The PROOF: e and pi are transcendental
by Super User, 3 years ago
Today’s video would have been impossible without the help from my analyst colleague and friend Marty Ross who did most of the heavy lifting in terms of identifying and adapting the least crazy transcendence proofs for e and pi in existence for this video.
Here is Marty’s writeup of the infinite series based proof that e is not a quadratic irrational http://www.qedcat.com/notes/e%20not%20quadratic.pdf and here is his formal write-ups of the proofs for the transcendence of pi and e that this video is based on http://www.qedcat.com/notes/e%20+%20pi%20transcendental.pdf. Marty’s version of the proofs is based on this paper by Steinberg and Redheffer https://projecteuclid.org/download/pdf_1/euclid.pjm/1103051870 which in turn has its origins in a proof by David Hilbert http://www.cs.toronto.edu/~yuvalf/Hilbert%20Ueber%20die%20Transzendenz%20der%20Zahlen%20e%20und%20pi.pdf.
Apart from Marty I’d also like to thank MIchael Fraklin for his help with recording this episode of Mathologer, as well as Danil Diitriev who as usual will take care of the preparing amazing Russian subtitles for this video.
The mysterious Buddhabrot fractal was discovered by Melinda Green. For an intro to this strange mathematical creature check out my Mandelbrot video. http://youtu.be/9gk_8mQuerg
Finally, here is a playlist of all my videos on irrational and transcendent numbers. http://www.youtube.com/playlist?list=PLmNp3NTX4KXK6-xgFJdMAbavzgQaKjRzY