[COMPLETE] Foundations of Geometry by David Hilbert - availle

[Rapunzelina]

Apart from the filenames missing the kb bit at the end, and some of them not including the section number, here are pl notes:

38: spot checked ok
39: pl ok

Conclusion (for you to judge if any need fixing):
- 7:54, text is "all of the theorems", recording has "all of the axioms"
- 11:01, at table, text is "hyperbolic", recording has "parabolic"
- 12:40, missing phrase "demonstration by Abel of the impossibility of solving"

Appendix is alright, except that as it is the last section in the audio book it also needs the phrase "End of The Foundations of Geometry by David Hilbert. Translated by E. J. Townsend", just after "end of appendix".

Preface is pl ok.


May I just say that this project has been a good exercise for my imagination (ability to picture images in the mind). Thanks!

[jamnitzer]

The following comments about Hilbert and the “Foundations of Geometry” are from “Plato's Ghost: The Modernist Transformation of Mathematics” [2008] by Jeremy Gray


So mathematicians acquired a highly non-intuitive way of thinking about lines, and as a result obtained a novel view of planes, and also a striking sense of what axioms imply what conclusions.

⋯

This reflects a further modernist turn, as the study of axiom systems became a topic of mathematics in its own right.

And Hilbert made repeated use of this device of choosing an axiom system with different models in order to show that such-and-such a theorem does not follow from the axioms. So much so that his former professor at Königsberg, Adolf Hurwitz, wrote to him, “You have opened up an immeasurable field of mathematical investigation that can be called the “mathematics of axioms” and goes far beyond the domain of geometry.”

The account of lines and planes given by Hilbert and Moulton is modernist in another way, in its attenuated relationship with the real world.

We may adapt an argument by Charles Rosen, who wrote: “In a Cubist painting … it is often hard to identify what object is represented until we have admired the painted surface … . Before modernism, … , the emotion or sentiment represented by music was evident at once … . With Schoenberg and Webern, … , and with Stravinsky (starting with the Rite of Spring) we must generally begin with a dispassionate understanding of the art and an appreciation of the technique in order to comprehend the emotional content… .”

⋯

The words of David Mumford, one of the leading algebraic geometers in the later half of the twentieth century, echo this observation. The 20th century has been, until recently, an era of “modern mathematics” in a sense quite parallel to “modern art” or “modern architecture” or “modern music.”

That is to say, it turned to an analysis of abstraction, it glorified purity and tried to simplify its results until the roots of each idea were manifest.

These trends started in the work of Hilbert in Germany, were greatly extended in France by a secret mathematical club known as “Bourbaki,” and found fertile soil in Texas, in the topological school of R. L. Moore.

[jamnitzer]

https://librivox.org/uploads/availle/foundationsofgeometry_preface_hilbert_128kb.mp3
https://librivox.org/uploads/availle/foundationsofgeometry_38_hilbert_128kb.mp3
https://librivox.org/uploads/availle/foundationsofgeometry_39_hilbert_128kb.mp3
https://librivox.org/uploads/availle/foundationsofgeometry_conclusion_hilbert_128kb.mp3
https://librivox.org/uploads/availle/foundationsofgeometry_appendix_hilbert_128kb.mp3

[jamnitzer]

May I just say that this project has been a good exercise for my imagination (ability to picture images in the mind).

That is part of what prompted me to try to animate some his images. (Section 23).
https://www.youtube.com/watch?v=yPq8Sw1cL4Y


Again, thank you have the careful proof reading and assistance with this project.

[Rapunzelina]

You're welcome! All sections are now PL OK!

Availle will let you know if she needs anything else from you before cataloguing, but I think that's it.
Congrats on completing your project!

[Availle]

It seems we're pretty much done - congratulations!

What I - and potential listeners probably too - would appreciate is a more exciting... well, let's call it "detailed" summary perhaps? Geometry is a wide field in mathematics, it being one of the basics and all, it would be nice to tell listeners a bit more about what they can expect in this book.

[Availle]

This project is now complete. All files can be downloaded from the catalog page:
https://librivox.org/foundations-of-geometry-by-david-hilbert/


A great book and a worthy addition to our catalog! Thank you both for your hard work on this project!