# Scripta Mathematica

We give below a number of articles about the journal

(1) Herbert Ellsworth Slaught, Scripta Mathematica,

(2) Jekuthiel Ginsburg, The policy of Scripta Mathematica,

(3) Jekuthiel Ginsburg, Scripta Mathematica,

We also give a version of an article written by the editor of

(4) Jekuthiel Ginsburg, A unknown mathematician of the fourteenth century,

**. These are:***Scripta Mathematica*(1) Herbert Ellsworth Slaught, Scripta Mathematica,

*The American Mathematical Monthly***40**(4) (1933), 230-232.(2) Jekuthiel Ginsburg, The policy of Scripta Mathematica,

*Scripta Mathematica*1 (1932), 1-2.(3) Jekuthiel Ginsburg, Scripta Mathematica,

*Science, New Series***86**(2218) (1937), 13.We also give a version of an article written by the editor of

*Scripta Mathematica*, Jekuthiel Ginsburg:(4) Jekuthiel Ginsburg, A unknown mathematician of the fourteenth century,

*Scripta Mathematica***1**(1932), 60-62.**1. Scripta Mathematica, by Herbert Ellsworth Slaught.**

A new periodical published by Yeshiva College, Amsterdam Avenue and 186th Street, New York, N. Y.

The mathematical world suffered a distinct loss when the publication of

But now, in the midst of the depression, Yeshiva College in New York City comes forward with financial support for a new quarterly journal, Scripta Mathematica, "the first of a series of publications planned by the college" with the ideal of "learning for the sake of learning." This journal, under the editorship of Jekuthiel Ginsburg, professor of mathematics in Yeshiva College, is to be devoted "to the philosophy, history, and expository treatment of mathematics," and will be entirely international in its scope. High standards for this journal will be assured by the character of its editorial board which includes as associate editors, Raymond Clare Archibald, Cassius Jackson Keyser, Louis Charles Karpinski, Gino Loria, Vera Sanford, Lao Genevra Simons, and David Eugene Smith. Although it will be seen that this publication is not in any sense a continuation of the

The two numbers already issued (September and December, 1932) show a wide variety of interest and appeal - to the scholar, to the casual reader in other fields as well as in mathematics, and to any intelligent person whose curiosity leads him to wonder about the difficulties encountered by the human race in developing such a fundamental subject as mathematics. Any light which can be thrown upon the age-long growing pains of mathematics by historical research is not only of interest on its own account but is likely to point the way by analogy to a sympathetic attitude toward the difficulties now experienced with mathematical studies by the children of the present generation. For this and many other reasons we welcome the advent in this country of a historical journal in the field of mathematics.

Space will not permit a critical review here of the many interesting topics discussed in these two numbers, but the reviewer hereby confesses to the surrender of his own cold and critical attitude and warmly recommends their careful reading to the whole constituency of this MONTHLY. Without prejudice to the other contributions, all of which seem very worthy, consider for example, the following random samples: "Gaspard Monge, Politician," by David Eugene Smith, an article based on Smith's manuscript collection now donated to Columbia University; "The Meaning and the Bearings of Mathematics," two articles by Cassius Jackson Keyser, written in his own clear and convincing style so well known to the mathematical world: "A L Cauchy in the History of Analytic Geometry," by Gino Loria; "Jacob ben Machir's Version of Menelaus's Work on Spherical Trigonometry," a translation by Jekuthiel Ginsburg, parts (1) and (2) and to be continued; "Rare Mathematical Books in the University of Michigan Library," by Louis C Karpinski; "The Ancient Peruvian Abacus," by L Leland Locke, author of the richly illustrated work on

The mathematical world suffered a distinct loss when the publication of

*Bibliotheca Mathematica*was suspended in 1915. Its editor, Gustav Eneström, shortly before his death, expressed the wish to David Eugene Smith that some way could be found to continue this journal in America. Acting on this suggestion, the Mathematical Association of America endeavoured to secure a subsidy fund sufficient to insure the success over a period of years of such an undertaking. Failing in this attempt, the Association, late in 1928, undertook an international canvass to determine whether a sufficiently large advance subscription list could be obtained to guarantee the project. The result was very enthusiastic moral support but not enough subscription pledges to warrant going ahead. Possibly the impending world-wide financial crash was already casting its shadow before it.But now, in the midst of the depression, Yeshiva College in New York City comes forward with financial support for a new quarterly journal, Scripta Mathematica, "the first of a series of publications planned by the college" with the ideal of "learning for the sake of learning." This journal, under the editorship of Jekuthiel Ginsburg, professor of mathematics in Yeshiva College, is to be devoted "to the philosophy, history, and expository treatment of mathematics," and will be entirely international in its scope. High standards for this journal will be assured by the character of its editorial board which includes as associate editors, Raymond Clare Archibald, Cassius Jackson Keyser, Louis Charles Karpinski, Gino Loria, Vera Sanford, Lao Genevra Simons, and David Eugene Smith. Although it will be seen that this publication is not in any sense a continuation of the

*Bibliotheca Mathematica*, which it is hoped will sometime be revived, it promises a series of historical articles which will be welcomed as supplementing those which frequently appear in the MONTHLY.The two numbers already issued (September and December, 1932) show a wide variety of interest and appeal - to the scholar, to the casual reader in other fields as well as in mathematics, and to any intelligent person whose curiosity leads him to wonder about the difficulties encountered by the human race in developing such a fundamental subject as mathematics. Any light which can be thrown upon the age-long growing pains of mathematics by historical research is not only of interest on its own account but is likely to point the way by analogy to a sympathetic attitude toward the difficulties now experienced with mathematical studies by the children of the present generation. For this and many other reasons we welcome the advent in this country of a historical journal in the field of mathematics.

Space will not permit a critical review here of the many interesting topics discussed in these two numbers, but the reviewer hereby confesses to the surrender of his own cold and critical attitude and warmly recommends their careful reading to the whole constituency of this MONTHLY. Without prejudice to the other contributions, all of which seem very worthy, consider for example, the following random samples: "Gaspard Monge, Politician," by David Eugene Smith, an article based on Smith's manuscript collection now donated to Columbia University; "The Meaning and the Bearings of Mathematics," two articles by Cassius Jackson Keyser, written in his own clear and convincing style so well known to the mathematical world: "A L Cauchy in the History of Analytic Geometry," by Gino Loria; "Jacob ben Machir's Version of Menelaus's Work on Spherical Trigonometry," a translation by Jekuthiel Ginsburg, parts (1) and (2) and to be continued; "Rare Mathematical Books in the University of Michigan Library," by Louis C Karpinski; "The Ancient Peruvian Abacus," by L Leland Locke, author of the richly illustrated work on

*The Ancient Quipu or Peruvian Knot Record*, published by the American Museum of Natural History; "The Concept of Infinity," by D Mordukhai-Boltovskoy, the first of a series of historical notes on this topic, translated from the Russian by Ginsburg; "A German-American Algebra of 1837," by Lao Genevra Simons. All told there are twenty-one signed articles in the two numbers, aside from several excellent Book Reviews and a Department of Notes and Queries conducted by Raymond Clare Archibald. Of this latter department the reviewer wishes to say that it had long been his desire to see such a department attached to, or connected with, this MONTHLY and edited by Archibald, than whom probably there is no one in America or in Europe who is better qualified to develop such a department. Already in the second number this department occupies eighteen pages, much of which is of absorbing interest. Under the heading,*"Bibliographia de Mathematicis,"*Archibald has listed some forty names of mathematicians together with references concerning them to articles or books many of which would be difficult for the average reader to obtain or the existence of which in many cases might be entirely unknown to the casual observer. He proposes to extend this list and keep it as complete as possible in the succeeding issues of the journal. In this and many other ways this department will render a real service. Perhaps, after all, it is better so rather than as a supplement to the MONTHLY. To Yeshiva College the reviewer would extend his congratulations, believing that the new journal will soon make an honourable name for itself in the mathematical world, and will fulfil a very useful mission.**2. The policy of Scripta Mathematica, by Jekuthiel Ginsburg.**

SCRIPTA MATHEMATICA is primarily designed to serve as a means of communication between scholars engaged in the study of mathematics as the raw material for a new knowledge. The historians develop mathematics as a function of the variable "time," while the philosopher's aim is-to discover the logic behind the laws of mathematics, the mathematics of mathematical laws. History of mathematics presents the science in the state of becoming; by means of philosophy the crystalline structure of the finished product is revealed. These two. aspects of the subjects are supplementary; one without the other loses the greater part of its value.

The pages of the periodical will therefore be devoted chiefly to the history and philosophy of mathematics. The expositorial treatment of mathematics will also be included for the purpose of giving to the reader a knowledge of what is being done at present in various branches of the subject, and of the history of mathematics in the making.

In the history of mathematics the editors will consider material solely from the point of view of originality and general interest, avoiding any geographic or national preferences; their viewpoint is that mathematics is one and indivisible whatever the origin of the component parts.

The editors will be equally impartial with respect to the periods studied. The unmapped regions of ancient and prehistoric mathematics will receive as much attention as the broader expanses of modern mathematical research. A dissertation throwing new light on the mathematical knowledge of the ancient Babylonians, Egyptians or Incas will be as welcome as the history of a modern mathematical theory.

As in the case of history, so in that of philosophy, it will be the object of the editors to arouse the interest of mathematicians and intelligent laymen. Attention will also be given to various mathematical theories, to the nature of mathematics and of various mathematical processes, their great power and their still greater limitations, and to the part mathematical processes and methods are playing in the world of thought. A special attempt will be made to consider such mathematical fallacies as may be current even among mathematicians and intelligent laymen. Attention will also be given to various mathematical theories which, of late, have become objects of popular interest.

SCRIPTA MATHEMATICA begins its career as a quarterly. Every issue will contain at least 96 pages of reading matter. A special effort will be made to have the articles free from such technicalities as would repel the intelligent reader who has not had a thorough training in mathematics.

It is expected that each issue will contain two or three leading articles which will discuss topics rather extensively. There will also be included a number of minor contributions in the various fields. There will be two departments devoted to book reviews and notes and queries. Reports summarising the work being done in the history of various mathematical subjects will also be given.

Attention will also be given to reports upon manuscripts and rare books in American libraries not generally accessible to students.

The pages of the periodical will therefore be devoted chiefly to the history and philosophy of mathematics. The expositorial treatment of mathematics will also be included for the purpose of giving to the reader a knowledge of what is being done at present in various branches of the subject, and of the history of mathematics in the making.

In the history of mathematics the editors will consider material solely from the point of view of originality and general interest, avoiding any geographic or national preferences; their viewpoint is that mathematics is one and indivisible whatever the origin of the component parts.

The editors will be equally impartial with respect to the periods studied. The unmapped regions of ancient and prehistoric mathematics will receive as much attention as the broader expanses of modern mathematical research. A dissertation throwing new light on the mathematical knowledge of the ancient Babylonians, Egyptians or Incas will be as welcome as the history of a modern mathematical theory.

As in the case of history, so in that of philosophy, it will be the object of the editors to arouse the interest of mathematicians and intelligent laymen. Attention will also be given to various mathematical theories, to the nature of mathematics and of various mathematical processes, their great power and their still greater limitations, and to the part mathematical processes and methods are playing in the world of thought. A special attempt will be made to consider such mathematical fallacies as may be current even among mathematicians and intelligent laymen. Attention will also be given to various mathematical theories which, of late, have become objects of popular interest.

SCRIPTA MATHEMATICA begins its career as a quarterly. Every issue will contain at least 96 pages of reading matter. A special effort will be made to have the articles free from such technicalities as would repel the intelligent reader who has not had a thorough training in mathematics.

It is expected that each issue will contain two or three leading articles which will discuss topics rather extensively. There will also be included a number of minor contributions in the various fields. There will be two departments devoted to book reviews and notes and queries. Reports summarising the work being done in the history of various mathematical subjects will also be given.

Attention will also be given to reports upon manuscripts and rare books in American libraries not generally accessible to students.

**3. Dinner of the Society of Friends of Scripta Mathematica.**

(1) The Dinner of the Society of Friends of

(2)

(3) Among the Scripta publications in preparation are a volume entitled "Fabre and Mathematics," by Professor Lao G Simons, and a volume entitled "Forum Lectures," being addresses given before the Forum of

*Scripta Mathematica*was held in honour of Professors Eric Temple Bell, Cassius Jackson Keyser, David Eugene Smith and Mr M Lincoln Schuster for their contributions to public enlightenment regarding mathematics as an essential means to general culture. The opening address was made by Professor William P Montague.(2)

*Scripta Mathematica*is a quarterly journal devoted to history and philosophy of mathematics published by Yeshiva College, and is edited by Jekuthiel Ginsburg with the cooperation of Raymond Clare Archibald, Adolph Frankel, Sir Thomas Little Heath, Louis Charles Karpinski, Cassius Jackson Keyser, Gino Loria, Vera Sanford, Joseph J Schwartz, Lao Genevra Simons and David Eugene Smith.(3) Among the Scripta publications in preparation are a volume entitled "Fabre and Mathematics," by Professor Lao G Simons, and a volume entitled "Forum Lectures," being addresses given before the Forum of

*Scripta Mathematica*by Professors Cassius Jackson Keyser, David Eugene Smith, Edward Kasner and Walter Rautenstrauch.**4. A unknown mathematician of the fourteenth century, by Jekuthiel Ginsburg.**

Sometime between the years 1361 and 1440, there lived on the Island of Majorca, one of the Baleares, a mathematician who seems not to have attracted the attention of historians of mathematics, and yet whose achievements were such as to demand recognition. His name, En-Bellsham Ephraim Gerondi, is practically unknown to modern writers of science, letters, or history, largely because the period in which he lived was one in which mathematical activity was at about its lowest ebb for a period of three centuries.

The apparent sterility of the period can be best illustrated by the fact that the most noteworthy names of the time are those of Simon Bredon in England, Johannes von Gmunden in Austria, and Nicole Oresme in France. The known contributions of none of them were epoch-making and yet these three men seem to have outranked any of their contemporary mathematicians.

The East was at that time gradually relinquishing its leadership in scientific activity. In fact, it was not far from the zero point, which it reached at the end of the fifteenth century, and the West was not yet ready to assume its responsibility. The result was the reduced world output of mathematicians. Three leading scholars, none of whom would be called a leader at any other period in the history of the world, and a rather small number of minor mathematicians whose combined works would hardly fill a single volume, is about all that the historians record for the entire Century.

The unanimous verdict of history may possibly be revised, however, as a result of such further research as may add new names to the list of scholars or may reveal hitherto undiscovered achievements of the known mathematicians.

That this is a possibility may be seen from the fact that the name of En-Bellsham Ephraim Gerondi has so long remained unknown, although some of his writings were embodied in a work in the Hebrew language by a contemporary, and although these writings include a theorem which, according to Tropfke, was not stated in that form in any European language before 1807.

The Island of Majorca, the home of the mathematician, was at that time a centre of a naval commerce which successfully competed for the Mediterranean trade with the cities of the Hansa League. More than 900 Majorcan ships, manned by more than 30,000 sailors, plied between Majorca and various cities on the coast of the Mediterranean. Palma, the capital of the island, was known as a great centre of the map- and instrument-making industry. Such industry implies the presence of a large number of skilled mechanics and mathematicians. It is at least possible that Gerondi was one of the mathematicians thus engaged. Whether this surmise is correct or not, he is known to have lived in Majorca, which was then, as now, under the rule of Spain, and to have written letters on mathematical subjects. These were in reply to queries by his friend, Simeon Duran, Chief Rabbi of Algier, who was also a native of Majorca and like many Christian and Jewish religious leaders, very interested in mathematical subjects. The correspondence is interesting and deals mostly with surfaces and volumes and with mathematical passages in the Talmud. Gerondi, in the course of his reasoning, gives statements of various theorems in plane and solid geometry. There is, however, one theorem, the form of which was hitherto supposed to have been first stated in 1807 by Meyer Hirsch in his

$S = 2\pi rh$,

where $S$ is the surface and $h$ is the altitude of a spherical segment, the radius of the sphere being $r$.

The correspondence is published in the

The correspondence shows that Gerondi, besides being a mathematician, was a diligent student of the Talmud. It must be said, however, that the Rabbi seems not to have had a very high opinion of his talmudical knowledge.

Some of the letters written by Gerondi reveal the fact that his life was not a happy one. So disturbed was he at the fact that Majorca was becoming a hotbed of religious intolerance and persecution that he implored Rabbi Simeon to assist him to escape from the island. The fear which he disclosed was fully warranted when we recall that he lived in the time of the savage massacres of 1391 and 1411, and only about one generation before the edict of expulsion issued by Ferdinand and Isabella. Although Jacob Cephanton (ff. c. 1430), apparently a native of Castille, a mathematician of some standing for the time, was able to carry on his writing, Spain and the adjacent islands were not promising territory for Jewish scholars. Whether or not he lost his life in the struggle is not known, or at least is not clear from any note in the

In view of the scarcity of information concerning the period, the knowledge that the theorem, in its modern form, was known at that time instead of being discovered in the nineteenth century, may be of interest. In any case, the list of mathematicians of the period should hereafter be extended so as to include the name of En-Bellsham Ephraim Gerondi.

The apparent sterility of the period can be best illustrated by the fact that the most noteworthy names of the time are those of Simon Bredon in England, Johannes von Gmunden in Austria, and Nicole Oresme in France. The known contributions of none of them were epoch-making and yet these three men seem to have outranked any of their contemporary mathematicians.

The East was at that time gradually relinquishing its leadership in scientific activity. In fact, it was not far from the zero point, which it reached at the end of the fifteenth century, and the West was not yet ready to assume its responsibility. The result was the reduced world output of mathematicians. Three leading scholars, none of whom would be called a leader at any other period in the history of the world, and a rather small number of minor mathematicians whose combined works would hardly fill a single volume, is about all that the historians record for the entire Century.

The unanimous verdict of history may possibly be revised, however, as a result of such further research as may add new names to the list of scholars or may reveal hitherto undiscovered achievements of the known mathematicians.

That this is a possibility may be seen from the fact that the name of En-Bellsham Ephraim Gerondi has so long remained unknown, although some of his writings were embodied in a work in the Hebrew language by a contemporary, and although these writings include a theorem which, according to Tropfke, was not stated in that form in any European language before 1807.

The Island of Majorca, the home of the mathematician, was at that time a centre of a naval commerce which successfully competed for the Mediterranean trade with the cities of the Hansa League. More than 900 Majorcan ships, manned by more than 30,000 sailors, plied between Majorca and various cities on the coast of the Mediterranean. Palma, the capital of the island, was known as a great centre of the map- and instrument-making industry. Such industry implies the presence of a large number of skilled mechanics and mathematicians. It is at least possible that Gerondi was one of the mathematicians thus engaged. Whether this surmise is correct or not, he is known to have lived in Majorca, which was then, as now, under the rule of Spain, and to have written letters on mathematical subjects. These were in reply to queries by his friend, Simeon Duran, Chief Rabbi of Algier, who was also a native of Majorca and like many Christian and Jewish religious leaders, very interested in mathematical subjects. The correspondence is interesting and deals mostly with surfaces and volumes and with mathematical passages in the Talmud. Gerondi, in the course of his reasoning, gives statements of various theorems in plane and solid geometry. There is, however, one theorem, the form of which was hitherto supposed to have been first stated in 1807 by Meyer Hirsch in his

*Geometrische Aufgaben*namely the theorem$S = 2\pi rh$,

where $S$ is the surface and $h$ is the altitude of a spherical segment, the radius of the sphere being $r$.

The correspondence is published in the

*Responsa*of Rabbi Simeon Duran (Ta Sh Betz) and bears on various questions of mathematics from a practical religious point of view. From certain statements by the Rabbi, it appears that Gerondi had great renown as a mathematician. For example, on his first letter to him, is the superscription "Query directed to En-Bellsham Ephraim Gerondi, the expert in the science of mathematics." His letters show a great admiration for the subject, although his only original contribution seems to be the statement of the theorem mentioned above.The correspondence shows that Gerondi, besides being a mathematician, was a diligent student of the Talmud. It must be said, however, that the Rabbi seems not to have had a very high opinion of his talmudical knowledge.

Some of the letters written by Gerondi reveal the fact that his life was not a happy one. So disturbed was he at the fact that Majorca was becoming a hotbed of religious intolerance and persecution that he implored Rabbi Simeon to assist him to escape from the island. The fear which he disclosed was fully warranted when we recall that he lived in the time of the savage massacres of 1391 and 1411, and only about one generation before the edict of expulsion issued by Ferdinand and Isabella. Although Jacob Cephanton (ff. c. 1430), apparently a native of Castille, a mathematician of some standing for the time, was able to carry on his writing, Spain and the adjacent islands were not promising territory for Jewish scholars. Whether or not he lost his life in the struggle is not known, or at least is not clear from any note in the

*Responsa*.In view of the scarcity of information concerning the period, the knowledge that the theorem, in its modern form, was known at that time instead of being discovered in the nineteenth century, may be of interest. In any case, the list of mathematicians of the period should hereafter be extended so as to include the name of En-Bellsham Ephraim Gerondi.

Last Updated December 2023