just an incredible educator and largely lead the charge spreading many of these new ideas. Usually credit is given to Chatelet, but she didn't really write any textbooks, just a commentary to help spread Newton's mechanics. Euler actually wrote the first bona-fide textbook on the matter. Laplace was being literal when he said "Read Euler, read Euler, read Euler".
I own a copy of his "Elements of Algebra" and it's interesting to read because he actually talks and uses the notion of infinitesimals in this basic algebra book. And it makes sense! He essentially just says "think of the biggest number, make it even bigger!!! Now, put it under 1, and just like that we 'get almost zero'"
You would never see something like that now, or even then really, and yet the idea is so simple a kid understands. His writing just has such an optimistic and playful sense to it.
I've been wondering if an llm might be tuned to recognize insightful explanations that are accessible and powerful, to then help train one for creating such. Trying for an AI tutor that's less like drilling textbook bogosity and superficiality, and more like tutoring by that rare someone known for their outlier-deep understanding of a field. Even if an llm only manages to serve as a delivery mechanism for human curated insights, having a deployment story of very widespread impact might help motivate a novel-y broad contribution and curation effort.
I own a copy of his "Elements of Algebra" and it's interesting to read because he actually talks and uses the notion of infinitesimals in this basic algebra book. And it makes sense! He essentially just says "think of the biggest number, make it even bigger!!! Now, put it under 1, and just like that we 'get almost zero'"
You would never see something like that now, or even then really, and yet the idea is so simple a kid understands. His writing just has such an optimistic and playful sense to it.