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I'm Vicki Hansen.

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I'm professor at the University of Dundee.

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And also a professor at Rochester Institute of Technology in New York.

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And I'm here in the position also as Vice President of the ACM,

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the Association for Computing Machinery.

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And as a representative of ACM, I have to say that I'm absolutely

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thrilled to be able to have said we sponsored this event in part.

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And I just want to give a very brief thank you to Ursula and her colleagues for

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such a wonderful event that they put together for the last few days.

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>> [APPLAUSE] >> Okay,

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so we have some great talks coming up this morning.

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Our first speaker is June Barrelgreen from the Open University.

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>> Thank you very much.

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Well, I'd like to also say thank you all very much for getting up and being here.

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I was sort of expecting one man and his dog, so it's really nice to see so

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many people.

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And also, a big thanks to Ursula as well, for we just had a fantastic day yesterday.

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And this, I know some fantastic talks after mine.

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And I'm, like one of the speakers yesterday, sort of here because Ursula

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was talking to me about the meeting that she was trying to organize and she

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showed me something which you will have seen often now and you're gonna see again.

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And I started whittering in the way that I do and

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she said, that sounds great, you're in the program.

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[LAUGH] And I thought what?

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What did I say?

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So [LAUGH] Anyway.

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So, I said, well, it was really to do with how, about mathematical archives or

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mathematics in archives and the kind of, some of the things that you can find.

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And I just thought that,

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this is just a sort of scatter gone approach to a few things.

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And so the title is sort of germane because this

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is the folio that you saw yesterday and

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Ursula mentioned the Konigsberg Bridges, and

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the thing that struck me was this diagram here.

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And I'll just blow it up and hopefully most of you will recognize

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that as being the Pythagorean Theorem in a particular form.

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So that's where the Pythagoras comes from in my talk.

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And the passages and bit comes at the end.

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And so then when I thought about the Pythagorean theorem, and I thought,

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well I'm going to be in Oxford, something else that you should certainly see

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is the amazing Euclid.The 9th century Euclid that's here in the Bodleian and has

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been digitized thanks to funds provided by the Clay Mathematics Institute.

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And just in case you can't quite see it,

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that's the Pythagorean theorem diagram there.

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And I just really recommend,

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if you haven't ever looked at this, the website's fantastic.

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You can look at this in really great detail.

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And it is just amazing.

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It's 9th century. It's a full edition of Euclid.

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It's the earliest we have.

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And it's just marvelous that it's here in Oxford and that it's now available for

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everyone in the world to see.

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So what other things?

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Well, so thinking about Euclid maybe think about Greek mathematics.

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And then, of course, I thought about Archimedes's palimpsests.

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And the historians of mathematics among you won't be learning

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anything new about this but maybe some of you haven't heard about this story before.

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So, this rather tattered looking book,

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in this form as you see it here, it's the main writing

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you can just see on it is as a Byzantine prayer book from the 13th century.

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But in fact it's a palimpsest,

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which means that this parchment was reused to make it into the prayer book.

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So what they did was wash down what was already there,

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turn it through 90 degrees and rebind it.

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And what's underneath was the Archimedes What's of Archimedes.

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And this book was actually in a monastery in Turkey,

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I think, and it was first photographed by Heiburg in 1906.

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And it was just incredible, actually, that he was able to read it, and see it, and

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do what he could with it, but of course it was still bound in that form.

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Now when he saw it, it was in actually much better condition than that.

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And it somehow disappeared from the monastery and

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then it reemerged later.

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And when it reemerged it was in this rather worse condition.

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Also I put this picture of Archimedes up here because it's just

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a little pet bug bear of mine.

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So if I have an opportunity to say something about it, I do.

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In this particular case, of course,

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I think most people would realize that this isn't a life.

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This isn't a portrait from life.

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>> [LAUGH] >> But of course, with these Greek

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mathematicians, what we do often get, we get busts and things of them and people

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can be slightly seduced into thinking that those were from life as well.

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And of course, they're not.

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So I just want, just a little sort of a reminder about that,

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but so that's why that picture's there.

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And in another life I used to work in an art gallery, but that's another story.

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So this was the Archimedes palimpsest.

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It appeared in Christie's in New York in 1998 where it was sold for

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two million dollars.

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You can see, I think here, how the writing is at right angles.

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It was bought by an anonymous buyer and has been

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subject to fantastic restoration work by scholars from many, many different fields.

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In order to bring the Archimedes works back to life.

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And I just wanted to sort of draw attention to the fact this is just such

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a marvelous conjunction of modern technology and ancient text.

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And these pictures I've got here show where they're actually

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looking at one of the pages of the palimpsest,

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what happened in between 1906 and when it appeared in Christie's.

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Somebody thought that it would make it more valuable if it had

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some pictures in it.

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So, they put some pictures in.

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[LAUGH] And they copied them from a text of a sort of the right kind of date and

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just by a marvelous, really piece of sort of serendipity.

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One of the experts who, when they were first looking at them,

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thought they recognized one of the pictures.

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And indeed they did, they saw it was an exact copy from another text.

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And this is just, this slide just sort of shows how they're looking

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at the machinery and technology that's using to go sort

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of behind the picture and see the writing, and so on.

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And there's plenty out there on the web.

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They've got a very nice website about it.

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And again, if you're interested it's just an extraordinary story, and

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it's fantastic that we've actually got this Archimedes text.

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And again it's like the Euclid one, of course.

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It's several centuries after Archimedes.

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One has to remember actually it's closer in time to us than it is to Archimedes and

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the similar thing with the Euclid text, actually.

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So, moving forward in time a bit, the Pale Manuscripts

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in the British Library and this is out of my period.

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I should say I'm really in, I'm really a 19th, early 20th century person.

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But, I have a post graduate student who was looking at these manuscripts,

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Rosey Cretney, and she was trying to see whether there was something

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in these manuscripts that related to some work she was doing on continued fractions.

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So, she was looking for some particular numbers.

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Well, it turns out that these manuscripts are rather large and rather disorganized.

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And they've been described by our dear late colleague Jackie Stedall,

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30 substantial volumes, several of which contained as many as 3 or

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400 pages of assorted notes, tables, rough work and jottings, many undated, untitled.

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Many folios in the modern volumes contain collections of tiny scraps or

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fragments carefully preserved but in no semblance of order.

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So if you can imagine trying to go through these and find just a sort of sequence of

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numbers, effectually what Rosey was looking for was really rather a hard task.

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But she is a student at the Open University and

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people sort of felt well really she should be doing her work at the Open University.

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Why don't you get?

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So the suggestion was made to her well why don't you get the British Library,

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to digitize the Pell manuscripts.

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And then you can sit at your desk and look for these numbers.

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So Rosey did a little sum.

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And this was [LAUGH] I think it was in 2011, around about that time.

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Whereupon the suggestion was withdrawn.

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[LAUGH] But anyway, I mean, again,

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it's just to sort of draw your attention to some of the problems we face

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when we're a historians of mathematics trying to find things in archives.

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When you're trying to find connections between things,

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that you can keep pace with a great pile of unordered material.

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Something else, another

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wonderful project now that's being digitized, the Newton Project.

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Again, fantastic website, wonderful resource for us historians of math, and

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one of the things I think you can see from something like this folio I've shown here.

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There's lots of things going on.

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There's diagrams.

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There's notation.

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There's writing.

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And actually try to transcribe something like that and

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putting it into print is quite a difficult task.

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So again, it's right marvelous that we can actually see the image for ourselves.

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And so far they've transcribe 6.4 million words.

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That was the last time I looked at the website.

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They keep a kind of running total of what they're doing.

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So, I mean, imagine trying to transcribe something like that.

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I mean, and then you have to make sense, of course, those texts before written,

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after written, so on, you can, you have to put it into context.

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But again, just to give you an idea of some of the sort of things that

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historians of seventeenth century mathematics have to deal with.

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Now I'm going to jump right forward to something that I've been working on.

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And this was a quotation from a talk given by David Hilbert,

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who was the leading German mathematician of his generation.

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And he gave this talk in Paris at the International Congress of Mathematicians

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and in the talk he lays out 23 problems which come a bit extended later.

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And these Hilbut problems became really famous in the history of mathematics.

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In mathematics they were the sort of like almost like the agenda for

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pure mathematics for people to work on.

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And in the sort of prelude to actually the problems,

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he talked a lot about what was a good problem and so on and so forth.

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And one of the things he said was this, an old French mathematician said that

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a mathematical theory not to be considered complete until you made it so

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clear that you can explain to the first man whom you meet on the street.

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So, then the question was, who was the old French mathematician.

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So we thought well, and actually with the anniversary of the Hilbert's

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problems in the millennium,

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a lot of things were written about the problems and Hilbert's address.

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But nobody, well one person, at that point addressed the question.

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So there were various proposals.

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In 1937, someone suggested it was Lagrange,

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2005 someone suggested it was Hermite.

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Now the 1889 one, you might think, well,

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that is a little bit odd because Hilbert's writing in 1900.

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Well, it turns out actually, that we found out that Hilbert

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took it from somebody else as an old French mathematician.

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And so Shawl 's name came up in connection with the previous person who'd used this,

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so we were still no further forward.

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It turned out that all of these were wrong.

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We found that out quietly.

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So, what did we find out?

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Well, we found out that actually the person who it all came to was Verigone and

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it went through through Shawl, through Henry Smith,

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a great professor of mathematics here at Oxford.

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And it was his talk, he framed it in almost the identical way to Hilbert.

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And we think it was from him that Hilbert got the phrase.

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So that's why he copied it exactly.

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But one of the things that we found in the correspondence between Chacon and

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Petalay was that Chacon said, and I've often repeated this to my students.

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But we only have this one letter from Chacon to Petalay, so

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we thought well, do we have evidence for this.

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And then of course I remembered that, rather curiously, because I'm a late 19th

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century person, I've had my arm twisted a bit like sort of being here today.

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I ended up doing some work on this person, William Henry Fox Tolbert.

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And again, who's well known to most people as a pioneer in photography.

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So not the obvious place to be looking for quotes about old French mathematicians.

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But it turned out that in the correspondence of Fox Talbot

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there was a letter from Gergonne this in French,

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this is an English translation where he does repeat exactly this in fact.

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Talbot's early career was in mathematics.

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His first papers he published were in mathematics.

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And he had an interest in mathematics, actually throughout his life.

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And the last papers he published were in mathematics.

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And in the course of doing my work on Fox Talbot, I, this

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is something I just can't resist showing, even if it's a little bit left field.

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Was that in 1915 a mathematician writing about English mathematics

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used Fox Tolbert as an example of sort of English mathematics.

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And he says well Fox Tolbert only vaguely remembered in connection with photography.

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How times change!

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So, I thought it's quite interesting.

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Another person, I'm not going to go into this, but it's just sort of quite

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interesting, Felix Hausdorff, who was really one of the founders of modern

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topology, also had another life, another sort of literary life.

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So, the scholars that have been working on his

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works have had to go through 26 hours in pages of manuscripts, but

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they're also having to deal with his his work with Paul.

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The literary side of him.

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So historians and mathematics get kind of pulled in lots of,

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lots of different directions.

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So it's just, they're still working on these manuscripts.

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But so now, just for my last few moments,

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I want to get on to my Pacifism a bit of my talk.

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And this is a diary that I found in St.

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John's College in Cambridge of a mathematic student.

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France's Paria White was doing the mathematical Tripos in 1915.

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And his diary for 1915 right up to July 1916 is there in St John's.

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And it's, he writes about two thirds of an A4 page every day.

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So it's an amazing document for somebody like me who's interested in trying to

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understand how, what sort of mathematics was being taught in Cambridge at the time.

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And of course you get lecture lists and so on, but to get a student's perspective.

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Also get the student's perspective on his lecturess was quite interesting.

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[LAUGH] And he's really, it's full of all kinds of things.

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But here we have, this is the very first entry in the diary.

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And actually what he's doing, he happened, he lived, his parents

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lived in Islington actually, not very far away as it happens from where I live.

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And he,

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on the first day of the diary he goes to the V & A to see the Rodin exhibition.

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And this was an exhibition of Rodin sculptures that Rodin had donated

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To the VNA to honor the French and British soldiers fighting in the first World War.

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But it's kind of not a likely place that if you were a Rodon

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scholar to be thinking, you know a student, a math student at Cambridge.

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And this diary is full of sort of lots of things.

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So I will point out one or two others.

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This is another one.

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It turns out he's very interested in law.

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So he goes off to the law courts and so he reports on the things that he hears.

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So this particular one, he's about to go.

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It looks a bit boring, and then he sees somebody

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He sees the lawyers coming in with the tackler and various things.

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He says, ho ho, it looks like a libel action, whoopee.

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And then he sees Gladys Cooper, and actually to find out which, he wanted to

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see who she was, and actually, he didn't think she was very beautiful,

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even though she was kind of one of the classic beauties of the day and so on.

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So I mean, there's lots of sort of things here.

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And then the sort of pacifism sort of the story is that

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he is a pacifist himself through religious conviction.

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And so he goes to all these meetings.

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So he joined the Union of Democratic Control.

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This was a, they were set up to.

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It wasn't strictly pacifist.

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It was just to stop interference.

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For government and foreign policy as one and

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it was really important group and their against conscription and various things.

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And the other wonderful thing in the diary is that he sticks into the diary all these

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invitations, various bits of papers, so we actually have these documents, and

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it's interesting for us as historians of mathematics particularly because G.

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H. Hardy Who was

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the leading British mathematician, pure mathematician of his generation, really,

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and very much features in this particular story.

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And we can trace White's, what happens to him and

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various other people who are conscientious Objectives and

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in reading the diary I sort of found out and discovered that actually there were

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proportionally rather more mathematicians where than one would have expected from

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the population as a whole and you see a very clear distinction for why it.

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The way he is treated in Cambridge is an intellectual position.

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When he goes home to Islington, it's terrible.

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His parents are really upset, and he's going to be white-feathered.

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It's really quite stark, the difference.

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So you kind of get interesting things like that.

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This is kind of interesting because here,

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he's writing about Something he's heard about Hardy.

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And Hardy's writing to Reese who he's writing this book with.

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And Reese is in, White thinks he's in Copenhagen, actually he was in Stockholm.

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But anyway, so he says, Hardy had occasion to write him on some mathematical subject.

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The letter contained a good many mathematical symbols.

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Also he mentioned the name of a German worker at the end.

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The Senna got hold of the letter, determined from the German name that it

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must be a code message, spent hours trying to interpret the symbols as a cipher and

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then failing it, he didn't let the letter go through.

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So, this is also Another

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issue for us is actually notation and symbols.

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For us looking particularly for historians of early period,

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because there isn't Standardized notation.

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It's a bit like this non-standard spelling.

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But with mathematics it's, I would hazard a guess to say it's slightly easier

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sometimes to work out a word someone's meaning if the spellings not quite right,

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compared to if the mathematical symbols are different, or

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there maybe a transcription error, or something.

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So.

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So I think this is a very nice example of that.

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So this is another one.

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He goes to see The Birth of a Nation, now this is a very famous film,

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it's a racism film, hugely criticized for its kind of content.

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But for its The technology that was employed in it was really,

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very cutting edge, so it's celebrated for

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its technological skill but not for the content.

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But again, I think historians of film wouldn't necessarily think about going to

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the diary of a Cambridge student to get their The reaction to the film.

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And it's, you know one of the things he says here,

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the pictures were some of them excellent.

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But the horses would gallop at about 100 miles an hour,

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and towards the end at about 200.

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You know, so it's kind of how he's seeing the film.

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and of course, remember,

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you know going to the cinema in those days wasn't Quite the same as going today.

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So as far as the conscientious objection side

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of the story is concerned, White Has to go up before the tribunals.

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They have these tribunals for people who are called up for conscription.

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And as the war progressed,

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of course, conscription became more and more encompassing.

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And so we can learn quite, for me, learning about

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the first World War is an amazingly Amazing sort of source in a sense.

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Because here we have him saying the conscientious cases are reached,

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soon became evident they wouldn't grant any exemptions.

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And the chairman asked each appellant whether he drank tea.

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And if so, whether this did not offend his conscience, owing to the tax.

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You know, sort of hearing these kinds of questions.

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And then he's He's told his appeal's dismissed and

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he's got to take non-competent service and he asked for leave to appeal further and

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he is refused.

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So, this is going on in Cambridge, then he goes home and his father and his sister

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are disappointed and upset because they think it's going to mean prison for him.

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And this is really obviously very distressing.

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He doesn't go to prison actually, so he ends up with a friend's ambulance service.

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But there's a point during the diary where he thinks actually they have come and

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arrested Lancelot Hogben and he thinks they're gonna be coming for

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him so he puts all his library books in a pile in his In his room, you know, so

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that they can be taken back to the library by someone else in case they

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come to take him to prison.

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And then this one, I think, is interesting, because here we have White

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going to the tribunal and listening to various cases and

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He talks about these both mathematicians, and

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then he mentions Eddington, and he says, undignified to see the vive chancellor and

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the master of pleading to be allowed to keep these men.

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What is the university coming to?

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And also in the Dairy, he keeps newspaper clippings as well.

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And one of the things that we can

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see from the newspaper clippings is that the university wants to give Eddington

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exemption because they want him to keep working on at the observatory.

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Eddington's a Quaker.

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He wants to.

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He wants it to go on the record that he wants exceptions for his beliefs.

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And so you see this sort of tension there.

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And Eddington is of course well

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known to historians of Science and scientists and so on.

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Particularly for his work in helping to cement Einsteins's

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theory of general relativity with the eclipse expedition.

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And I just thought it quite appropriate perhaps ti finish my talk with this

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because of course this is the centenary Of, and just very, very recently,

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of Einstein's theory of general relativity.

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And it was Eddington's

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expedition to Principe to where they took the photographs of the star and showed

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that gravitation would actually bend the path of light going around a massive star.

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So, of course, this lead me to the Einstein archives online, so

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that's another fantastic archival resource for people working on Einstein or

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just generally interested in Einstein and

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so, with that, I'll finish.

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Thank you very much.

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[APPLAUSE]