
An Introduction to the History of Transcendental Numbers
A note of late March 2017.
You may encounter a problem opening my Maple worksheets (as indeed I do myself) here at my web site  it would appear to depend on the internet
browser being used.
Thus, if I attempt to open one of my worksheets using Interner Explorer there is never a problem, whereas if I use Firefox then all that one sees
 this is just an example  is something like this:
{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB
{CSTYLE "Maple Input" 1 0 "Courier" 0 0 128 0 128 1 0 1 0 0 1 0 0 0 0 }
{CSTYLE "2D Math" 1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }
{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "2D Output" 2 20 "" 0 0 0 128 0 1 0 1 0 0 0 0 0 0 0 }
{CSTYLE " " 1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }
{CSTYLE "" 1 257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }
{CSTYLE "" 1 258 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }
{CSTYLE "" 1 259 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" and so on (almost at infinitum)... I asked Maplesoft for advice on this and they recommended doing the following (and I found it worked):
is the title of a Maplebased talk I gave on May 6^{th} 2004 to the Dublin Branch of the Irish Mathematics
Teachers Association.
A Panorama of Number Theory or The View from Baker's GardenOn 24th February 2018 I sent the following email to the Irish Mathematics Departments listserver: The remarkable mathematician (and, incidentally, a Fields Medalist) Alan Baker died (from a stroke) earlier this month, on Sunday 4th. His passing should not go unnoticed. When Serre was awarded a Fields Medal in 1954, Hermann Weyl remarked at the ceremony that Serre was the brightest star in the mathematical firmament (I am relying on my memory here, having read this some 50 years ago; it was in the Proceedings of the Zurich Congress). The same could be truly said of Baker when he burst onto the scene in the mid 60's with regard to his work in Transcendental Numbers, Diophantine approximations and equations. He truly revolutionized these subjects. In particular he proved a vast extension of the (true claim) of Hilbert's seventh problem (which had been independently settled by Gelfond and Schneider in 1934). As reported by the great C.L. Siegel, Hilbert himself had declared (in a lecture attended by C.L.S.) that he expected the Riemann hypothesis would be settled in his lifetime, perhaps Fermat's Last Theorem in the lifetime of those listening, but his seventh problem? "No one present would live to see that!" (source: Constance Reid's Hilbert biography). No newspaper  not even in England (A.B. was born in London, and  a happy coincidence for me  shared my mother's birthday, 19th August)  seems to have published an obituary, a sad reflection on their values. I am offering to give a talk on Baker's work in any department in the country (from Tralee to Derry), a talk that even first year students could follow. John Cosgrave P.S. Some fourteen years ago I prepared a document (in Maple, and also html converted) 'A History of transcendental numbers'. It began as a small document as a basis for a talk to the Irish Mathematics Teachers Association, but it took on a life of its own, and the final (77 A4 pages to print) document is on this page: https://johnbcosgrave.com/archive/transcendental_numbers.htm The html document is here: https://johnbcosgrave.com/archive/download/Public%20and%20other%20lectures/transcendental%206thMay04/transcendentalTOC.html and the Alan Baker part is here: https://johnbcosgrave.com/archive/download/Public%20and%20other%20lectures/transcendental%206thMay04/transcendental33.html#MapleAutoBookmark33 Not one Mathematics dept. took up my offer, and just one person (Ted Hurley in Galway) wrote to thank me for informing of Baker's death. This is the world in which we now find ourselves.
Michel Waldschmidt
generously provides a wealth of valuable
papers and transparencies
Tanguy Rivoal (zeta function at 3, 5, 7, ... ) Paula B. Cohen (now Tretkoff)'s homepage
David Angell's University of New South Wales course on Irrationality and Transcendence

Contact details. jbcosgrave at gmail.com
