at the University of Berlin, and of Alfred Gabriel Nathorst, the Swedish Of this congress Dr. Alexander Graham Bell is honorary president; Dr. Henry Fairfield Osborn, presi- | geologist. dent; Mr. Madison Grant, treasurer; Mrs. C. Neville Rolfe (Mrs. Sybil Gotto) honorary secretary; and Dr. C. C. Little, secretary-general. The vice-presidents include Dr. Cesare Arton, Cagliari Italy; Dr. Kristine Bonnevie, Institute for Heredity Investigation, University of Christiania, Norway; Major Leonard Darwin, London; Dr. V. Delfino, Buenos Aires; Dr. E. M. East, Harvard University; M. Gamio, Director Archeology and Anthropology, Mexico; Sir Auckland Campbell Geddes, British Ambassador to the United States; Dr. Corado Gini, Rome; Hon. Mr. Justice Frank E. Hodgins, Supreme Court of Ontario; Dr. Frédéric Houssay, Paris; Dr. H. S. Jennings, Johns Hopkins University; G. H. Knibbs, Melbourne; Dr. Herman Lundborg, Upsala; Dr. L. Manouvrier, Paris; M. L. March, Paris; Dr. Jon Alfred Möjen, Christiana; Dr. T. H. Morgan, Columbia University; Dr. R. Pearl, Johns Hopkins University; Dr. Edmond Perrier, Paris; Dr. Ernesto Pestalozza, Rome; Dr. V. Guiffrida, Ruggieri, Italy; Professor R. Vogt, University of Copenhagen; and Professor Wille, University of Christiania. SCIENTIFIC ITEMS We record with regret the death of Sherburne Wesley Burnham, professor of practical astronomy in the University of Chicago and astronomer of the Yerkes Observatory; of Charles Henry Fernald, emeritus professor of zoology at Amherst Agricultural College; of Wilhelm von Waldeyer, professor of anatomy Dr. James Rowland Angell has been elected president of Yale University to succeed Dr. Arthur Twining Hadley at the close of the present university year. Dr. Angell is a son of the late President Angell of the University of Michigan, and a graduate of that university of the class of 1890. He has been professor at the University of Minnesota, professor, dean and acting president of the University of Chicago, chairman of the National Research Council, and president of the Carnegie Corporation. Dr. Angell is a distinguished psychologist, having been president of the American PsychoAssociation logical and being member of the National Academy of Sciences. The Yale Corporation announces that it has endeavored to choose for its head the ablest educational administrator available in the United States, irrespective of the college of his graduation or the place of his residence. a The Carnegie Corporation of New York has entered into an agreement with Leland Stanford Jr. University, by which a food research institute is to be established at the university for the intensive study of the problems of production, distribution and consumption of food. The corporation expressed hope that the new organization will in time be known as the Hoover Institute. The corporation will provide $700,000 for its support for ten years. Dr. C. L. Alsberg, Chief of the Bureau of Chemistry of the U. S. Department of Agriculture, has been elected the first director. Y 2 1921 Professor Einstein's Visit to the United States; The Massachusetts Institute of Technology and President Nichols; The Service for Scientific News; Scientific A 茶 CTIVITY. Today, every walk in life has been divided and sub-divided. Oxford books reflect this progress both in their wide variety and ever increasing number. A selection of those recently issued. SPACE AND TIME IN CONTEMPORARY PHYSICS By MORITZ SCHLICK Net $2.50 An adequate, yet clear account of Einstein's epoch-making theories of relativity. ON GRAVITATION AND RELATIVITY By RALPH ALLEN SAMPSON The Halley lecture delivered by the Astronomer Royal for Scotland. By G. H. HARDY Inaugural lecture by the Savilian Professor of Geometry at Oxford. By ALFRED E. GARVIE An interesting introduction to the study of religions. 90c $1.15 Net $2.25 $5.65 FUNGAL DISEASES OF THE COMMON LARCH By W. E. HILEY An elaborate investigation into larch canker with descriptions of all other known diseases of the larch and numerous fine illustrations. By M. E. HARDY THE GEOGRAPHY OF PLANTS $3.00 More advanced than the author's earlier work discussing fully the conditions in which plants flourish and their distribution throughout the earth. $5.65 DOM MINA SCHOOLS OF GAUL By THEODORE HAARHOFF An important study of Pagan and Christian education in the last century of the THE ELEMENTS OF DESCRIPTIVE ASTRONOMY $1.35 A simple and attractive description of the heavens calculated to arouse the interest Net $3.00 Twelve essays by noted scholars summarizing the work of the leading European thinkers in the last fifty years. DEVELOPMENT OF THE ATOMIC THEORY By A. N. MELDRUM 70c A brief historical sketch attributing to William Higgins, not John Dalton as generally supposed, priority in the discovery of the theory. At all booksellers or from the publishers. OXFORD UNIVERSITY PRESS American Branch OXFORD BOOKS "The standard of textual excellence." THE SCIENTIFIC MAY, 1921 THE HISTORY OF MATHEMATICS* By Professor ERNEST W. BROWN YALE UNIVERSITY HE earliest dawn of science is without doubt not different from that of intelligence. But the civilized man of to-day, far removed as he is from the lowest of existing human races, is probably as far again from the being whom one would not differentiate from the animals as far as mental powers are concerned. What this difference is, neither ethnologist nor psychologist can yet tell. Perhaps the nearest approach to a definition, at least from the point of view of this article, is contained in the distinction between unconscious and conscious observation. We are familiar with both sides even in ourselves: records can be impressed on the brain and remain there apparently dormant until some stimulus brings them to fruition, and again, record and stimulus can appear together so that a train of thought is immediately started. The faculty of conscious observation is a fundamental requirement of a scientific training, and no development can take place until it has been acquired to some extent. Although this is only the first step, it was probably a long one in the history of the race, just as it is relatively long in the lives of the majority of individuals. Reasoning concerning the observation follows, but not much success can be attained until a considerable number of observations have been accumulated. We may indeed put two and two together to make four, but experience shows that with phenomena the answer is more often wrong than right: we need much more information in order to get a correct answer. We expect, then, that the earlier stage of a science will be one not so much of discovery as of conscious observation of phenomena which are apparent as soon as attention is called to them. The habit once acquired, the search for the less obvious facts of nature begins, and *A lecture delivered at Yale University, February 26, 1920, the first of a series on the History of Science under the auspices of the Gamma Alpha Graduate Scientific Fraternity. VOL. XII.-25. in the search many unexpected secrets are found. Once a body of facts has been accumulated, correlation follows. The attempt is made to find something common to them all and it is at this stage that science, in the modern sense, may perhaps be said to have its birth. But this is only a beginning. The mind that can grasp correlation can soon proceed to go further and try to find a formula which will not only be a common property, but which will completely embrace the facts; that is, in modern parlance, a law which groups all the phenomena under one head. The formula or law once discovered, consequences other than those known are sought, and the process of scientific discovery begins. Realms which could never have been opened up by observation alone are revealed to the mind which has the ability to predict results as consequences of the law, and thence is found the means by which the truth of the law is tested. If the further consequences are shown to be in agreement with what may be observed, the evidence is favorable. If the contrary, the law must be abandoned or changed so as to embrace the newly discovered phenomena. The process of trial and error, or of hypothesis and test, is a recurring one which embraces a large proportion of the scientific work of to-day. Scientific development has two main aspects. One is the framing of laws in order to discover new phenomena and develop the subject forward so as to open out new roads into the vast forest of the secrets of nature. The other is the turning backward in order to discover the foundations on which the science rests. Just as no teacher would think it wise to start the young pupil in chemistry or physics by introducing him at the outset to the fundamental unit of matter or energy as it is known at the time, but will rather start in the middle of the subject with facts which are within the comprehension of his mind and the experience of his observation, science itself has been and must necessarily be developed in the same manner. We proceed down to the foundations as well as up to the phenomena. This two-fold aspect of scientific research has had revolutionary results in the experience of the last half century. It has fundamentally changed the ideas of those who study the so-called laboratory subjects in which observation with artificially constructed materials goes hand in hand with the framing of laws and hypotheses, but it has changed the study of mathematics in an even more fundamental manner. In the past, geometry and arithmetic were suggested by observation and practical needs and the development of both with symbolic representation proceeded on lines which were dictated by the problems which The methods of discovery in working forward were not essentially different from those of an observational science, except perhaps that the testing of a new law was unnecessary on account of the arose. |