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be concerned with the subject of topology (which is not accurate) and

since topology, according to the 14th edition of Dewey, is a subfield

of non- Euclidean geometry (which is not accurate either). Although

the classification is not correct, it is better than the other possibili-

ties I mentioned, and I would far rather leave it there than to move it

to 512.812, which is where the new, presumably more modern and

accurate, 16th edition of the Dewey classification system would have

it put. Why would they place it there? Because, I am sure, that the

designers of this system are under the impression that "measure

theory" deals with ideas connected with divisibility and the old-

fashioned theory of measurement, sometimes called "mensuration."

94

They made a guess which sounded plausible, but they are wrong. It is

certainly easy to be misled by the similarity of the words "measure

theory" and "mensuration," but I regret that the Library of Congress

found it necessary to guess not only about the classification of a single

book, but about an entire subject.

Another error that it is easy to commit is to group together books

dealing with subjects (or objects) identified in part by the name of a

man. For example, the 16th edition of Dewey classifies together, in

517.81, books dealing with Riemann surfaces and the Riemann zeta

function, even though the content of these books is quite different.

Again, one not familiar with the technical nature of these two subjects

could not know that they are so different, but I do not feel that one who

does not have this familiarity should be revising the classification

system without considerable advice.

I have chosen only two examples of errors of this type; others could

be adduced if there were any point in doing so.

CROSS FIELDS

There is another phenomenon that occurs in mathematical termin-

ology, although I am sure that it is probably present in most other

fields, as well, I refer to the interplay between various subareas

which makes difficulties for a linear system of classification. In a

sense, mathematics can be broken into five main areas of specializa-

tion: algebra, geometry, analysis, a newer area called topology, and

applied mathematics (including statistics, mathematical physics, etc.).

(In making this division, I have ignored topics such as mathematical

logic or the history of mathematics, since I regard these areas as

applied logic and applied history.) In addition to these five main

fields there are familiar cross fields such as analytic geometry,

which is primarily geometry, and algebraic geometry, which was

geometry in the past but has recently become primarily algebraic and

should be called "algebra with geometric terminology" or simply

"geometric algebra." Recently, the similar-sounding fields of

"algebraic topology" and "topological algebra" have appeared on the

scene. Unfortunately, it is the case that at the present time both

terms are misnomers. What is presently done in the temple of

"algebraic topology" is algebra, and I think no one disputes it. Worse

yet, what most people now do under the name of "topological algebra"

is neither algebra nor topology, but really analysis. Even mathe-

maticians, who tend to be somewhat perverse in their humor, do not

like this terminological mess and these two misleading terms are

gradually being replaced by the more technical and temporarily more

accurate terms "homological algebra" and "functional analysis."

I have gone into this fairly extended and relatively technical dis-

cussion, not primarily to amuse you with the quixotic character of

mathematicians who can't say what they mean or to amuse myself by

joking at librarians who can't guess what the mathematicians mean

95

by what they say. My point is that even carefully chosen words devel-

op new and different meanings, that subject areas merge and change

in content and In direction, and that the outsider has little hope of

guessing correctly.

The remarks I have just made apply to myself just as much as

anyone. Although I have spent some time studying mathematics and

have a fairly good exposure to the kind of things studied in its various

branches and specialties, I do NOT have the knowledge to classify

accurately the mathematics books published today in a system as

detailed as the Dewey or the Library of Congress systems. On a

number of occasions when I have been consulted by our mathematics

librarian, I have not been able to specify the classification without

consulting one of my colleagues in the mathematics department. The

subject of mathematics is entirely too large and complex for a single

man, even a specialist in the field, to keep up in it and to have a de-

tailed knowledge of its interconnections, let alone the main results.

Not only has the universal scholar disappeared, but even the universal

geometer has gone from the scene.

CLASSIFICATION BY SERIES

I have already noted, with disparaging tones, the practice of clas-

sifying books in series. Unquestionably this is appropriate in the

case of journals and many of the publications of universities and

learned societies. However, I have serious doubt as to its wisdom in

the case of a sequence 2 (I purposely avoid the term "series") of

books put out by a commercial publisher, unless there is a clear

underlying principle or unless the books deal with the same subject.

One of the absurd results of this method of classification is that a

translation, or a later edition, of a book may be separated from the

original. Surely this is a mistake !

I am aware of the greater simplicity and the routine nature of as-

signing a number to an incoming member of a serial publication.

Nevertheless, I believe it to be a poor procedure to follow and an

evasion of the problem of finding the proper classification. Perhaps

one reason I object is that practically all of the publication of mathe-

matical books is in sequences, but another reason is that I believe

that this method is nothing more than a classification by color and

design of the binding. One problem I have heard of is the inability of

placing a standing order on a sequence of books without assigning the

work to the serials division and thus accepting a serial classification.

Although it may not be good economics, in most cases I would prefer

to order the books separately than do this.

THE DEWEY SYSTEM IN MATHEMATICS

There are a few comments that I should like to make concerning

the Dewey mathematical classification. The main one is that it is

96

about fifty years out of date. Nevertheless, I suspect that it is prob-

ably rather satisfactory in a small library, particularly one which

does not contain many books in the newer areas of research. For in-

stance, I think it would do quite satisfactorily for a teaching-oriented

liberal arts college with only a thousand or so books. The trouble

comes when one attempts to give a detailed classification of the books

in the newer branches where there is considerable research activity,

since the system does not take these areas into account. Even the

new 16th edition does not take much cognizance of the extensive de-

velopments of the earlier decades of this century, so it is hardly

possible to find a location for the diverse further investigations in

these newer areas. As an example, the important new branch of

topology is relegated to 513.83, which, in addition to being an obscure

location, is also inexact, since topology is not a subfield of non-

Euclidean geometry. To subdivide the books in the several new

branches of topology, as might be desired, would cause the numbering

system to become unwieldy. It would seem that a larger category

must be assigned to this field if one wishes to maintain the present

level of detail in the system.

The other side of the coin is that there is considerable waste in

the Dewey mathematical classification as it stands. Let me recall

the basic outline of the system. It is as follows:

510 Mathematics (including works on Mathematics in general,

collections, dictionaries, journals, etc.)

511 Arithmetic

512 Algebra

513 Elementary Euclidean geometry (including non-Euclidean

geometry) 3

514 Trigonometry

515 Descriptive geometry and projections

516 Analytic geometry (including algebraic geometry 4 )

517 Calculus

518 Not assigned 5

519 Probabilities 6

6

The category 511, though needed for smaller libraries, is mostly

wasted and should probably be consolidated with algebra in research

libraries. I believe that the University of Illinois library has only

about 200 books in this category, of which about one- half deal with

commercial arithmetic and a large number are old textbooks which

have mistakenly found their way into the stacks. Most of 512 is wasted

in our library, only our subcategory 512.8 is available for modern

mathematics, and it contains almost five times as many books as all

the other subcategories combined (even though we do have a number

of old algebra textbooks in these other divisions). The same situation

occurs in 513 and 516, although to a lesser degree. Entry 514 is a

dramatic waste, since trigonometry is such a tiny subject. We have

97

about 200 books in this category and would probably do just as well

with one tenth as many. Still worse, from a mathematician's point

of view, is 515; it is all waste, for the mathematical portion of

"descriptive geometry" is a very small portion of "projective geo-

metry" and the remainder (that is, the major portion of the subject)

is not mathematics at all, but mechanical drawing. At the University

of Illinois the category 517 is well used and, in fact, our local ground

rules permit us to let it spill over into the unassigned category 518.

In addition to a few textbooks on calculus, these categories contain

many hundreds of books in mathematical analysis. As might be ex-

pected, 519 has a substantial number of entries, even though the ap-

plications of mathematics to physics and engineering are not included

there. This may give an idea how uneven the system is in a large,

up-to-date mathematical library.

I have already indicated that I think the Dewey system is fairly well

suited for a small library which does not attempt to acquire modern

research books in mathematics, but whose books are mostly those

that would be needed for undergraduate instruction. The system is

rather appropriate for books on this level, and was probably designed

with these libraries in mind. But I also believe that for a library of

this size and depth there is not much need to go beyond the ten cate-

gories 510 to 519. Some additional division might prove useful,

particularly in the 510 group, but I doubt that much is really needed.

In a large library where there will be several thousand books on

mathematics more division is helpful but only to the extent that it

truly conforms to the nature of the subject. Obviously a classification

system can never be up-to-date, for there are sudden spurts in the

development of certain areas followed by long periods of inactivity.

One must be conservative in changing the system and no change is

worthwhile unless it is a basic and a fundamental change. Despite

these remarks, I do feel that the Dewey system in mathematics needs

to be updated if it is to provide a detailed system of classification,

for it does not even get close to the frontier. However, one of the

questions that must be decided is whether such a detailed system is

really desirable and whether it is even possible at the present time.

To my mind, the 16th edition of Dewey does not solve any of the

real problems. It corrects a few errors, but propagates most of the

old ones plus a few new ones that would be unfortunate to introduce.

It is certainly not a step forward, and I doubt that its good features

are worth the cost and confusion that a change would cause.

POSSIBLE CHANGES AND MODIFICATIONS

There are many problems that must be solved by any new system

and I am sure that everyone here is better acquainted with most of

them than I, so I shall refrain from going into much detail. Still, let

me list a few desiderata for any new system that occur to me.

98

1) It should accomodate small libraries easily.

2) It should be appropriate for large research libraries.

3) It should allow the classifier to assign class numbers to the

books quickly and accurately.

4) It should be simple enough so the faculty can understand it.

5) It should permit future modifications.

6) It should not be too expensive to adopt.

There are certainly other desirable things that we might hope for.

but we have already been somewhat optimistic. As you might expect.

I am not going to present a completely-worked out solution to this

problem today. I do believe that a thoroughly satisfactory system is

possible. However, I believe that any such solution must be the pro-

duct of joint thinking and arguing on the part of both librarians and

mathematicians. I am convinced that neither group can reach a real!

satisfactory solution without the other, for I believe that a non-speci;

ist is unable to decide what the basic categories in a field are and is

unable to determine how these categories are related without con-

sulting a specialist. Further, I believe that the specialists are not

sufficiently aware of library procedure and problems to anticipate

all the difficulties that come up in practice.

Desired property 3, perhaps, can use some amplification. I can-

not overemphasize the importance of quick and accurate classificatic

In the mathematics of today (as in most fields) the first few years of

most books' lives are the most useful ones. If it takes several month

to obtain a book and then several weeks to classify it, much of its

value has been dissipated. Also, if the actual classification of the

book turns out to be inexact, it may not reach the hands of a user

while it is of prime value. I should also like to note that there is

still some indefiniteness about the nature of the classifier referred

to in 3 it is obvious that the more detailed and specific the classifi-

cation system is, the more specialized the classifier must be in orde

to be quick and accurate in his work.

Desired property 4 is not to be overlooked, either. You know bett

than I how well the average professor really understands the system

he is using and complaining about. (I leave open the question of whet

er he might complain more or less, if he understood it.)

Before I turn to a slightly different topic, I should like to make

reference to a method used in the classification of research papers

by the Mathematical Reviews, which is published by the American

Mathematical Society. This system has almost no resemblance to

either the Dewey or the Library of Congress system, partly because

it is right up-to-date, partly because it was made by mathematicians

partly because it is designed for papers and not books, and partly be-

cause it does not take into consideration many problems that a librar

classification must consider. Nevertheless it is interesting and any

of you who are concerned with this problem would do well to write to

the editors of the Mathematical Reviews and get a copy.

99

HOW ELABORATE?

Before a more satisfactory system is created, there is a basic

question that must be settled. It is to decide how elaborate and de-

tailed the system is to be and, of course, this is intimately tied with

who does the classifying. Clearly there is an advantage in having a

system in which one knows exactly where the books on the Fredholm

integral equation of the first kind are to be found. However, the ad-

vantages of such a refined system largely evaporate if, either (1) most

books dealing with this topic also deal with another topic, or (2) the

subdivisions are so small and numerous that they are frequently

missed and the book shelved elsewhere, more or less by mistake. I

believe that only a mathematician who specializes in the area can

really determine whether (1) is apt to be the case, and to a large ex-

tent (2) is up to the classifier.

I maintain that a system is too elaborate for a given institution

when most of the detailed categories have only a few entries. I be-

lieve it is too elaborate for the classifier in a given institution if he

is unable to classify quickly and accurately most (say 95%) of the

books. I would further say that the system is too elaborate for the

faculty of the institution if they are not able to keep in mind the

scheme used in classifying books in their area of specialization.

Although an updated system would be a great help, I do not believe

that I would meet my own adequacy criterion on speed and accuracy

for a system as detailed as the present Dewey or Library of Congress

systems. Further, I do not think that any single person, be he li-

brarian or mathematician, can meet this criterion in any case there

are not enough of them to go around. Therefore, unless each institu-

tion is to have a panel for the classification of mathematics a situa-

tion I find somewhat difficult to imagine I believe the alternatives

are (1) to have the more technical books classified by some central-

ized bureau, (2) to encourage the classification to be done in part by

the author and/or the publisher, and (3) to simplify the system of

classification mostly by reducing the number of subdivisions. Ac-

tually I would like all three of these to be employed to some extent,

but I think that the third is by far the most important and most

practical.

It seems to me that the Library of Congress is the natural organ-

ization to attend to the more technical books, but it is my understand-

ing that they do not always suggest classification and, as I have indi-

cated, when they do make such suggestions in mathematics they are

frequently wrong. Certainly they need more mathematical advice

than they are presently getting. If they are not able to obtain technical

advice directly, then they should turn to the various technical socie-

ties, such as the American Mathematical Society, the American

Chemical Society, etc. Another possibility is that various of the re-

viewing organs (which appear to be staffed primarily by scientific

personnel), might lend their aid in the classification of the more

technical books and/ or the propagation of this information. In any

case, I see no reasonable alternative to some type of collaboration

between people trained in library science and people trained in the

particular disciplines.

An elaborate system puts extreme demands on the classifier and

on the user. The more detailed the system, the more difficult it is

for both the classifier and the researcher to learn and to use, the

more rapidly it goes out of date, the more sensitive it is to errors of

classification and to shifts in the emphasis in the subject matter. My

personal feeling is that a highly refined classification in mathematics

is not practical at this time.

Since I have come out for a simple system, let me be specific as to

how simple I would make it. I have in mind a system of basic cate-

gories that would be used by small non-research mathematics li-

braries with additional categories that would be of use to a more ex-

tensive library. For the smaller library, after giving items like

mathematical tables, collected works, history of mathematics, and

dictionaries and encyclopedias of mathematics their separate entries

and adding 30% out of conservatism, I come up with the grand total of

twenty. I think that even the largest research mathematics library

does not really need more than fifty divisions in mathematics. (My

real figure is thirty-two, but conservatism makes me jump to the

larger figure. I have discussed this matter with a colleague at North-

western University, and his suggested figure was seven, but I think he

may be somewhat radical.) One of the best research mathematics

libraries in the country, at the Institute for Advanced Study at Prince-

ton, has found that it does nicely with two categories books and

journals. (It is only honest to admit that they are not at all concerned

with elementary books and purposely want to keep the system simple,

since most of their users are only there for a year or so.)

SUMMARY

Let me summarize my remarks.

1) I believe the present Dewey system in mathematics has profound

drawbacks and should be changed to conform more to the present

nature of the subject.

2) I suggest the Library of Congress obtain help from a panel of

mathematical specialists both in regard to the system and the actual

classification of individual books. Assistance might be forthcoming

from its sister organization, the National Academy of Sciences, or

from the editorial board of the Mathematical Reviews, or from the

International Mathematics Union, or from the American Mathematical

Society.

3) I believe it should be examined as to how detailed a mathemati-

cal classification system we need and can properly apply. My own

101

opinion is that we could reduce drastically the number of categories

without harm and with a gain in simplicity.

4) I think the list of approved subject headings should be revised

in the light of current mathematics. If a small number of classifica-

tion entries is employed, a fuller list of subject headings might be

useful. In any case a modernization is in order.

5) I feel that the author of a book has the most intimate knowledge

of its content and is best qualified to indicate appropriate subject

headings. To some extent, he could assist in the classification.

6) The publisher should be encouraged to print the classification

number and the subject headings inside the book along with the num-

ber of the Library of Congress card which many of them now carry.

Agreement on the classification number and the headings might be

accomplished at the time of the application for copyright.

In conclusion, I would like to say that I am at least cognizant that

there are many difficulties which would have to be surmounted in

accomplishing these proposals and not so idealistic that I expect

much to come of them. However, I believe that the cost of inaugurating

and implementing these hastily sketched suggestions would be small

compared to the present procedures. I believe that the salvation, at

least of mathematical classification, lies in its simplification and in

the use of specialists for consultation, and not in the use of library

gimmicks such as classification by series.

Notes

1. Another joke is that a book entitled Rings and Ideals was clas-

sified as fiction.

2. The collection of numbers: 1, |-, g-, ^, ...,-,..., is a

sequence. If we attempt to add it up, we get the famous "harmonic

series," l+5- + y + ;r+- + n + wnich fails to converge

and so is better left as a sequence. It seems that mathematicians

turn sequences into series by trying to add them whereas librarians

do so by classification and binding them together. Sometimes they

are best left alone.

3. This is a 16th edition heading; in the 14th edition the term is

Geometry.

4. The Algebraic Geometry was added in the 16th edition.

5. No subject is assigned to 518 in the 14th edition, but the 15th

edition assigned it to Special Functions.

6. The heading Probabilities was changed to Probabilities and

Statistical Mathematics in the 16th edition.

102

Classification in a

Special Library

Isabel Howell

Director, State Library Division,

Tennessee State Library and Archives

A paper which is to be read before an audience of librarians and

students at a conference held as one of the activities of a distinguished

Graduate Library School should doubtless begin with a definition of

terms. This would be fine, but this paper is scheduled near the end of

a three-day session, and it seems likely that a great deal of defining

of terms will have taken place already before this combatant takes the

field. Already many a shower of word-arrows will have darkened the

sky before this knight-errant thunders over the turf. In which quarter

the battle will have been fought to a pale, pink finish and where the

refugees may have fled before this Don Quixote is wheeled into posi-

tion for the charge, there is no way to predict. But this paper has a

specific title, and the writer has a specific purpose and even at the

risk of repeating what is already well-known to everybody, I feel ob-

liged to begin With a few general remarks, call them definitions, if

you please, for the sake of the record.

The simplest definition of a special library is this: A special li-

brary is a collection of books devoted to a special subject. But for

purposes of organizing a discussion of classification this simplicity

since topology, according to the 14th edition of Dewey, is a subfield

of non- Euclidean geometry (which is not accurate either). Although

the classification is not correct, it is better than the other possibili-

ties I mentioned, and I would far rather leave it there than to move it

to 512.812, which is where the new, presumably more modern and

accurate, 16th edition of the Dewey classification system would have

it put. Why would they place it there? Because, I am sure, that the

designers of this system are under the impression that "measure

theory" deals with ideas connected with divisibility and the old-

fashioned theory of measurement, sometimes called "mensuration."

94

They made a guess which sounded plausible, but they are wrong. It is

certainly easy to be misled by the similarity of the words "measure

theory" and "mensuration," but I regret that the Library of Congress

found it necessary to guess not only about the classification of a single

book, but about an entire subject.

Another error that it is easy to commit is to group together books

dealing with subjects (or objects) identified in part by the name of a

man. For example, the 16th edition of Dewey classifies together, in

517.81, books dealing with Riemann surfaces and the Riemann zeta

function, even though the content of these books is quite different.

Again, one not familiar with the technical nature of these two subjects

could not know that they are so different, but I do not feel that one who

does not have this familiarity should be revising the classification

system without considerable advice.

I have chosen only two examples of errors of this type; others could

be adduced if there were any point in doing so.

CROSS FIELDS

There is another phenomenon that occurs in mathematical termin-

ology, although I am sure that it is probably present in most other

fields, as well, I refer to the interplay between various subareas

which makes difficulties for a linear system of classification. In a

sense, mathematics can be broken into five main areas of specializa-

tion: algebra, geometry, analysis, a newer area called topology, and

applied mathematics (including statistics, mathematical physics, etc.).

(In making this division, I have ignored topics such as mathematical

logic or the history of mathematics, since I regard these areas as

applied logic and applied history.) In addition to these five main

fields there are familiar cross fields such as analytic geometry,

which is primarily geometry, and algebraic geometry, which was

geometry in the past but has recently become primarily algebraic and

should be called "algebra with geometric terminology" or simply

"geometric algebra." Recently, the similar-sounding fields of

"algebraic topology" and "topological algebra" have appeared on the

scene. Unfortunately, it is the case that at the present time both

terms are misnomers. What is presently done in the temple of

"algebraic topology" is algebra, and I think no one disputes it. Worse

yet, what most people now do under the name of "topological algebra"

is neither algebra nor topology, but really analysis. Even mathe-

maticians, who tend to be somewhat perverse in their humor, do not

like this terminological mess and these two misleading terms are

gradually being replaced by the more technical and temporarily more

accurate terms "homological algebra" and "functional analysis."

I have gone into this fairly extended and relatively technical dis-

cussion, not primarily to amuse you with the quixotic character of

mathematicians who can't say what they mean or to amuse myself by

joking at librarians who can't guess what the mathematicians mean

95

by what they say. My point is that even carefully chosen words devel-

op new and different meanings, that subject areas merge and change

in content and In direction, and that the outsider has little hope of

guessing correctly.

The remarks I have just made apply to myself just as much as

anyone. Although I have spent some time studying mathematics and

have a fairly good exposure to the kind of things studied in its various

branches and specialties, I do NOT have the knowledge to classify

accurately the mathematics books published today in a system as

detailed as the Dewey or the Library of Congress systems. On a

number of occasions when I have been consulted by our mathematics

librarian, I have not been able to specify the classification without

consulting one of my colleagues in the mathematics department. The

subject of mathematics is entirely too large and complex for a single

man, even a specialist in the field, to keep up in it and to have a de-

tailed knowledge of its interconnections, let alone the main results.

Not only has the universal scholar disappeared, but even the universal

geometer has gone from the scene.

CLASSIFICATION BY SERIES

I have already noted, with disparaging tones, the practice of clas-

sifying books in series. Unquestionably this is appropriate in the

case of journals and many of the publications of universities and

learned societies. However, I have serious doubt as to its wisdom in

the case of a sequence 2 (I purposely avoid the term "series") of

books put out by a commercial publisher, unless there is a clear

underlying principle or unless the books deal with the same subject.

One of the absurd results of this method of classification is that a

translation, or a later edition, of a book may be separated from the

original. Surely this is a mistake !

I am aware of the greater simplicity and the routine nature of as-

signing a number to an incoming member of a serial publication.

Nevertheless, I believe it to be a poor procedure to follow and an

evasion of the problem of finding the proper classification. Perhaps

one reason I object is that practically all of the publication of mathe-

matical books is in sequences, but another reason is that I believe

that this method is nothing more than a classification by color and

design of the binding. One problem I have heard of is the inability of

placing a standing order on a sequence of books without assigning the

work to the serials division and thus accepting a serial classification.

Although it may not be good economics, in most cases I would prefer

to order the books separately than do this.

THE DEWEY SYSTEM IN MATHEMATICS

There are a few comments that I should like to make concerning

the Dewey mathematical classification. The main one is that it is

96

about fifty years out of date. Nevertheless, I suspect that it is prob-

ably rather satisfactory in a small library, particularly one which

does not contain many books in the newer areas of research. For in-

stance, I think it would do quite satisfactorily for a teaching-oriented

liberal arts college with only a thousand or so books. The trouble

comes when one attempts to give a detailed classification of the books

in the newer branches where there is considerable research activity,

since the system does not take these areas into account. Even the

new 16th edition does not take much cognizance of the extensive de-

velopments of the earlier decades of this century, so it is hardly

possible to find a location for the diverse further investigations in

these newer areas. As an example, the important new branch of

topology is relegated to 513.83, which, in addition to being an obscure

location, is also inexact, since topology is not a subfield of non-

Euclidean geometry. To subdivide the books in the several new

branches of topology, as might be desired, would cause the numbering

system to become unwieldy. It would seem that a larger category

must be assigned to this field if one wishes to maintain the present

level of detail in the system.

The other side of the coin is that there is considerable waste in

the Dewey mathematical classification as it stands. Let me recall

the basic outline of the system. It is as follows:

510 Mathematics (including works on Mathematics in general,

collections, dictionaries, journals, etc.)

511 Arithmetic

512 Algebra

513 Elementary Euclidean geometry (including non-Euclidean

geometry) 3

514 Trigonometry

515 Descriptive geometry and projections

516 Analytic geometry (including algebraic geometry 4 )

517 Calculus

518 Not assigned 5

519 Probabilities 6

6

The category 511, though needed for smaller libraries, is mostly

wasted and should probably be consolidated with algebra in research

libraries. I believe that the University of Illinois library has only

about 200 books in this category, of which about one- half deal with

commercial arithmetic and a large number are old textbooks which

have mistakenly found their way into the stacks. Most of 512 is wasted

in our library, only our subcategory 512.8 is available for modern

mathematics, and it contains almost five times as many books as all

the other subcategories combined (even though we do have a number

of old algebra textbooks in these other divisions). The same situation

occurs in 513 and 516, although to a lesser degree. Entry 514 is a

dramatic waste, since trigonometry is such a tiny subject. We have

97

about 200 books in this category and would probably do just as well

with one tenth as many. Still worse, from a mathematician's point

of view, is 515; it is all waste, for the mathematical portion of

"descriptive geometry" is a very small portion of "projective geo-

metry" and the remainder (that is, the major portion of the subject)

is not mathematics at all, but mechanical drawing. At the University

of Illinois the category 517 is well used and, in fact, our local ground

rules permit us to let it spill over into the unassigned category 518.

In addition to a few textbooks on calculus, these categories contain

many hundreds of books in mathematical analysis. As might be ex-

pected, 519 has a substantial number of entries, even though the ap-

plications of mathematics to physics and engineering are not included

there. This may give an idea how uneven the system is in a large,

up-to-date mathematical library.

I have already indicated that I think the Dewey system is fairly well

suited for a small library which does not attempt to acquire modern

research books in mathematics, but whose books are mostly those

that would be needed for undergraduate instruction. The system is

rather appropriate for books on this level, and was probably designed

with these libraries in mind. But I also believe that for a library of

this size and depth there is not much need to go beyond the ten cate-

gories 510 to 519. Some additional division might prove useful,

particularly in the 510 group, but I doubt that much is really needed.

In a large library where there will be several thousand books on

mathematics more division is helpful but only to the extent that it

truly conforms to the nature of the subject. Obviously a classification

system can never be up-to-date, for there are sudden spurts in the

development of certain areas followed by long periods of inactivity.

One must be conservative in changing the system and no change is

worthwhile unless it is a basic and a fundamental change. Despite

these remarks, I do feel that the Dewey system in mathematics needs

to be updated if it is to provide a detailed system of classification,

for it does not even get close to the frontier. However, one of the

questions that must be decided is whether such a detailed system is

really desirable and whether it is even possible at the present time.

To my mind, the 16th edition of Dewey does not solve any of the

real problems. It corrects a few errors, but propagates most of the

old ones plus a few new ones that would be unfortunate to introduce.

It is certainly not a step forward, and I doubt that its good features

are worth the cost and confusion that a change would cause.

POSSIBLE CHANGES AND MODIFICATIONS

There are many problems that must be solved by any new system

and I am sure that everyone here is better acquainted with most of

them than I, so I shall refrain from going into much detail. Still, let

me list a few desiderata for any new system that occur to me.

98

1) It should accomodate small libraries easily.

2) It should be appropriate for large research libraries.

3) It should allow the classifier to assign class numbers to the

books quickly and accurately.

4) It should be simple enough so the faculty can understand it.

5) It should permit future modifications.

6) It should not be too expensive to adopt.

There are certainly other desirable things that we might hope for.

but we have already been somewhat optimistic. As you might expect.

I am not going to present a completely-worked out solution to this

problem today. I do believe that a thoroughly satisfactory system is

possible. However, I believe that any such solution must be the pro-

duct of joint thinking and arguing on the part of both librarians and

mathematicians. I am convinced that neither group can reach a real!

satisfactory solution without the other, for I believe that a non-speci;

ist is unable to decide what the basic categories in a field are and is

unable to determine how these categories are related without con-

sulting a specialist. Further, I believe that the specialists are not

sufficiently aware of library procedure and problems to anticipate

all the difficulties that come up in practice.

Desired property 3, perhaps, can use some amplification. I can-

not overemphasize the importance of quick and accurate classificatic

In the mathematics of today (as in most fields) the first few years of

most books' lives are the most useful ones. If it takes several month

to obtain a book and then several weeks to classify it, much of its

value has been dissipated. Also, if the actual classification of the

book turns out to be inexact, it may not reach the hands of a user

while it is of prime value. I should also like to note that there is

still some indefiniteness about the nature of the classifier referred

to in 3 it is obvious that the more detailed and specific the classifi-

cation system is, the more specialized the classifier must be in orde

to be quick and accurate in his work.

Desired property 4 is not to be overlooked, either. You know bett

than I how well the average professor really understands the system

he is using and complaining about. (I leave open the question of whet

er he might complain more or less, if he understood it.)

Before I turn to a slightly different topic, I should like to make

reference to a method used in the classification of research papers

by the Mathematical Reviews, which is published by the American

Mathematical Society. This system has almost no resemblance to

either the Dewey or the Library of Congress system, partly because

it is right up-to-date, partly because it was made by mathematicians

partly because it is designed for papers and not books, and partly be-

cause it does not take into consideration many problems that a librar

classification must consider. Nevertheless it is interesting and any

of you who are concerned with this problem would do well to write to

the editors of the Mathematical Reviews and get a copy.

99

HOW ELABORATE?

Before a more satisfactory system is created, there is a basic

question that must be settled. It is to decide how elaborate and de-

tailed the system is to be and, of course, this is intimately tied with

who does the classifying. Clearly there is an advantage in having a

system in which one knows exactly where the books on the Fredholm

integral equation of the first kind are to be found. However, the ad-

vantages of such a refined system largely evaporate if, either (1) most

books dealing with this topic also deal with another topic, or (2) the

subdivisions are so small and numerous that they are frequently

missed and the book shelved elsewhere, more or less by mistake. I

believe that only a mathematician who specializes in the area can

really determine whether (1) is apt to be the case, and to a large ex-

tent (2) is up to the classifier.

I maintain that a system is too elaborate for a given institution

when most of the detailed categories have only a few entries. I be-

lieve it is too elaborate for the classifier in a given institution if he

is unable to classify quickly and accurately most (say 95%) of the

books. I would further say that the system is too elaborate for the

faculty of the institution if they are not able to keep in mind the

scheme used in classifying books in their area of specialization.

Although an updated system would be a great help, I do not believe

that I would meet my own adequacy criterion on speed and accuracy

for a system as detailed as the present Dewey or Library of Congress

systems. Further, I do not think that any single person, be he li-

brarian or mathematician, can meet this criterion in any case there

are not enough of them to go around. Therefore, unless each institu-

tion is to have a panel for the classification of mathematics a situa-

tion I find somewhat difficult to imagine I believe the alternatives

are (1) to have the more technical books classified by some central-

ized bureau, (2) to encourage the classification to be done in part by

the author and/or the publisher, and (3) to simplify the system of

classification mostly by reducing the number of subdivisions. Ac-

tually I would like all three of these to be employed to some extent,

but I think that the third is by far the most important and most

practical.

It seems to me that the Library of Congress is the natural organ-

ization to attend to the more technical books, but it is my understand-

ing that they do not always suggest classification and, as I have indi-

cated, when they do make such suggestions in mathematics they are

frequently wrong. Certainly they need more mathematical advice

than they are presently getting. If they are not able to obtain technical

advice directly, then they should turn to the various technical socie-

ties, such as the American Mathematical Society, the American

Chemical Society, etc. Another possibility is that various of the re-

viewing organs (which appear to be staffed primarily by scientific

personnel), might lend their aid in the classification of the more

technical books and/ or the propagation of this information. In any

case, I see no reasonable alternative to some type of collaboration

between people trained in library science and people trained in the

particular disciplines.

An elaborate system puts extreme demands on the classifier and

on the user. The more detailed the system, the more difficult it is

for both the classifier and the researcher to learn and to use, the

more rapidly it goes out of date, the more sensitive it is to errors of

classification and to shifts in the emphasis in the subject matter. My

personal feeling is that a highly refined classification in mathematics

is not practical at this time.

Since I have come out for a simple system, let me be specific as to

how simple I would make it. I have in mind a system of basic cate-

gories that would be used by small non-research mathematics li-

braries with additional categories that would be of use to a more ex-

tensive library. For the smaller library, after giving items like

mathematical tables, collected works, history of mathematics, and

dictionaries and encyclopedias of mathematics their separate entries

and adding 30% out of conservatism, I come up with the grand total of

twenty. I think that even the largest research mathematics library

does not really need more than fifty divisions in mathematics. (My

real figure is thirty-two, but conservatism makes me jump to the

larger figure. I have discussed this matter with a colleague at North-

western University, and his suggested figure was seven, but I think he

may be somewhat radical.) One of the best research mathematics

libraries in the country, at the Institute for Advanced Study at Prince-

ton, has found that it does nicely with two categories books and

journals. (It is only honest to admit that they are not at all concerned

with elementary books and purposely want to keep the system simple,

since most of their users are only there for a year or so.)

SUMMARY

Let me summarize my remarks.

1) I believe the present Dewey system in mathematics has profound

drawbacks and should be changed to conform more to the present

nature of the subject.

2) I suggest the Library of Congress obtain help from a panel of

mathematical specialists both in regard to the system and the actual

classification of individual books. Assistance might be forthcoming

from its sister organization, the National Academy of Sciences, or

from the editorial board of the Mathematical Reviews, or from the

International Mathematics Union, or from the American Mathematical

Society.

3) I believe it should be examined as to how detailed a mathemati-

cal classification system we need and can properly apply. My own

101

opinion is that we could reduce drastically the number of categories

without harm and with a gain in simplicity.

4) I think the list of approved subject headings should be revised

in the light of current mathematics. If a small number of classifica-

tion entries is employed, a fuller list of subject headings might be

useful. In any case a modernization is in order.

5) I feel that the author of a book has the most intimate knowledge

of its content and is best qualified to indicate appropriate subject

headings. To some extent, he could assist in the classification.

6) The publisher should be encouraged to print the classification

number and the subject headings inside the book along with the num-

ber of the Library of Congress card which many of them now carry.

Agreement on the classification number and the headings might be

accomplished at the time of the application for copyright.

In conclusion, I would like to say that I am at least cognizant that

there are many difficulties which would have to be surmounted in

accomplishing these proposals and not so idealistic that I expect

much to come of them. However, I believe that the cost of inaugurating

and implementing these hastily sketched suggestions would be small

compared to the present procedures. I believe that the salvation, at

least of mathematical classification, lies in its simplification and in

the use of specialists for consultation, and not in the use of library

gimmicks such as classification by series.

Notes

1. Another joke is that a book entitled Rings and Ideals was clas-

sified as fiction.

2. The collection of numbers: 1, |-, g-, ^, ...,-,..., is a

sequence. If we attempt to add it up, we get the famous "harmonic

series," l+5- + y + ;r+- + n + wnich fails to converge

and so is better left as a sequence. It seems that mathematicians

turn sequences into series by trying to add them whereas librarians

do so by classification and binding them together. Sometimes they

are best left alone.

3. This is a 16th edition heading; in the 14th edition the term is

Geometry.

4. The Algebraic Geometry was added in the 16th edition.

5. No subject is assigned to 518 in the 14th edition, but the 15th

edition assigned it to Special Functions.

6. The heading Probabilities was changed to Probabilities and

Statistical Mathematics in the 16th edition.

102

Classification in a

Special Library

Isabel Howell

Director, State Library Division,

Tennessee State Library and Archives

A paper which is to be read before an audience of librarians and

students at a conference held as one of the activities of a distinguished

Graduate Library School should doubtless begin with a definition of

terms. This would be fine, but this paper is scheduled near the end of

a three-day session, and it seems likely that a great deal of defining

of terms will have taken place already before this combatant takes the

field. Already many a shower of word-arrows will have darkened the

sky before this knight-errant thunders over the turf. In which quarter

the battle will have been fought to a pale, pink finish and where the

refugees may have fled before this Don Quixote is wheeled into posi-

tion for the charge, there is no way to predict. But this paper has a

specific title, and the writer has a specific purpose and even at the

risk of repeating what is already well-known to everybody, I feel ob-

liged to begin With a few general remarks, call them definitions, if

you please, for the sake of the record.

The simplest definition of a special library is this: A special li-

brary is a collection of books devoted to a special subject. But for

purposes of organizing a discussion of classification this simplicity

Online Library → University of Illinois (Urbana-Champaign campus). → The role of classification in the modern American library : papers presented at an institute conducted by the University of Illinois Graduate School of Library Science, November 1-4, 1959 (Volume 1959) → online text (page 11 of 15)