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Oct 5, 2003, 12:05:56 PM10/5/03

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I'm trying to trace the use of blackboard bold

symbols (Z, N, Q, R, ...) in printed mathematics.

There are two distinct sets of letterforms in

common use: one mimics the way that these letters

are often written, as seen in Adobe's Mathematical

Pi, for instance:

http://www.myfonts.com/fonts/linotype/universal-mathematical-pi/mathematical-pi-6/testdrive.html?s=N+Q+R+Z+C&p=72

symbols (Z, N, Q, R, ...) in printed mathematics.

There are two distinct sets of letterforms in

common use: one mimics the way that these letters

are often written, as seen in Adobe's Mathematical

Pi, for instance:

http://www.myfonts.com/fonts/linotype/universal-mathematical-pi/mathematical-pi-6/testdrive.html?s=N+Q+R+Z+C&p=72

and the other just uses traditional inline letters:

http://www.myfonts.com/fonts/mathtype/euclid-math-two/euclid-math-two/testdrive.html?s=N+Q+R+Z+C&p=72

(Note: this mysterious "Euclid" is simply a

copy of the Computer Modern and AMS fonts.)

These symbols often seem to be associated with the

name Bourbaki. However the original Éléments de

Mathematique -- at least Livre II from 1958 -- uses

ordinary boldface for N, Z, Q.

Does anyone have any information about when and where

these symbols were first used in print, and which

style was first printed? I do know that the AMS has

used the inline style since the early seventies.

Thanks for any help or ideas!

Robin

Oct 5, 2003, 3:08:30 PM10/5/03

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Robin Houston <ro...@remove-this-bit.kitsite.com> writes:

>I'm trying to trace the use of blackboard bold

>symbols (Z, N, Q, R, ...) in printed mathematics.

...

>Does anyone have any information about when and where

>these symbols were first used in print, and which

>style was first printed?

[After writing all the following blather, I noticed

that the only part which is truly responsive to the

question asked is "something not completely unlike

your first set of examples appeared from Prentice-Hall

in 1965, and I find no earlier instances in my home

library". Read the rest at your peril.]

It is my impression that such symbols were first used

in polycopied/mimeographed notes, and similar materials

prepared on typewriters. Although (as I recently mentioned

in another thread in c.t.t) there was at least one office

typewriter (an Olympia) for sale by the mid 1960s with a

built-in "poor man's bold" doublestrike function, for a

long time--until the era of Typ-It insertible type bars,

and not too much later the IBM Executive and Selectric

lines of typewriters--about the best that could easily

be done to fake "bold" was to overstrike an uppercase I

(or a single quote) on your R or C. Given a Selectric,

one had the further option of doublestriking your R, C,

Z, Q, or N with a slight offset (this involved manual

intervention with the device that carried the "golf-ball"

type element, and was very hard to do consistently).

The typed notes prepared by typists in the Princeton

mathematics department sometime in the late 1950s,

and published by D. Van Nostrand Company in 1959 as

"Advanced Calculus" by Nickerson, Spencer, and Steenrod,

show no effort to fake bold in any way; Typ-It (or its

equivalent) has been used for various symbols like

\union and \in. The typed notes from the same source,

prepared in 1961 and published in 1962 by Princeton

University Press as "Lectures on Modular Forms"

(Annals of Mathematics Study 48) by Gunning is also

devoid of boldfakery, and has assorted Type-It symbols.

By 1966, however, Gunning (in "Lectures on Riemann Surfaces",

PUP Princeton Mathematical Notes) uses doublestruck C and R;

the typewriter is almost surely a Selectric (and thus, for

instance, script letters--which were typed with Typ-It in

"Lectures on Modular Form"--have been written in by hand).

Gunning very much liked the use of "blackboard bold"

(I believe it was from him that I learned to use it,

at just around that time); his 1965 textbook (with Rossi),

"Analytic Functions of Several Complex Variables", in

the Prentice-Hall Series in Modern Analysis, produced from

notes written in 1960-1962, is typeset with a *realllly*

*ugly* \mathbb{C} (it must be seen to be believed), more

in the "Mathematical Pi" than the "Euclid Math Two" style.

Going back to typescript notes: Serre's 1964 lectures at

Harvard, "Lie Algebras and Lie Groups", printed from (surely

author-supplied, camera-ready) typescript by W. A. Benjamin,

Inc., in 1965, uses a double-underline (handwritten) beneath

C and Z to denote the complex numbers and the integers,

respectively; Narasimhan's 1966 "Introduction to the Theory

of Analytic Spaces", printed from (author-supplied, camera-

ready) typescript as Springer LNM 25, looks like Selectric

Courier to me, and has all Fraktur and script characters

written in by hand, *but* has somehow arranged to have very

elegant typewritten versions of \mathbb{C} and \mathbb{R},

I have no idea how. Karoubi's thesis (University of Paris,

1967) is typewritten with no distinction for C, R, etc.,

at all (though when C stands for some category, it has a

handwritten x beneath it--very odd). Mumford's original

"Red Book" ("Introduction to Algebraic Geometry--Preliminary

version of first 3 Chapters"), which is undated and has no

publisher noted anyway (I assume it was printed by Harvard

in or about 1969) uses a mixture of over- and doublestriking

for \mathbb: doublestruck A (for "affine space"), P overstruck

with I (for "projective space").

Of all these, the authors closest to Bourbaki (Serre and

Karoubi) have, if anything, the type that's furthest from

blackboard bold.

Lee Rudolph

Oct 5, 2003, 3:16:07 PM10/5/03

to

In article <3F804164...@remove-this-bit.kitsite.com>, Robin

Houston <ro...@remove-this-bit.kitsite.com> wrote:

Houston <ro...@remove-this-bit.kitsite.com> wrote:

Compare the old AMS TeX font msym to the more recent font msbm.

The old msym is like the Mathematical Pi quoted, while the new msbm is

like the Eudlid Math 2.

Of course "new" is a relative term, and msbm has indeed been around for

a long time. But in the TeXBook (at least the first edition) in the

index under "blackboard bold" you will see a letter R in the old msym

style.

Of course this way of writing was devised for writing by hand (on a

blackboard, for example); and then adapted for use by a typewriter

(those ancient machines used before personal computers for producing

documents in a home or office environment). Produce the blackboard

bold R by typing an I and an R close together.

--

G. A. Edgar http://www.math.ohio-state.edu/~edgar/

Oct 5, 2003, 5:30:40 PM10/5/03

to

G. A. Edgar wrote:

> Compare the old AMS TeX font msym to the more recent font msbm.

> The old msym is like the Mathematical Pi quoted, while the new msbm is

> like the Eudlid Math 2.

> Compare the old AMS TeX font msym to the more recent font msbm.

> The old msym is like the Mathematical Pi quoted, while the new msbm is

> like the Eudlid Math 2.

This contradicts Barbara Beeton's claim in

http://groups.google.com/groups?selm=786755680....@MATH.AMS.ORG

I quote:

> i assure you that the doubled strokes in msym, in the sti openface

> font, and in msym are all in exactly the same places -- i checked

> all three from contemporaneous source documents before replying.

> i will be happy to produce the evidence, which is part of my

> permanent library.

Is there any reliable way to check for sure? I have access to

libraries, it's just knowing what to look for... Are there

any journals that indisputably used msym during some period?

Thanks everyone who's replied, I hope we can get to the bottom

of this one!

Robin

Oct 5, 2003, 7:47:47 PM10/5/03

to

In article <3F808D80...@remove-this-bit.kitsite.com>, Robin

Houston <ro...@remove-this-bit.kitsite.com> wrote:

Houston <ro...@remove-this-bit.kitsite.com> wrote:

OK, here are the two AMS fonts:

<http://www.math.ohio-state.edu/~edgar/BBBfonts.gif>

Don't you agree that msym looks like Mathematical Pi? (The little

swish on the Q is maybe different.) And msbm is the same as Euclid

Math 2.

Oct 6, 2003, 3:39:06 AM10/6/03

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"G. A. Edgar" <ydp4f...@sneakemail.com> writes:

>OK, here are the two AMS fonts:

>

><http://www.math.ohio-state.edu/~edgar/BBBfonts.gif>

>

>Don't you agree that msym looks like Mathematical Pi? (The little

>swish on the Q is maybe different.) And msbm is the same as Euclid

>Math 2.

>OK, here are the two AMS fonts:

>

><http://www.math.ohio-state.edu/~edgar/BBBfonts.gif>

>

>Don't you agree that msym looks like Mathematical Pi? (The little

>swish on the Q is maybe different.) And msbm is the same as Euclid

>Math 2.

you're right, of course. i remember thinking that msbm was a great

improvement, at the time it was released, but over the years there

have been people hankering after the shapes of msym. looking at them

side by side again, after all this time, i realise i was right (for my

value of "better") and they were wrong ;-)

--

Robin (the partially spineless) Fairbairns, Cambridge

Oct 6, 2003, 4:32:28 AM10/6/03

to

G. A. Edgar wrote:

> OK, here are the two AMS fonts:

>

> <http://www.math.ohio-state.edu/~edgar/BBBfonts.gif>

> OK, here are the two AMS fonts:

>

> <http://www.math.ohio-state.edu/~edgar/BBBfonts.gif>

Very useful, thanks! I see now that I have misinterpreted

Barbara's remark: she was talking only about the _location_

of the doubled strokes, which is indees the same as in msbm.

(This is different from Alan Jeffrey's bbold font, for

example, which seems to be what's shown in

http://www.w3.org/TR/MathML2/double-struck.html)

> Don't you agree that msym looks like Mathematical Pi?

Yes, absolutely. So perhaps msbm was indeed the first

use of the "inline" style for blackboard bold. That would

be surprising, since inline fonts certainly predate

blackboard bold: for example

http://www.myfonts.com/fonts/linotype/cloister-open-face/cloister-open-face/testdrive.html?s=N+Q+R+Z+C&p=72

is a font designed in 1929.

One would expect printers to use the fonts they had already

available, where possible.

Robin

Oct 6, 2003, 10:25:50 AM10/6/03

to

"G. A. Edgar" <ydp4f...@sneakemail.com> wrote in message news:<051020031516078853%ydp4f...@sneakemail.com>...

> Of course this way of writing was devised for writing by hand (on a

> blackboard, for example); and then adapted for use by a typewriter

> (those ancient machines used before personal computers for producing

> documents in a home or office environment). Produce the blackboard

> bold R by typing an I and an R close together.

I agree this style must have originated as a way to produce "bold"

letters by hand on paper or blackboard. As an attempt to narrow the

date of origin I recall not seeing this as an undergraduate at a

mathematically sophisticated school in the early 1960's but

encountering it as a graduate student in the mid-60's. But I imagine

something like this was used in Europe or Germany, especially, before

that.

Oct 6, 2003, 10:47:00 AM10/6/03

to

Yesterday I wrote:

>By 1966, however, Gunning (in "Lectures on Riemann Surfaces",

>PUP Princeton Mathematical Notes) uses doublestruck C and R;

...

>(I believe it was from him that I learned to use it,

>at just around that time);

and so on. Since writing that, I have exchanged e-mail with

Professor Gunning. Like others, he has heard that the notation

goes back to Bourbaki--more specifically, he says he picked it

up in the Kodaira-Spencer seminars (at Princeton, early 1960s),

and that someone there (whose name he can't recall) attributed

it to Bourbaki. He confirms that it was in the early 1960s

that he himself was converted to the notation, and started

passing it on to students; and he says (I paraphrase, since

I didn't ask permission to quote) that Addison-Wesley didn't

give him and Rossi any trouble about using blackboard bold

for the complex numbers (but that he and Rossi *did* have

trouble convincing A-W to allow non-bold vectors and yet

bold germs). He has also promised to ask other veterans

of the K-S seminar for their memories, which I will pass

on as they arrive. (I think I will not act on his implicit

suggestion that one might ask Serre; but if anyone else has

the chutzpah to do so, I don't doubt something useful might

be learned from the experiment.)

I hope to spend some time in the library stacks today, and

may have more data by this afternoon.

Lee Rudolph

Oct 6, 2003, 3:04:50 PM10/6/03

to

I remember noticing as an undergraduate math major (1967-1971) that

the books that I read and that used a distinctive font for these sets,

all used some sort of ordinary bold (upright or slanted). While all my

teachers used blackboard bold on the blackboard. I jumped to the

conclusion that BBB was simply a way to make a bold-like distinction

in a medium where it was not otherwise possible. I have always felt

it is overused in print. Most articles in my field (complex analysis)

don't have any other bold C in them and a simple bold letter C would

be quite sufficient.

By the way, none of my teachers added more than one extra stroke to

their ordinary uppercase letters to produce BBB. The example BBB in

the TeXBook (my edition anyway) is pretty obviously a CMR I and R

run together. (I thing it looks better than any currently available

doublestroke font and have considered adapting cmr to produce something

along those lines.)

Dan

--

Dan Luecking Department of Mathematical Sciences

University of Arkansas Fayetteville, Arkansas 72701

luecking at uark dot edu

Oct 6, 2003, 3:08:37 PM10/6/03

to

On Mon, 06 Oct 2003 09:32:28 +0100, Robin Houston

<ro...@remove-this-bit.kitsite.com> wrote:

<ro...@remove-this-bit.kitsite.com> wrote:

>G. A. Edgar wrote:

>> OK, here are the two AMS fonts:

>>

>> <http://www.math.ohio-state.edu/~edgar/BBBfonts.gif>

>

>Very useful, thanks! I see now that I have misinterpreted

>Barbara's remark: she was talking only about the _location_

>of the doubled strokes, which is indees the same as in msbm.

>(This is different from Alan Jeffrey's bbold font, for

>example, which seems to be what's shown in

>http://www.w3.org/TR/MathML2/double-struck.html)

>

>> Don't you agree that msym looks like Mathematical Pi?

>

>Yes, absolutely. So perhaps msbm was indeed the first

>use of the "inline" style for blackboard bold.

When you say "inline" do you perhaps mean "outline"? I have never heard

"inline" used in this sense.

Oct 6, 2003, 3:14:03 PM10/6/03

to

Dan Luecking <Look-...@uark.edu> writes:

> By the way, none of my teachers added more than one extra stroke to

> their ordinary uppercase letters to produce BBB. The example BBB in

> the TeXBook (my edition anyway) is pretty obviously a CMR I and R

> run together. (I thing it looks better than any currently available

> doublestroke font and have considered adapting cmr to produce

> something along those lines.)

You mean like the bbm.sty and fonts do?

--

David Kastrup, Kriemhildstr. 15, 44793 Bochum

UKTUG FAQ: <URL:http://www.tex.ac.uk/cgi-bin/texfaq2html>

Oct 6, 2003, 5:33:25 PM10/6/03

to

Dan Luecking wrote:

> When you say "inline" do you perhaps mean "outline"? I have

> never heard "inline" used in this sense.

> When you say "inline" do you perhaps mean "outline"? I have

> never heard "inline" used in this sense.

Let me quote from the typographic glossary in Robert

Bringhurst's excellent book _The Elements of Typographic Style_:

Inline: A letter in which the inner portions of the main

strokes have been carved away, leaving the edges more

or less intact. Inline faces lighten the color while

preserving the shapes and proportions of the original

face. _Outline_ letters, on the other hand, are produced

by drawing a line around the outsides of the letters

and removing the entire original form. Outline letters,

in consequence, are fatter than the originals and have

less definition.

Robin

Oct 8, 2003, 4:44:54 PM10/8/03

to

On 06 Oct 2003 21:14:03 +0200, David Kastrup <d...@gnu.org> wrote:

>Dan Luecking <Look-...@uark.edu> writes:

>> ... The example BBB in

>> the TeXBook (my edition anyway) is pretty obviously a CMR I and R

>> run together. (I think it looks better than any currently available

>> doublestroke font and have considered adapting cmr to produce

>> something along those lines.)

>

>You mean like the bbm.sty and fonts do?

No, I don't mean like that. I'm pretty sure I've checked all

"currently available" (free) doublestroke fonts. There's a

blackboard.ps by Olaf Kummer available on CTAN that lists them

(or at least those that were known to the author). And I usually

check out any new ones announced here.

As to bbm: compare the example "R" in the TeXBook (in index under

blackboard bold) to the bbm "R". Not at all alike.

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