Weierstrass’s Speech, Delivered upon Assuming the Office of Rector of the University of Berlin on October 15, 1873

(Translated by Academician A. N. Krylov).

(From the Translator)

After the war of 1870–71 there appeared a saying that France had been defeated by the German schoolteacher; the present war shows that since that time the German professor has done the same.

Germany, having after the French war attained unity and a predominant position among the family of nations, understood that unceasing effort and unceasing care were necessary in order to maintain it. She early saw that the unshakable foundation of her power could only be a broadly developed and properly organized industry; and she saw the basis of such an organization of industry in the wide dissemination of technical knowledge, which in turn has as its firm foundation general science, from which it draws the methods and principles for its development. Germany had long understood that the bearers and engines of science are produced by the proper organization of the higher school in the broad sense of the word.

A majestic building requires also a solid foundation: Germany placed the pledge of her power in science, and was not mistaken.

At the present time Russia has fallen into ruin; she will have to work persistently in order to restore her power, at the same time reorganizing the whole order of her life on new principles. In this creative activity science must occupy a lofty position, for it alone possesses the means of judging the future while laying the proper foundations for the present. Without the proper organization of the higher school, a broad development of science is impossible. These considerations have led us to think that acquainting Russian readers with the remarkable speech delivered by the famous mathematician-thinker Karl Weierstrass (K. Weierstrass) on October 15, 1873, upon assuming the office of rector of the University of Berlin, would not be without use.

In this speech the great scholar, in vivid and deeply considered words, sets forth the teaching, developed chiefly by German thinkers,

Advances in the Physical Sciences. 6

with a view to the proper organization of the higher school, and with it also of the secondary school, which the higher school must raise to its own level, and not accommodate itself to it for the sake of number and to the detriment of quality.

All the speeches delivered in this hall during the last three years, except for those of a purely business character, bear the stamp of that great time in which they arose. They are incomparable with ordinary academic speeches intended for a narrow circle of listeners; these were “addresses to the nation,” inevitably imbued with the vigorous breath of life: whether the orator showed to the hostile people, in wrath and indignation at its audacious violation of peace, its true image, expressing at the same time confidence in the victory of his own people; whether another orator offered a reverent greeting to the sovereign leader of the German military forces, as to the Caesar of the restored empire; whether a third, in a historical-political survey, linked the present with the past, foretelling the tasks and goals of the future.

Future historians will count these speeches among the most valuable monuments of our time; we, however, reckon them among those primary sources in which our university preserves the memory of three other glorious years, when the sons of the newest age proved worthy to stand beside the sons of the past.

Gracious sirs, in former times representatives of the university speaking from this rostrum were not only permitted, but even enjoined, to leave aside events directly affecting both them and all of us, as sons of the fatherland and citizens of the state, and touching vividly and deeply upon all questions of the common good; now, it seems, such a time has passed. The enemy land has been cleansed. The foundation of a new state has been laid. Several weeks ago a glorious epoch received, before the eyes of all, its completion with the unveiling of a brilliant monument: “To the Victorious Army from the Grateful Fatherland.” But this completion does not yet mean the advent of an age of peace for our people; on the contrary, in the near future we are threatened by a struggle caused by the opposition of irreconcilable principles; its emergence is only hastened by our very successes, and hardly anyone now living will see its victorious outcome; such an outcome is possible only with the full exertion of all spiritual forces.

That is why the thought of the future and of those serious demands which it will make upon the rising generation compels me, following the old custom, to address my greeting chiefly to those young comrades whose preparation for scholarly activity, for spiritual freedom and courageous firmness of will in

in the turmoil of the present time constitutes more than a direct task and sacred duty of our higher school. I greet all of you, dear comrades, with a heartfelt “welcome,” and especially those among you who today for the first time have the good fortune to exercise their newly acquired right of academic citizenship. You are entering a new circle of your life, and, no doubt, all of you are filled with the most joyful hopes and the most noble intentions. I wish that these hopes may be fulfilled in full measure, and that your intentions may be transformed into fruitful activity. But I should not like to confine myself to wishes alone; I should like to communicate to you something, the knowledge of which is necessary for you, so that from the very beginning you may proceed along your academic path toward a definite goal quite consciously and without hesitation, so that the future which now appears to you so enticing may not bring you bitter disappointments and compel you to express regret that:

Ideals had vanished,
Which once filled the youthful heart.

“Alma mater” is the reverent name given to the university by men whose spirit and character were brought up in it, as they recall on holidays their student years. But the university is not a mother who pours out her love blindly, squandering it upon the unworthy and the weak, indulging senseless desires. Whoever enters the university with the intention of truly receiving that higher intellectual and moral development which can be provided to him here, and together with it the best preparation for his future activity, must not wish only to acquire, must not expect that the wealth accumulated by the spiritual activity of many generations will be given to him without his own having, of course under the guidance of experienced and knowledgeable teachers, labored for its accumulation, investing for this purpose all his will and all his strength. He must not regard as the chief aim of his studies the accumulation of knowledge and skills immediately or in the future practically applicable, but must, above all, as this has aptly been called, strive to learn how to learn. He needs the knowledge that the internal organization of our higher schools is not some arbitrary institution subject to any change, but that it has naturally and continuously developed out of the very essence of the school’s purpose: by educating, to provide well-prepared young people both for the continuity and advancement of science and for service to the fatherland; and this internal organization does not tolerate unfounded external

influence. Therefore each man must judge for himself whether the preparation he has received, in kind and in scope, is sufficient for the assimilation of academic instruction, and he must not demand that the university deviate from its direct task and adapt itself to his personal needs.

Of all these, as well as other equally important questions, you could, dear comrades, learn best if you were acquainted with what has been said on this subject by many of my predecessors in their speeches on taking office, or on other occasions; what has been said is so exhaustive, clear, and instructive that scarcely anything essential can be added to it. In fact, I should consider it useful if at least the most significant of these speeches, perhaps with some explanations, were collected by a skillful hand into a small book—this would make an excellent “guide for students in the organization of their academic life.” It seems to me that it would be best if such a book were given to every student upon his enrollment, together with the rules; perhaps then even these latter would be illumined by the rays of that ideal light in which the university and its essential institutions present themselves to the young student. Indeed, gentlemen, let us suppose that such a book lies before us; I shall show you, by a few examples, what a store of instructive and encouraging material can be drawn from it.

Should you ask about the very idea of the university, about its tasks and purpose, Fichte, the first elected rector of this higher school, answers you: “The higher school exists in order to ensure the continuity and reliability of the progress of education of the human race, whereby, through its mediation, each age may transmit to the next, with prudence and according to firm rules, its higher intellectual development, so that this latter age may likewise increase it and, thus augmented, transmit it to the next, and so on to the end of days.”

Should you then wish to clarify for yourselves wherein lies the distinctive feature of the academic method of instruction, concerning which you are told that it cannot be replaced by even the best book manuals, Rudorff, whose loss we today recall with sorrow, gives you the following explanation: “the essential and indispensable thing in the higher school and in its method of instruction consists in this: that science itself, through direct personal intercourse, is permeated by the elevation of the teacher-investigator and by a youthful, still unspent force, as it were personified, and draws one toward independent work. Not merely the simple communication of knowledge, but chiefly—the teaching of cogni-

—to develop and investigate constitutes the true task of university teaching.”

You, however, are being made to fear that, with such ideal views of the tasks and methods of teaching at a university, it becomes like a fantastical aerial castle, in which there is no place for preparation for the needs of the state, for direct practice and technique, which works wonders and outstrips space and time. “Not at all,” our unforgettable Beck reassures you: “the truly practical consists precisely in this: that the ideal thought, hatched in the ideal, should make its way into life; that the ideal, nowhere and never fully attainable in reality, should be realized approximately; in this way the wheels of life are set in motion, and not by teaching the youth to move mechanically or, more precisely, by training it to let itself be drawn along in the habitual circle of routine business activity, instead of setting the mechanism in motion by the very force and fullness of the mind.”

You hear much about the stagnation of present-day universities and about their unwillingness to adapt to changes of ideas over time, and so forth. To this the same Beck already gave an answer in the following excellent words: “A scholarly institution must not and cannot be immobile; nevertheless, nothing is more useful to it than constancy of spirit and of fundamental principles, if from the very beginning they were sound and good—and here they were so. In such constancy, movement forward is contained of itself.”

I shall not multiply the number of these excerpts, but I would like to draw your special attention to the broad and free conceptions of Fichte and Trendelenburg concerning the very concept and necessity of academic freedom in learning and teaching, as well as to the latter’s insistent admonition to students to begin, in good time, the serious study of sources.

I shall add a few more observations of my own, although I fear that, after all you have heard, they may seem too commonplace to you.

The success of academic teaching is based, as you have already heard, for the most part on the fact that the teacher continually directs the student toward independent inquiries. But this is achieved not by instructions of one kind or another, but above all and chiefly by the fact that, in presenting the subject, the teacher, by the very arrangement of the material and by setting forth the guiding ideas, shows the student the path along which a mature thinker, already in command of all that has been investigated, proceeds in the proper sequence to new results, or to a better grounding of those already known.

The teacher does not, in this case, miss the opportunity to indicate those limits which science at that time had not yet crossed, and also to mention those points from which one may expect the further development of science in the nearest future. He also does not refuse the student an initiation into the course of his own investigations, not concealing even the mistakes made and the disappointments experienced. True, in this way the lectures turn out not so colorful, elegant, and more comprehensible to mentally oblique listeners than lectures (like, for example, those delivered by the majority of French professors according to fully prepared lithographed notes, sometimes even assigned to their assistants to read)¹). In any case, if from such lectures it is possible to gain more knowledge, the former provide greater development.

Every student, after some preparation, must occupy himself also with independent questions. For the majority it is difficult to find for themselves a question that is within their power to solve and at the same time is of scientific interest.

The great mathematician Jacobi, whose teaching I had no occasion to make use of, something I shall never cease to regret, once gave his listeners the following advice: “To sit and wish to make discoveries is not the way to penetrate into science; to clarify for oneself all already known particulars to complete distinctness, to work on problems, whatever they may be all the same—this is the path along which one may encounter the true problems of science and the beginnings that lead to discoveries.”

True, only very capable minds are in a position to do this. To others one may better recommend another path, following which Jacobi himself, as is known, found occasion for many of his works. In old, little-read collections of scientific institutions, as well as in the extensive scientific correspondence of scholars of former times, there is contained an enormous quantity of scientific material, from which anyone who is able can extract much that stimulates his own work and, along the way, can learn much that is useful.

I shall touch in passing on two more points. The striving toward investigation corresponds to the need, implanted in the very inner essence of man, to notice order and lawful connection in the successive and joint existence of things. Individual scientific disciplines acquire their significance because they all

¹) It should be noted that the facts reported by Weierstrass relate to the period of the 1870s in France. Before this period and after it France always stood ahead of other countries in the matter of organizing academic teaching. (Ed.).

contribute to this goal, not disconnectedly, but forming, as it were, a single chain which, beginning with mathematics as its extreme link, extends through the various branches of the natural and historical sciences, in the broad sense of the word, to philosophy as the other extreme link. Mathematics and the natural sciences are concerned with the manifestations of the forms of being in space and time: the former—with ideal ones, existing only in thoughts and only in general as possibilities; the latter—with those realized in action in the material world. Thus mathematics is a necessary prerequisite of the natural sciences, and not an auxiliary discipline in the ordinary sense; conversely, the naturalist, by conducting experiments and observations, in the results obtained by him supplies mathematics with something far greater than a simple collection of problems. Then the historical sciences—properly, history, linguistics, and so on—the task of which is, in the course of the development of the human race, to investigate the moving forces and to set forth the governing laws, are connected with the natural sciences by the fact that the development of human life, both in the people and in each individual person, is conditioned by the interaction between that person himself and everything that exists outside him. Finally, philosophy, embracing the results of all the sciences, purifies them, spiritualizes them, and works toward the realization of the scientific ideal, which consists in the knowledge of unity and of the absolute in the infinite diversity of the phenomena of nature and mental life. In this sense one may say that knowledge of the essence of things is the ultimate goal of all scientific inquiry, and that by the degree to which, on the way toward this goal, mankind has advanced in each century, one may judge also the education of that century.

How, and to what extent, each individual person can and should contribute to the general education of his century is not easy to determine. For you, dear comrades, the following indications will suffice. First of all, it has been established that there is no more fruitless occupation than to take on much and to go deeply into nothing; next, only by devoting yourselves to the deeper study of one principal subject will you in general learn to understand the essence of scientific inquiry. Moreover, now, when all scientific fields not only contain an enormous accumulation of material, but many are also in a state of very rapid development, no one can attain the point of mastering the entire totality of knowledge, as was possible in former times for especially gifted and tirelessly working people. Nevertheless, even at the present time it is possible for a well-prepared and diligent young person, alongside a thorough study of the principal subject, to engage, at least to such an extent as to obtain a correct conception of the tasks and scientific sig—