I'm Vicki Hansen.
I'm professor at the University of Dundee.
And also a professor at Rochester Institute of Technology in New York.
And I'm here in the position also as Vice President of the ACM,
the Association for Computing Machinery.
And as a representative of ACM, I have to say that I'm absolutely
thrilled to be able to have said we sponsored this event in part.
And I just want to give a very brief thank you to Ursula and her colleagues for
such a wonderful event that they put together for the last few days.
>> [APPLAUSE] >> Okay,
so we have some great talks coming up this morning.
Our first speaker is June Barrelgreen from the Open University.
>> Thank you very much.
Well, I'd like to also say thank you all very much for getting up and being here.
I was sort of expecting one man and his dog, so it's really nice to see so
many people.
And also, a big thanks to Ursula as well, for we just had a fantastic day yesterday.
And this, I know some fantastic talks after mine.
And I'm, like one of the speakers yesterday, sort of here because Ursula
was talking to me about the meeting that she was trying to organize and she
showed me something which you will have seen often now and you're gonna see again.
And I started whittering in the way that I do and
she said, that sounds great, you're in the program.
[LAUGH] And I thought what?
What did I say?
So [LAUGH] Anyway.
So, I said, well, it was really to do with how, about mathematical archives or
mathematics in archives and the kind of, some of the things that you can find.
And I just thought that,
this is just a sort of scatter gone approach to a few things.
And so the title is sort of germane because this
is the folio that you saw yesterday and
Ursula mentioned the Konigsberg Bridges, and
the thing that struck me was this diagram here.
And I'll just blow it up and hopefully most of you will recognize
that as being the Pythagorean Theorem in a particular form.
So that's where the Pythagoras comes from in my talk.
And the passages and bit comes at the end.
And so then when I thought about the Pythagorean theorem, and I thought,
well I'm going to be in Oxford, something else that you should certainly see
is the amazing Euclid.The 9th century Euclid that's here in the Bodleian and has
been digitized thanks to funds provided by the Clay Mathematics Institute.
And just in case you can't quite see it,
that's the Pythagorean theorem diagram there.
And I just really recommend,
if you haven't ever looked at this, the website's fantastic.
You can look at this in really great detail.
And it is just amazing.
It's 9th century. It's a full edition of Euclid.
It's the earliest we have.
And it's just marvelous that it's here in Oxford and that it's now available for
everyone in the world to see.
So what other things?
Well, so thinking about Euclid maybe think about Greek mathematics.
And then, of course, I thought about Archimedes's palimpsests.
And the historians of mathematics among you won't be learning
anything new about this but maybe some of you haven't heard about this story before.
So, this rather tattered looking book,
in this form as you see it here, it's the main writing
you can just see on it is as a Byzantine prayer book from the 13th century.
But in fact it's a palimpsest,
which means that this parchment was reused to make it into the prayer book.
So what they did was wash down what was already there,
turn it through 90 degrees and rebind it.
And what's underneath was the Archimedes What's of Archimedes.
And this book was actually in a monastery in Turkey,
I think, and it was first photographed by Heiburg in 1906.
And it was just incredible, actually, that he was able to read it, and see it, and
do what he could with it, but of course it was still bound in that form.
Now when he saw it, it was in actually much better condition than that.
And it somehow disappeared from the monastery and
then it reemerged later.
And when it reemerged it was in this rather worse condition.
Also I put this picture of Archimedes up here because it's just
a little pet bug bear of mine.
So if I have an opportunity to say something about it, I do.
In this particular case, of course,
I think most people would realize that this isn't a life.
This isn't a portrait from life.
>> [LAUGH] >> But of course, with these Greek
mathematicians, what we do often get, we get busts and things of them and people
can be slightly seduced into thinking that those were from life as well.
And of course, they're not.
So I just want, just a little sort of a reminder about that,
but so that's why that picture's there.
And in another life I used to work in an art gallery, but that's another story.
So this was the Archimedes palimpsest.
It appeared in Christie's in New York in 1998 where it was sold for
two million dollars.
You can see, I think here, how the writing is at right angles.
It was bought by an anonymous buyer and has been
subject to fantastic restoration work by scholars from many, many different fields.
In order to bring the Archimedes works back to life.
And I just wanted to sort of draw attention to the fact this is just such
a marvelous conjunction of modern technology and ancient text.
And these pictures I've got here show where they're actually
looking at one of the pages of the palimpsest,
what happened in between 1906 and when it appeared in Christie's.
Somebody thought that it would make it more valuable if it had
some pictures in it.
So, they put some pictures in.
[LAUGH] And they copied them from a text of a sort of the right kind of date and
just by a marvelous, really piece of sort of serendipity.
One of the experts who, when they were first looking at them,
thought they recognized one of the pictures.
And indeed they did, they saw it was an exact copy from another text.
And this is just, this slide just sort of shows how they're looking
at the machinery and technology that's using to go sort
of behind the picture and see the writing, and so on.
And there's plenty out there on the web.
They've got a very nice website about it.
And again, if you're interested it's just an extraordinary story, and
it's fantastic that we've actually got this Archimedes text.
And again it's like the Euclid one, of course.
It's several centuries after Archimedes.
One has to remember actually it's closer in time to us than it is to Archimedes and
the similar thing with the Euclid text, actually.
So, moving forward in time a bit, the Pale Manuscripts
in the British Library and this is out of my period.
I should say I'm really in, I'm really a 19th, early 20th century person.
But, I have a post graduate student who was looking at these manuscripts,
Rosey Cretney, and she was trying to see whether there was something
in these manuscripts that related to some work she was doing on continued fractions.
So, she was looking for some particular numbers.
Well, it turns out that these manuscripts are rather large and rather disorganized.
And they've been described by our dear late colleague Jackie Stedall,
30 substantial volumes, several of which contained as many as 3 or
400 pages of assorted notes, tables, rough work and jottings, many undated, untitled.
Many folios in the modern volumes contain collections of tiny scraps or
fragments carefully preserved but in no semblance of order.
So if you can imagine trying to go through these and find just a sort of sequence of
numbers, effectually what Rosey was looking for was really rather a hard task.
But she is a student at the Open University and
people sort of felt well really she should be doing her work at the Open University.
Why don't you get?
So the suggestion was made to her well why don't you get the British Library,
to digitize the Pell manuscripts.
And then you can sit at your desk and look for these numbers.
So Rosey did a little sum.
And this was [LAUGH] I think it was in 2011, around about that time.
Whereupon the suggestion was withdrawn.
[LAUGH] But anyway, I mean, again,
it's just to sort of draw your attention to some of the problems we face
when we're a historians of mathematics trying to find things in archives.
When you're trying to find connections between things,
that you can keep pace with a great pile of unordered material.
Something else, another
wonderful project now that's being digitized, the Newton Project.
Again, fantastic website, wonderful resource for us historians of math, and
one of the things I think you can see from something like this folio I've shown here.
There's lots of things going on.
There's diagrams.
There's notation.
There's writing.
And actually try to transcribe something like that and
putting it into print is quite a difficult task.
So again, it's right marvelous that we can actually see the image for ourselves.
And so far they've transcribe 6.4 million words.
That was the last time I looked at the website.
They keep a kind of running total of what they're doing.
So, I mean, imagine trying to transcribe something like that.
I mean, and then you have to make sense, of course, those texts before written,
after written, so on, you can, you have to put it into context.
But again, just to give you an idea of some of the sort of things that
historians of seventeenth century mathematics have to deal with.
Now I'm going to jump right forward to something that I've been working on.
And this was a quotation from a talk given by David Hilbert,
who was the leading German mathematician of his generation.
And he gave this talk in Paris at the International Congress of Mathematicians
and in the talk he lays out 23 problems which come a bit extended later.
And these Hilbut problems became really famous in the history of mathematics.
In mathematics they were the sort of like almost like the agenda for
pure mathematics for people to work on.
And in the sort of prelude to actually the problems,
he talked a lot about what was a good problem and so on and so forth.
And one of the things he said was this, an old French mathematician said that
a mathematical theory not to be considered complete until you made it so
clear that you can explain to the first man whom you meet on the street.
So, then the question was, who was the old French mathematician.
So we thought well, and actually with the anniversary of the Hilbert's
problems in the millennium,
a lot of things were written about the problems and Hilbert's address.
But nobody, well one person, at that point addressed the question.
So there were various proposals.
In 1937, someone suggested it was Lagrange,
2005 someone suggested it was Hermite.
Now the 1889 one, you might think, well,
that is a little bit odd because Hilbert's writing in 1900.
Well, it turns out actually, that we found out that Hilbert
took it from somebody else as an old French mathematician.
And so Shawl 's name came up in connection with the previous person who'd used this,
so we were still no further forward.
It turned out that all of these were wrong.
We found that out quietly.
So, what did we find out?
Well, we found out that actually the person who it all came to was Verigone and
it went through through Shawl, through Henry Smith,
a great professor of mathematics here at Oxford.
And it was his talk, he framed it in almost the identical way to Hilbert.
And we think it was from him that Hilbert got the phrase.
So that's why he copied it exactly.
But one of the things that we found in the correspondence between Chacon and
Petalay was that Chacon said, and I've often repeated this to my students.
But we only have this one letter from Chacon to Petalay, so
we thought well, do we have evidence for this.
And then of course I remembered that, rather curiously, because I'm a late 19th
century person, I've had my arm twisted a bit like sort of being here today.
I ended up doing some work on this person, William Henry Fox Tolbert.
And again, who's well known to most people as a pioneer in photography.
So not the obvious place to be looking for quotes about old French mathematicians.
But it turned out that in the correspondence of Fox Talbot
there was a letter from Gergonne this in French,
this is an English translation where he does repeat exactly this in fact.
Talbot's early career was in mathematics.
His first papers he published were in mathematics.
And he had an interest in mathematics, actually throughout his life.
And the last papers he published were in mathematics.
And in the course of doing my work on Fox Talbot, I, this
is something I just can't resist showing, even if it's a little bit left field.
Was that in 1915 a mathematician writing about English mathematics
used Fox Tolbert as an example of sort of English mathematics.
And he says well Fox Tolbert only vaguely remembered in connection with photography.
How times change!
So, I thought it's quite interesting.
Another person, I'm not going to go into this, but it's just sort of quite
interesting, Felix Hausdorff, who was really one of the founders of modern
topology, also had another life, another sort of literary life.
So, the scholars that have been working on his
works have had to go through 26 hours in pages of manuscripts, but
they're also having to deal with his his work with Paul.
The literary side of him.
So historians and mathematics get kind of pulled in lots of,
lots of different directions.
So it's just, they're still working on these manuscripts.
But so now, just for my last few moments,
I want to get on to my Pacifism a bit of my talk.
And this is a diary that I found in St.
John's College in Cambridge of a mathematic student.
France's Paria White was doing the mathematical Tripos in 1915.
And his diary for 1915 right up to July 1916 is there in St John's.
And it's, he writes about two thirds of an A4 page every day.
So it's an amazing document for somebody like me who's interested in trying to
understand how, what sort of mathematics was being taught in Cambridge at the time.
And of course you get lecture lists and so on, but to get a student's perspective.
Also get the student's perspective on his lecturess was quite interesting.
[LAUGH] And he's really, it's full of all kinds of things.
But here we have, this is the very first entry in the diary.
And actually what he's doing, he happened, he lived, his parents
lived in Islington actually, not very far away as it happens from where I live.
And he,
on the first day of the diary he goes to the V & A to see the Rodin exhibition.
And this was an exhibition of Rodin sculptures that Rodin had donated
To the VNA to honor the French and British soldiers fighting in the first World War.
But it's kind of not a likely place that if you were a Rodon
scholar to be thinking, you know a student, a math student at Cambridge.
And this diary is full of sort of lots of things.
So I will point out one or two others.
This is another one.
It turns out he's very interested in law.
So he goes off to the law courts and so he reports on the things that he hears.
So this particular one, he's about to go.
It looks a bit boring, and then he sees somebody
He sees the lawyers coming in with the tackler and various things.
He says, ho ho, it looks like a libel action, whoopee.
And then he sees Gladys Cooper, and actually to find out which, he wanted to
see who she was, and actually, he didn't think she was very beautiful,
even though she was kind of one of the classic beauties of the day and so on.
So I mean, there's lots of sort of things here.
And then the sort of pacifism sort of the story is that
he is a pacifist himself through religious conviction.
And so he goes to all these meetings.
So he joined the Union of Democratic Control.
This was a, they were set up to.
It wasn't strictly pacifist.
It was just to stop interference.
For government and foreign policy as one and
it was really important group and their against conscription and various things.
And the other wonderful thing in the diary is that he sticks into the diary all these
invitations, various bits of papers, so we actually have these documents, and
it's interesting for us as historians of mathematics particularly because G.
H. Hardy Who was
the leading British mathematician, pure mathematician of his generation, really,
and very much features in this particular story.
And we can trace White's, what happens to him and
various other people who are conscientious Objectives and
in reading the diary I sort of found out and discovered that actually there were
proportionally rather more mathematicians where than one would have expected from
the population as a whole and you see a very clear distinction for why it.
The way he is treated in Cambridge is an intellectual position.
When he goes home to Islington, it's terrible.
His parents are really upset, and he's going to be white-feathered.
It's really quite stark, the difference.
So you kind of get interesting things like that.
This is kind of interesting because here,
he's writing about Something he's heard about Hardy.
And Hardy's writing to Reese who he's writing this book with.
And Reese is in, White thinks he's in Copenhagen, actually he was in Stockholm.
But anyway, so he says, Hardy had occasion to write him on some mathematical subject.
The letter contained a good many mathematical symbols.
Also he mentioned the name of a German worker at the end.
The Senna got hold of the letter, determined from the German name that it
must be a code message, spent hours trying to interpret the symbols as a cipher and
then failing it, he didn't let the letter go through.
So, this is also Another
issue for us is actually notation and symbols.
For us looking particularly for historians of early period,
because there isn't Standardized notation.
It's a bit like this non-standard spelling.
But with mathematics it's, I would hazard a guess to say it's slightly easier
sometimes to work out a word someone's meaning if the spellings not quite right,
compared to if the mathematical symbols are different, or
there maybe a transcription error, or something.
So.
So I think this is a very nice example of that.
So this is another one.
He goes to see The Birth of a Nation, now this is a very famous film,
it's a racism film, hugely criticized for its kind of content.
But for its The technology that was employed in it was really,
very cutting edge, so it's celebrated for
its technological skill but not for the content.
But again, I think historians of film wouldn't necessarily think about going to
the diary of a Cambridge student to get their The reaction to the film.
And it's, you know one of the things he says here,
the pictures were some of them excellent.
But the horses would gallop at about 100 miles an hour,
and towards the end at about 200.
You know, so it's kind of how he's seeing the film.
and of course, remember,
you know going to the cinema in those days wasn't Quite the same as going today.
So as far as the conscientious objection side
of the story is concerned, White Has to go up before the tribunals.
They have these tribunals for people who are called up for conscription.
And as the war progressed,
of course, conscription became more and more encompassing.
And so we can learn quite, for me, learning about
the first World War is an amazingly Amazing sort of source in a sense.
Because here we have him saying the conscientious cases are reached,
soon became evident they wouldn't grant any exemptions.
And the chairman asked each appellant whether he drank tea.
And if so, whether this did not offend his conscience, owing to the tax.
You know, sort of hearing these kinds of questions.
And then he's He's told his appeal's dismissed and
he's got to take non-competent service and he asked for leave to appeal further and
he is refused.
So, this is going on in Cambridge, then he goes home and his father and his sister
are disappointed and upset because they think it's going to mean prison for him.
And this is really obviously very distressing.
He doesn't go to prison actually, so he ends up with a friend's ambulance service.
But there's a point during the diary where he thinks actually they have come and
arrested Lancelot Hogben and he thinks they're gonna be coming for
him so he puts all his library books in a pile in his In his room, you know, so
that they can be taken back to the library by someone else in case they
come to take him to prison.
And then this one, I think, is interesting, because here we have White
going to the tribunal and listening to various cases and
He talks about these both mathematicians, and
then he mentions Eddington, and he says, undignified to see the vive chancellor and
the master of pleading to be allowed to keep these men.
What is the university coming to?
And also in the Dairy, he keeps newspaper clippings as well.
And one of the things that we can
see from the newspaper clippings is that the university wants to give Eddington
exemption because they want him to keep working on at the observatory.
Eddington's a Quaker.
He wants to.
He wants it to go on the record that he wants exceptions for his beliefs.
And so you see this sort of tension there.
And Eddington is of course well
known to historians of Science and scientists and so on.
Particularly for his work in helping to cement Einsteins's
theory of general relativity with the eclipse expedition.
And I just thought it quite appropriate perhaps ti finish my talk with this
because of course this is the centenary Of, and just very, very recently,
of Einstein's theory of general relativity.
And it was Eddington's
expedition to Principe to where they took the photographs of the star and showed
that gravitation would actually bend the path of light going around a massive star.
So, of course, this lead me to the Einstein archives online, so
that's another fantastic archival resource for people working on Einstein or
just generally interested in Einstein and
so, with that, I'll finish.
Thank you very much.
[APPLAUSE]