## Reviews of the works of Federigo Enriques

Federigo Enriques wrote a large number of works and the literature contains many reviews of them. In the references to Enriques's biography we list forty reviews. Here we give extracts from some of these reviews. On the whole we have quoted the reviewer's overview of the work and we refer the interested reader to the reviews themselves for a more detailed description of the works. In many cases our extract is the first few lines of the review followed by the last couple of sentences. Rather than give a full reference to the review, we have simply quoted the reference number in our biography of Enriques. We give them in chronological order:

**Fragen der Elementargeometrie (1907).**

An extract from review [93]:

The mistake is sometimes made of supposing that the success of the movement against the study of the text of Euclid in the schools has been due entirely to the action of the party of which Professor Perry is one of the leaders. Even in England, however, where the needs of the practical man are allowed more weight than abroad, the abandonment of the old routine is due in part to a growing consciousness in mathematical circles that as a logical system Euclid fails to answer to modern philosophical requirements. Outside England the change is of less recent date, and it is entirely to be attributed to the initiative of the mathematicians themselves. Enriques's collection of essays on Problems of Elementary Geometry has for its object to explain as simply and intelligibly as possible precisely what modern Mathematics has to say in correction, in explanation, and in completion of the old Greek Geometry. It thus indirectly expounds the point of view which outside England led, already many years ago, to the revolution in the study of Geometry above referred to. The Italian original, which appeared in 1900, consisted of two parts, the first deals with the Axioms of Geometry, the second, translated into German and enlarged, constitutes the volume before us. ... It only remains to say that the public is indebted to all those concerned in the production of this book, whether to the inspirer, the editor, the authors, the painstaking translator or the publisher. The volume is in every respect to be recommended to the reading of the mathematical public.

**Les Problèmes de la science et la logique (1909).**

An extract from review [81]:

In his 'Problemi della Scienza' Enriques offers a critique of problems relating to the logical and the psychological development of scientific knowledge. The first part of that work is concerned with the more general problems of the logic of science; the second part discusses the concepts of geometry, mechanics, physics, and biology. The French volume under review is a translation of the first part of the Italian book. The aim of the author is to unify the various domains of knowledge by means of a "positive science of gnoseology," an epistemology dominated by a spirit "critical and positive." First, then, there is no absolute, either in mathematics, or in natural science, or in morals, or in metaphysics. Consequently, everything being only a linking of relatives, there are no insoluble problems. There is no 'reality in itself.' The 'positive' definition of the 'real' is, according to Enriques, the correspondence between sensations and desired results

**Problems of Science (1914).**

An extract from review [62]:

The able work, 'Problemi della Scienza', from the pen of F Enriques, Professor of Geometry in the University of Bologna, well deserved an English translation. It is a thorough and synthetic review of the problems of scientific methodology. Amid the present riot of pragmatism and intuitionism, such a work of clear and patient intellectual analysis will be especially useful to thoughtful students. It has now become a commonplace that philosophy can not ignore science; and yet in practice the breach still continues. A work like the present will be a valuable accession to the philosopher's library. The man of science too will find in Professor Enriques' work an exposition of the wider and deeper problems which lie beyond the threshold of specialism. After an introduction dealing with the presuppositions and limitations of the scientific concept of reality, the author proceeds to review the basic principles of logic, geometry, mechanics, and the mechanical theory of life. He displays a wide erudition and a power of lucid synthesis in discussing the fundamental questions. Many of his criticisms are very helpful; for instance, his analysis of our spatial knowledge and of mass and force. On the whole, Professor Enriques' work is to be regarded as a. suggestive and stimulating contribution to a sane scientific cosmology.

An extract from review [47]:

Among mathematicians Enriques, who is professor of projective and descriptive geometry in the University of Bologna, has long been favourably known for his contributions to geometry, especially for his admirable treatise on "Projective Geometry" and for his penetrating essays on "The Foundations of Geometry." In the work before us the distinguished geometrician addresses a far wider circle of students and thinkers: not only mathematicians, but psychologists, logicians, philosophers, astronomers, mechanicians, physicists, chemists, biologists and others. For the discussion, which is as wide-ranging as the philosophic writings of Henri Poincare or as that of John Theodore Merz in the first two volumes of his "History of European Thought in the Nineteenth Century," deals with fundamental questions drawn from every large department of modern science. ... We know of no other work that gives so keen a sense of the unity of all branches of science.

An extract from review [73]:

This is a translation of Enriques's 'Problemi della Scienza', of which the first Italian edition appeared in 1906. In the introductory note Professor Royce points out that this work of synthetic scientific methodology "stands somewhat above and apart from those philosophical controversies which the anti-intellectual movement [of James and Bergson] has inspired," and contrasts Enriques's tendency with the tendencies just referred to. Professor Enriques himself characterises the spirit of this critical study of certain problems relating to the logical and psychological development of scientific know-ledge as both " critical and positive." He does not use these words in their usual meaning, but he thinks that he has interpreted things in a clearer and more scientific way, and has reconciled, without eclectic compromises, certain speculative tendencies by which his thought was prompted at the outset. ... The book is able, interesting, and important. The importance is as great for teachers as it is for philosophers.

An extract from review [16]:

The first edition of the Italian text of the 'Problemi della Scienza' of Professor Enriques appeared in 1906. It has already become known to a wide circle of European students. It is a pleasure to welcome its appearance in English. The book contains six chapters treating in order the following topics: the general problem of knowledge and related matters; facts and theories and their interactions; the general problems of logic; the philosophical and psychological questions which are naturally raised in connection with the science of geometry; mechanics, its objective significance and the psychological development of its principles; the extension of mechanics into physics and the relation of the mechanical hypothesis to the phenomena of life. This book is of quite unusual value. It is written by a mathematician and consequently takes proper account of recent mathematical developments. It contains a masterly analysis of the problems of science, especially in their relation to matters of mathematical expression and of philosophical import. It merits the close attention alike of physicists and philosophers and mathematician.

An extract from review [10]:

The present work is a translation of the 'Problemi della Scienza' of Professor Enriques, the eminent Italian mathematician. It covers very much the same ground as Poincare's three books on the philosophy of science. It may be divided into five parts; the first is a general introduction and explanation of the author's position (which he calls Critical Positivism), the second deals with Logic and its applicability to the real world, the third deals with geometry, the fourth with the classical mechanics, and the last with electro-dynamics and the alterations which it has entailed in the mechanics of Newton. The whole work gives an impression of very deep and wide learning; Professor Enriques draws his examples not only from the subjects in which he is specially an expert, but also from economics, jurisprudence, and biology. Unhappily the style is very heavy, and one can never forget for a moment that one is reading a translation from .a foreign tongue.

**Gli Elementi d'Euclide e la critica antica e moderna (1925).**

An extract from review [83]:

This is the first volume of a series "Per la Storia e la Filosofia delle Matematiche," published under the auspices of the Istituto Nazionale per la Storia delle Scienze Fisiche e Matematiche, and edited by Professor Enriques of the University of Bologna. It is the outcome of a suggestion made by certain leaders in the in the training of teachers of mathematics and it proceeds upon the principle that it is only by a historic survey of the classical textbooks of geometry that a sound basis can be laid for a critical study of the subject. The results of abandoning of Euclid as a text has, in the opinion of Professor Enriques, been a serious loss in the equipment of the teacher. ... It will therefore be seen that, with such an editor as Professor Enriques to assure the scholarship of the commentary, the work will be helpful to any student of the subject and to any reader of the most influential textbook on mathematics ever written. It is significant that the teachers of Italy, which now ranks among the half dozen leading nations in mathematical activity, should feel the need of such an edition of Euclid at a time when some of our American educators are proclaiming the uselessness and indeed the happy death of the science of geometry.

**Isaac Newton's Principii di Filosofia Naturale, Teoria della Gravitazione (1925).**

An extract from review [86]:

This is the third volume in the series "Per la Storia e la Filosofia delle Matematiche" edited by Professor Enriques. It consists of a translation of Newton's 'Philosophiae naturalis principia mathematica', which appeared in 1687, together with a brief biography of Newton and an appendix of about fifty pages of notes. In this appendix there is given a historical survey of the following topics: (1) The concept of mass or quantity of matter; (2) Force and the laws of motion; (3) Motion, space, and time, absolute and relative; (4) Newton's mechanics as a cosmic science. In the third of these "notes" the historical development of the Einstein theory is sketched.

**The Historic Development of Logic. The Principles and Structure of Science in the Conception of Mathematical Thinkers (1929).**

An extract from review [91]:

Logos was once a central object of philosophical thought, but with the advent of a chthonic deity, Experience, the spirit of Logos passed into subsistential obscurity. Enriques does not claim completely to have recovered the spirit, but his noteworthy attempt should remind us how little has been done in the history of logic since Prantl. While logicians dispute among themselves concerning the subject-matter of logic, whether it ought to be things, words, or ideas, Logos continues to be actualized in all forms of rational activity. Mathematics, the model of all rational science, has been Enriques' particular concern, both professionally and philosophically. In order to determine the profounder bases of the principles employed by the mathematical sciences, Enriques has delved into the historical sources of logic, mathematics, and philosophy.

**Gli Elementi d'Euclide e la critica antica e moderna (1930).**

An extract from review [84]:

It is always entertaining to attend the wake at the ever-recurring death of Euclid-killed by the innumerable hands of innumerable educators. No mathematician of all time has been slaughtered more often than he, and none has had the satisfaction of a glorious resurrection so frequently. In considering this intellectual if not corporeal phenomenon, however, we have to bear in mind that the phenomenon is related to the spirit of The Elements (Stoicheia) and not to the body of the text. The thirteen "books" of these elements were written for scholars of university rank; they were too subtle for the adolescent mind. The idea of using the book in training schoolboys, which began in the seventeenth century and continued for two hundred years, was carried out with some approach to success so long as carefully selected boys were admitted to the schools of England, but it failed as soon as education became democratic, and even before that time in most of the Continental countries ... It is encouraging, however, to observe that the greatest textbook that the world has ever seen-The Elements of Euclid- is by no means dead, and that in the region of sound scholarship it continues to stand as a monument to the achievements of the Greek mind. As evidence of this fact we now have a new edition of the work itself, and this from the hand of one of the outstanding Italian mathematicians of our time, Professor Federigo Enriques of the University of Rome.

**Gli Elementi d'Euclide e la critica antica e moderna (1932).**

An extract from review [41]:

The book before us is the third volume of the Italian translation of Euclid's Elements, with historical and critical commentary, under the general editorship of Professor Federigo Enriques. No more fully qualified editor could be found than Professor Enriques, as all those will know who have seen other volumes edited by him, such as his 'Elementi di Geometria' (in which he had the co-operation of Ugo Amaldi), his work 'Per la storia della logica', and the three large volumes entitled 'Questioni riguardanti le matematiche elementari'. The fundamental idea which suggested the preparation of this edition is stated in the preface to the first volume (1925) to have been the practice of the "Scuola di Magistero" under which the critical study of a subject is placed on a historical basis, having recourse to classical models and observing the variations which have been introduced, by degrees, in successive treatises and commentaries that have appeared from time to time. "And certainly in no field can this programme be better carried out than in that of elementary geometry, since the development of this subject through the centuries is completely dominated by the great work of Euclid, insomuch that its history is bound up with that of Euclidean criticism."

**Storia del pensiero scientifico. Vol. I: Il mondo antico (1932).**

An extract from review [78]:

Of the two authors of this book, the one, Federigo Enriques, needs no introduction to our readers, but the other does, for this is I believe our first opportunity of speaking of him. G de Santillana is Enriques' assistant in the Institute of the history of science attached to the University of Rome, which is a kind of national seminary for our studies. In this respect Italy is giving a splendid example to other countries, even to countries which are much richer but "cannot afford" to promote the history of science. They cannot afford it, not because they lack money, but because they lack intelligence and imagination. ... the book it is a history of scientific thought in classical antiquity and in the early middle ages down to the beginning of the VIIIth century. It is written for students, not for specialists. ... Enriques belongs like myself to the group of historians of science who have become historians only gradually and almost in spite of themselves under the increasing pressure of humanistic longings and philosophical perplexities. ... The text is full of wisdom, and is written with Italian lucidity, vivacity and grace.

**Lezioni sulla teoria geometrica delle equazioni e delle funzioni algebriche. IV. Funzioni ellittiche e abeliane (1934).**

An extract from review [43]:

After a considerable delay, Messrs. Enriques and Chisini have completed their great treatise, the first three volumes of which are already well known to the geometrical world. The present volume will be better appreciated as a sequel to the preceding volumes than as an independent treatise on algebraic functions. But as this sequel it makes extremely interesting reading. It is in a sense a comment on the more geometrical theory which precedes it, explaining the function-theory aspects of various questions in the theory of sets of points on a curve. While the general outlines of the usual theory of algebraic functions are given, those questions which are of interest to geometers are considered in more detail than those of purely function-theoretic interest. ... this is a volume which should be in the possession of all who possess the three earlier volumes, and should prove as useful a work of reference for geometers as its predecessors.

**Signification de l'histoire de la pensée scientifique (1934).**

An extract from review [58]:

Professor Enriques states his views on the value of the history of science for the understanding of scientific as well as philosophic ideas. He sees science not as a body of stable truths, but as a historical process in which human experience becomes widened; science is not something achieved but a process of achievement. That is why, according to him, we must learn the origin and development of ideas before we can see their significance and interrelations. Both positivistic and pragmatistic interpretations of science come in for criticism, while the anti-rational historicism of the last century is shown to have led to an experimental rationalism.

**Gli Elementi d'Euclide e la critica antica e moderna (1936).**

An extract from review [40]:

This is the fourth and final volume of the Italian translation of Euclid's Elements, with historical and critical commentary, under the general editor-ship of Federigo Enriques, first undertaken in 1924 (the date of the preface to the first volume is May, 1924). The first volume (Books I-IV) appeared in 1925, the second (Books V-IX) in 1930, the third (Book X) in 1932. The editors may be congratulated on the completion of an edition which will be of permanent value. ... There is no doubt of the competence of the editors, and the general editorship of Professor Enriques is a guarantee for the trustworthiness and the unity of the work.

**Histoire de la Pensée Scientifique (1936).**

An extract from review [76]:

These three small volumes form numbers 384, 385, and 386 of 'Actualités Scientifiques et Industrielles', and are evidently designed for beginners. The first volume contains chronological tables, a map, introductory sections on ancient texts and modern histories, and a Part I devoted to Ionia, the new civilization, etc. All the volumes have footnotes, and bibliographies at the end of each section; and in the text the most important interpretations of the most important points are explained. The exposition is clear and free from extravagances, and the scholarship sound.

An extract from review [92]:

These three serial manuals deal in six chapters with Greek scientific thought over the period of the few hundred years which includes the Ionian "physiologers" or naturalists, the Pythagoreans, the Eleatics, Empedocles, Anaxagoras, and the atomists. The authors published their first account in Italian: 'Storia del Pensiero Scientifico', four years prior to the present French series. They show themselves well at home in the cultural context of Greek thought. Enriques is well known for his mathematical, logical, philological, and historical knowledge which makes him pre-eminently equipped for the philosophical history of the sciences, as his 'Historic Development of Logic' shows.

**Le probleme de la connaissance. Empirisme et rationalisme grecs (1937).**

**Platon et Aristote (1937).**

An extract from review [52] and [53]:

These pamphlets contain Chapters VII-XI in the authors' forth-coming history of scientific thought. They are written in a clear and unpretentious style, often humorous, and with an economy of detail that suggests a comprehensive knowledge of the field. They deal with the successive contributions to the philosophy and methodology of science by the Sophists of the fifth century B.C. and by Socrates, Democritus, Plato, and Aristotle.

**Le Matematiche nella Storia e nella Cultura (1938).**

An extract from review [28]:

Professor Enriques has brought his wide scholarship, his penetrating intelligence, and his customary charm of manner, to what is not quite, in the usual sense, a history of mathematics; history is there, in plenty, but to a great extent in outline only; and the historical development is broken off at the eighteenth century to make room for a longish digression, about a third of the book, on the relation of mathematics to other sciences, before returning to the modern development of various branches of analysis and geometry. It is this middle section which is perhaps the most valuable, especially the chapters on Mathematics and philosophy, What are mathematics?, and the Psychology of mathematics. It is not by accident that this latter chapter is the last of this section, as though to sum it up; the author is before all a man of humane comprehension, and his interest throughout is in the type of mental process of his characters, rather than in the precise results they have obtained. He has no patience with the view that different races tend to think in different ways, and sees rather in environment and the spirit of the age the source of the changes which in the large affect mathematical thought. ... though pre-eminently a book for the general reader, it is clearly the work of a scholar.

An extract from review [42]:

Federigo Enriques has produced a remarkably well constructed book, which succeeds in showing the relationship of mathematics to history and to culture. The author has focused wide learning on the task in hand and has produced a book which, though not long, is clear and to the point. He has shown that the development of mathematics is related to the growth of ideas. The volume is divided into three books. The first of these deals with the evolution of mathematics from antiquity to the eighteenth century. ... The second book, which has seven chapters, treats mathematics and its relation to culture or civilization ... The third book, which deals with certain directions taken by mathematics in the nineteenth century, can be considered separately, because it is not necessary to the unity of the volume, although the background offered by the first two books is valuable in understanding the third. More than a knowledge of the development of mathematics is necessary to appreciate this third book, which will prove useful to the advanced students of mathematics who have already received a working knowledge of the subject.

**La théorie de la connaissance scientifique de Kant à nos jours (1938).**

An extract from review [57]:

Professor Enriques neatly summarizes the evidence from modern science against the Kantian doctrines of space, time, substance, causality, and logic. In contrast to the theories of knowledge of absolute idealism, pragmatism, classical rationalism, and nominalism, he reformulates his own view that although the complete truth is never achieved, each of the provisional theories of the sciences contains something of the truth more adequately exhibited in the historical evolution of scientific constructions.

**Le superficie algebraich (1949).**

An extract from review [87]:

Federigo Enriques, at the time of his recent death, had stood for over half a century in the first rank of algebraic geometers. The algebro-geometric development of the theory of algebraic surfaces, which is the subject of the volume under review, is the result of the work of many mathematicians, but the three names of Castelnuovo, Enriques and Severi stand out as its principal architects, and almost all the principal theorems of the subject are due to one or other of these three great geometers. The manuscript of this posthumous work appears to have been virtually complete at the time of the author's death; it has been seen through the press by his pupils Pompilj and Franchetta, and a moving preface has been contributed by Castelnuovo. ... This treatise, embodying the fruits of a lifetime's labour by its author, gives a clear account of the present state of the theory of algebraic surfaces as developed by the methods of the Italian school, and will be a standard work of reference in the field for a considerable time.