Weyl on Hilbert and Hilbert on others

We give some extracts from Hermann Weyl's paper 'David Hilbert and his mathematical work', Bull. Amer. Math. Soc. 50 (1944), 612-654:


Weyl on Hilbert

Hilbert was singularly free from national and racial prejudices; in all public questions, be they political, social or spiritual, he stood forever on the side of freedom, frequently in isolated opposition against the compact majority of his environment. He kept his head clear and was not afraid to swim against the current, even amidst the violent passions aroused by the first world war that swept so many other scientists off their feet. It was not mere chance that when the Nazis "purged" the German universities in 1933 their hand fell most heavily on the Hilbert school and that Hilbert's most intimate collaborators left Germany either voluntarily or under the pressure of Nazi persecution. He himself was too old, and stayed behind; but the years after 1933 became for him years of ever deepening tragic loneliness. ...

Hilbert's was a nature filled with the zest of living, seeking intercourse with other people, above all with younger scientists, and delighting in the exchange of ideas. Just as he had learned from Hurwitz, so he taught his own pupils, at least those in whom he took a deeper personal interest: on far-flung walks through the woods surrounding Göttingen or, on rainy days, as "peripatetics" in his covered garden walk. His optimism, his spiritual passion, his unshakable faith in the supreme value of science, and his firm confidence in the power of reason to find simple and clear answers to simple and clear questions were irresistibly contagious. If Kant through critique and analysis arrived at the principle of the supremacy of practical reason, Hilbert incorporated, as it were, the supremacy of pure reason - sometimes with laughing arrogance (arrogancia in the Spanish sense), sometimes with the ingratiating smile of intellect's spoiled child, but most of the time with the seriousness of a man who believes and must believe in what is the essence of his own life. His enthusiasm was compatible with critical acumen, but not with scepticism. The snobbish attitude of pretended indifference, of "merely fooling around with things," or even of playful cynicism, were unknown in his circle. You had better think twice before you uttered a lie or an empty phrase to him: his directness could be something to be afraid of. He was enormously industrious and liked to quote Lichtenberg's saying: "Genius is industry." Yet for all this there was light and laughter around him. He had great suggestive power; it sometimes lifted even mediocre minds high above their natural level to astonishing, though isolated achievements. I do not remember which mathematician once said to him: "You have forced us all to consider important those problems which you considered important." His vision and experience inspired confidence in the fruitfulness of the hints he dropped. He did not hide
his light under a bushel. ...

Were it my aim to give a full picture of Hilbert's personality I should have to touch upon his attitude regarding the great powers in the lives of men: social and political organization, art, religion, morals and manners, family, friendship, love, and I should also probably have to indicate some of the shadows cast by so much light. ...

Hilbert was not only a great scholar, but also a great teacher. Witnesses are his many pupils and assistants, whom he taught the handicraft of mathematical research by letting them share in his own work and its overflow, and then his lectures, the notes of many of which have found their way from Göttingen into public and private mathematical libraries. ...

His speech was fairly fluent, not as hesitant as Minkowski's, and far from monotonous. He had no difficulty in finding the pregnant words, and liked to emphasize short pivotal phrases by repeating them several times. On the whole, his lectures were a faithful reflection of his spirit; direct, intense; how could they fail to be inspiring?

We now give some quotes by Hilbert describing other mathematical colleagues.

First, comments by Hilbert on Hermann Minkowski delivered in a memorial address in 1909 to the Göttingen Gesellschaft der Wissenschaften:


Hilbert on Minkowski

Our science, which we loved above everything, had brought us together. It appeared to us as a flowering garden. In this garden there are beaten paths where one may look around at leisure and enjoy oneself without effort, especially at the side of a congenial companion. But we also liked to seek out hidden trails and discovered many a novel view, beautiful to behold, so we thought, and when we pointed them out to one another our joy was perfect.

Hilbert gave an address to honour Otto Blumenthal on 30 September 1905:


Hilbert on Blumenthal

When I think of our friend Otto Blumenthal, his entire being, his activity, his mind, nothing seems more appropriate to me than being able to identify the most characteristic feature of his personality as the drive to work, the genuine joy in working and creative energy. It reveals itself in small things and large; we noticed it at an early stage, when as a student he tried to obtain the most comprehensive education in the many fields of mathematics, physics and chemistry. And now that he has become our colleague, we see his zeal in preparing for lectures, his willingness to take over a course which has to be held but which absolutely nobody feels like doing; the effort that he puts into helping his students, how he organises student lectures and takes over intractable doctoral candidates of whom we despair ...

Hilbert wrote a letter of reference for Paul Bernays:


Hilbert on Bernays

Paul Bernays's publications cover a variety of areas of mathematical science: the representation of positive integers by binary quadratic forms (dissertation supervised by Edmund Landau), elementary theory of landau's function of Picard's theorem (habilitation thesis in Zurich), Legendre's condition in the calculus of variations, one-dimensional gas as an example of an ergodic system, axiomatic treatment of Russell's propositional calculus (habilitation thesis, Göttingen, not printed). Several papers on philosophical topics, in "Abhandlungen der Friesschen Schule".

All this scientific work is characterised by thoroughness and solidarity. Often it focuses on a specific fundamental question requiring elucidation, which is analysed with astuteness and foresight, or on an existing important difficulty that is then overcome with great skill. Bernays's knowledge is extraordinarily broad and deep, and it extends into the domains of philosophy, physics and biology.

He is characterised by a loving dedication to science; beyond that he is a noble-minded person of reliable character, highly esteemed everywhere. In all problems concerning the foundations of science, above all those of mathematical science, he is the most thorough expert, and in particular the most valued and most successful member of my staff.

On 5 January 1929 the Mathematical Institute at Göttingen opened and Hilbert gave a speech at the opening ceremony. In it he mentions that the initial idea was due to Felix Klein, but it was Richard Courant who brought the idea to fruition:


Hilbert on the Mathematical Institute and Courant

Allow me a few words of introduction to the celebration we are holding today in honour of this wonderful institute, the halls of which now festively receive us here in the midst of distinguished and welcome guests. From eminent secretaries and curators to young assistants and Privatdocents, many have invested their energy and labour in the creation of this institute; you will soon be hearing more on this topic from one better qualified than myself. If I may say just one thing at the outset: there is one man without whom nothing of what you see here would have come to be, a man who set in motion the mechanism for the creation of this institute and who maintained it to its successful end. it is our dear friend and colleague Richard Courant.

The idea of this institute, cherished and nurtured by Felix Klein, lived once upon a time and was charming and lovely, like Sleeping Beauty, and we who have been here a while took proud pleasure from it; but the Wicked Witch of inflation put this Sleeping Beauty into a sleep so deep that all forgot about her until Prince Charming Courant awakened her to new life. ...

Ladies and Gentlemen, realising the idea of building the institute was a great and difficult task entailing smaller problems. Courant treated each of these with the same love and devotion, always knowing how to find and cajole the most suitable and understanding man for the task - never taking the stage himself but remaining in the background, so that in many circles his efforts were hardly noticed while each one of those mobilised for the work contributed his share with the same joy as though he had set himself the task.

Everyone should know that the institute is, in reality, his work. And that, if he was able to achieve this great success - and here we have the one and only reason for this accomplishment - it was because he put his wholehearted energy in the work from the beginning. And for this reason we want to give him out wholehearted thanks.


JOC/EFR October 2013

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