If ya’ll are interested in what Beecher is talking about in regards to how un-rigorous* math was in the beginning of the century, the book  The Artist and the Mathematician is a very approachable short history of brining rigor back into the mathematicx. It also goes on to discuss the movements in this time period with word play, and languagge play.  I wish i had a copy to quote from but i don’t.

*rigor is the whole idea that Hoffstetler is talking about where you need to be exact in your steps, you can’t “handwave” (another math term maening you say something just clearly follows) becuase then how do you know that you’ve actually proven anything.