This small corner contains an unpublished paper of mine, New Proofs of the Irrationality of e² and e⁴ (pdf format), which I submitted to the MAA Monthly back in 2002. A referee pointed out that the main idea was to be found in Liouville, a point evidently lost on no less a person than C. L. Siegel (see his classic book on transcendental numbers). I also prepared an accompanying Maple worksheet (27KB). 

I wrote the above paper after I had read the 2nd edition of Aigner and Ziegler's Proofs from the BOOK. I sent my proof to Günter Ziegler (before I heard from the Monthly Editor), and he liked it, to the extent that he was going to include it in the 3rd edition of their book. 

After I heard from the Monthly, I informed Günter Ziegler, who included Liouville's argument in the 3rd edition, thanking me for bringing it to their attention. While I was disappointed to have been anticipated by Liouville, I was more pleased to receive an autographed copy of the third edition from Günter.

Contact details. jbcosgrave at gmail.com