Terence Sir your lecture video on “Discrepancy theory” is

nice.

It has been brought to my attention that the above link is broken (the original web site was taken down by Dublin City University). The CORRECT link is now: http://johnbcosgrave.com/archive/transcendental_numbers.htm

]]>“(discussed for instance in these lecture notes of mine)”… missing a link.

*[Link added, thanks – T.]*

I wrote to thank him, and he replied in a letter dated 4/11/69: “Dear Cosgrave, Thank you for your letter. It is many years since I worked in Diophantine approximations; I am at the moment engaged on problems of quite a different type. But I would be happy to meet you and discuss any specific difficulties you may have encountered. If you phone me at home (352-1363) one evening, we could arrange a time convenient for us both. Yours sincerely. K.F. Roth.”

I have that letter in front of me now (I keep it inside his Sequences book, the one he wrote with Halberstam, autographed by dear Heini himself), and I will send a photo of the letter to anyone who wishes to have it:

Incidentally, when I was with him, I asked about the circumstances in which he found the proof of his (remarkable) theorem on rational approximations to algebraic numbers (Theorem 3 of T. Tao’s note on Roth). Many years later I wrote what he replied in the Roth section of the following student aimed lecture (never delivered!) of mine: “An introduction to the history of transcendental numbers”, availabe at

]]>Okay, yes I remembered, it was the theorem that Prof Terry Tao has numbered as 3; it was related to Liouville’s Theorem – my mistake. Nevertheless, I read all that in the same article – Hilbert 7th problem.

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