Dear George, Although I have yet to read the Saunders MacLane's notes on "Geometrical Mechanics" for a course given in Chicago in 1968 in some more detail, just perusing them seems to me that the notes in question are based on several sources which are explicitly mentioned in them and that are well known in the subject matter. I doubt therefore that Saunders himself may have thought of them as original in any way. Doubtless they must have been useful to his students as well as to himself, for instance when writing Chapter VIII (Forms of Space) and Chapter IX (Mechanics) of his very nice book "Mathematics Form and Function", Springer-Verlag, 1968. I am still not sure myself whether to write "Mac Lane" or "MacLane", and I certainly did not know the story behind his opting for the latter. I am sure that these notes will be useful to anybody not familiar with the material exposed on them, and that we should certainly thank Harry Dole for his having provided us with them. Sincerely, Marta ************************************************ Marta Bunge Professor Emerita Dept of Mathematics and Statistics McGill University Montreal, QC, Canada H3A 2K6 bunge@math.mcgill.ca ************************************************ ________________________________ From: George Janelidze <George.Janelidze@uct.ac.za> Sent: October 25, 2017 6:23 PM To: Harry Dole; categories@mta.ca Subject: categories: Re: Kinetic Energy Is A Riemann Metric On Configuration Space Dear Mr. Dole, I am one of many who is (or will be) very grateful to you for these beautiful notes. I have never seen them before. Do you know how accurate they are? Had Mac Lane seen them? While making a copy of them I read on your webpage: "...Below are the lecture notes dating back to 1968. Interestingly, there’s no space in “MacLane”... As a comment to that here is what Mac Lane says in his book "A Mathematical Autobiography" (Page 6): "...The space in Mac Lane was added years later by me, when my first wife, Dorothy, found it difficult to type our name without a space". Best regards, George Janelidze [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

=0A= Dear Harry, Marta, Peter and All,=0A= =0A= On my shelves is a slightly-under-A4-sized=3D20=0A= booklet of lectures on=0A= =0A= Algebraic Functions=0A= =0A= by Saunders Mac Lane (with the space, all three times typed!)=3D20=0A= delivered at Harvard in Spring 1939. The notes were taken=0A= by Edwin N. Nilson. The place and date on the booklet is=3D20=0A= Cambridge, Massachusetts 1947.=0A= The notes culminate in=3D20=0A= Section 25. Applications of Riemann-Roch theorem.=0A= At the time Weil had given ``an ingenious new proof''.=3D20=0A= =0A= Saunders' ``hobbies'' were many!=0A= =0A= I knew of Mac Lane's notes on mechanics and wrote to=0A= him asking for them but did not get a copy. So thank you=0A= Harry for making them available.=0A= =0A= Speaking of mechanics, I might mention that I believe=3D20=0A= Chapter 13 Classical Mechanics (last chapter)=0A= of ``Advanced Calculus'' by Loomis and Sternberg=0A= is based in large part on the PhD thesis of=0A= our colleague John W. Gray. =3D20=0A= =0A= Interesting you should mention Dr Pars, Peter.=0A= He was at the University of Sydney when I was in=0A= my final undergrad years. He taught us a course on=0A= the calculus of variations. It was very hands on with many=0A= nice examples: quite a good background for learning a=0A= more grown up approach later. So I met Pars before=0A= I met Saunders.=0A= =0A= Ross=0A= =0A=

On 28 Oct 2017, at 10:52 AM, ptj@maths.cam.ac.uk wrote:=0A= =3D20=0A= Yes, I am sure Saunders saw his excursions into geometrical mechanics=0A= as a `hobby', and wasn't seeking to make original contributions (other=0A= than, perhaps, a new way of looking at established results). I remember,= =0A= when I was in Chicago in 1975--76, he asked me whether I knew L.A. (Alan)= =0A= Pars, a Cambridge mathematician whose book on dynamics was one of his=0A= favoured sources. (At the time I didn't know him -- he had retired long= =0A= before I first went to Cambridge -- but I did meet him subsequently.=0A= He was then in his nineties, and was delighted to learn that Saunders=0A= was a fan of his work.)=0A= =3D20=0A= Regarding the spelling of Saunders's surname: my recollection is that,=0A= once he had decided to adopt the space in `Mac Lane', he was quite=0A= insistent that everyone should use it. Since that happened well before=0A= 1968, it's surprising that he allowed `MacLane' to stand on the title=0A= page of those 1968 notes.=0A= =0A= =0A=

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