I retired in 2004 and since then have used some of my spare time reading up on ‘classical’ discoveries in maths, principally Number Theory.
I found that I invariably ended up writing my own ‘take’ on particular topics. I have consolidated my notes on completed topics as pdfs and these can be accessed through the web pages shown in the sidebar. The most substantial of them are those on binary quadratic diophantine equations, and on the prime number theorem, which can be found under ‘Notes on Numbers’.
The blog represents odds and ends and work in progress. The most substantial of the posts are on Weierstrass’ proof of the Lindemann-Weierstrass theorem (February 2010) and Roger Apéry’s proof that zeta(3) is irrational (October 2011), although I must say that the short post on the coin problem/ Frobenius number (January 2012) is also a favourite of mine.
As well there are pages with links to resources I have found useful.
The banner at the top of the blog shows the portion of the manuscript of Riemann’s 1859 memoir ‘Ueber die Anzahl … ‘ (complete with ink smudge) in which he comments on his famous hypothesis: ‘One would of course like to have a rigorous proof of this but I have put aside the search for such a proof after some fleeting vain attempts because it is not necessary for the immediate objective of my endeavours’ (translation from H M Edwards’ book on Riemann’s Zeta Function).
I suspect that if he had decided differently we wouldn’t still be wondering 150 years later.
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