The German mathematician David Hilbert was born in Konigsberg on January 23, 1862. He studied and taught at Konigsberg University until he transferred to the University of Gottingen in 1895, where he made an immense contribution to various fields of mathematics. For example, in 1900, he proposed 23 mathematical problems for investigation, most of which have since been solved.
Hilbert was described as a gay young man with a reputation as a snappy dancer and a charmer who flirted outrageously with a great number of women — traits that would not suggest Asperger Syndrome. However, this chapter will present evidence that he may in fact have displayed characteristics of this syndrome.
Life History
Richard Courant found Hilbert to be “a unique personality, profoundly immersed in his work and totally dedicated to his science, a teacher and leader of the very highest order, inspiring and most generous, tireless and persistent in all of his efforts” (Reid, 1970, p. 2). His mother Maria Therese was an unusual woman — she was interested in philosophy and astronomy, and fascinated by prime numbers. His father was a county judge, “rather narrow in his point of view with strict ideas about proper behavior, a man so set in his ways that he walked the same path every day and so rooted in Konigsberg that he left it only for his annual vacation on the Baltic” (Reid, 1970, p. 3).
As a boy, Hilbert had an intense desire for truth, but he described himself as a dull and silly youth. He found memorization exceedingly difficult, and language classes caused him more sorrow than joy. He was not particularly quick at comprehending new ideas. A member of the Hilbert family recalled, “all I know of uncle David is that his whole family considered him a bit off his head. His mother wrote his school essays for him. On the other hand, he could explain mathematics problems to his teachers. Nobody really understood him at home” (Reid, 1970, p. 6). Mathematics appealed to him, and he was delighted with it because it was easy and effortless. It required no memorization.
Hilbert found the perfect mate, married, and fathered a child in 1893. The boy, Franz Hilbert, was “disturbed.” Hilbert said “I must consider myself as not having a son” (Reid, 1970, p. 139; Einstein also ignored a son with mental illness). It is not clear whether or not Franz had schizophrenia, but he did announce that he wanted to save the family from evil spirits that were after them. It was said that he lacked tact and would speak of his views inappropriately.
Work
Hilbert did not grasp complicated ideas in a flash and took his time to get to the bottom of matters. He set high standards of simplicity and clarity for his talks to the mathematics club. After his death, Nature described Hilbert as a “mathematical Alexander.” This is typical of persons with Asperger Syndrome and genius; there is a parallel with Wittgenstein.
Hilbert’s conception of mathematical existence was freedom from contradiction. He divided his working life into periods during which he occupied himself almost exclusively with one particular problem. If he was engrossed in integral equations, integral equations seemed everything. When he dropped a subject, he dropped it for good and turned to something else. There were five periods in his working life:
- theory of invariance (1885-1893)
- theory of algebraic number fields (1893-1898)
- foundations — (a) of geometry (1898-1902); (b) of mathematics
in general (1922-1930) - integral equations (1902-1912)
- physics (1910-1922).
Max Von Lau, a Nobel Prize winner, noted, “Pure mathematics … did not fail to impress me, especially in the brilliant courses of David Hilbert.” He went on to say that Hilbert was “the greatest genius I ever laid eyes on” (Reid, 1970, p. 68).
Hilbert’s lectures were in some ways like Wittgenstein’s, in that he prepared them only in the general sense and then tried to work out the details in the lecture. At times they were mathematics in the making. His lectures were a faithful reflection of his spirit (direct, intense).
Social Behavior
For Hilbert, comradeship and human solidarity were essential to scientific production (contrary to an Asperger trait). He complained about a lack of mathematical conversation. Students had to be careful about offering a lie or an empty phrase to him, and his directness could be something to be afraid of (Reid, 1970, p. 53). He was not good with children.
Hilbert was described as “a bit of an arrested juvenile” (Reid, 1970, p. 131). He would come to a lecture hall in short-sleeved opennecked shirt — inconceivably inappropriate attire for a professor in that day. He pedaled through the streets with bouquets from his garden for his “flames,” but was just as likely to bear as his gift a basket of compost balanced on the handlebars. At a concert or restaurant, no matter how elegant, if he felt a draught, he borrowed a fur or a feather boa from one of the ladies present. He liked pretty young ladies and delighted in explaining mathematical ideas to them. He fancied himself a dashing man of the world.
Hilbert thought the war was stupid, and said so (not unlike Bertrand Russell’s views). He refused to sign a declaration in favor of the war and was treated as a traitor.
Narrow Interests/Obsessiveness
Hilbert had an extraordinarily focused attention on mathematics — he once described himself as a mathematical Eskimo. Richard Courant said that Hilbert had “a fantastic balance between intense concentration and complete relaxation” (Reid, 1970, p. 109).
Routines/Control
As we have seen, Hilbert imposed strict self-control in terms of work. He was also controlling of others; when he went to a restaurant after a lecture, the subject of conversation was “only algebraic number fields” (Reid, 1970, p. 51). His active influence on the mathematicians of his time was embodied in a statement that one of them made directly to him: “You have made us all think only that which you would have us think” (Reid, 1970, p. 214).
He absolutely denied the reality of his physical illness — pernicious anemia — which was more or less fatal at the time he got it. It seems that his wife was entirely devoted to him and looked after him. However, there is no sense of reciprocal social interaction with her. She simply provided for all his needs, while he was totally controlling, dominant, and he appears to have entirely imposed his will on her in the home situation. He would have been lost without her and could not have lived the life he lived.
An example of the importance of routines in Hilbert’s life appears in an anecdote told about him: One day, at a party in their house, his wife asked him to go upstairs and put on a clean shirt. After some time, when he had failed to reappear, she went upstairs and found him asleep in bed. For Hilbert, the natural sequence of things was to take off his coat, then his tie, then his shirt, and so on, and then go to sleep (Reid, 1970).
Language/Humor
Hilbert delivered his lectures with many repetitions to make sure that everyone understood him and repeated briefly what had been covered in a previous lecture. His sentences followed each other simply, naturally, and logically. We have no definite evidence of abnormalities in this area. What was very unusual about his language was its content, with an almost exclusive focus on mathematics.
Naivety/Childishness
Hilbert was said to have had “all the naivety and the freedom from bias and tradition which is characteristic only of true great investigators” (Reid, 1970, p. 53). His mathematical approach was to go back to questions in their original conceptual simplicity. George Polya said that Hilbert always “looked so innocent” (Reid, 1970, p. 132).
Hilbert demonstrated a “naive and imperative egoism” that was always “egoism in the interest of his mission, never of his own person.” He once made an interesting comment about Einstein: “Do you know why Einstein said the most original and profound things about space and time in our generation? Because he had learned nothing at all about the philosophy and mathematics of time and space” (clearly, he thought spending too much time reading others’ work was counterproductive) (Reid, 1970, pp. 141-142).
Lack of Empathy
Alfred North Whitehead wrote, “The leading characteristic of mathematics is that it deals with properties and ideas which are applicable to things just because they are things, and apart from any particular feelings, or emotions, or sensations, in any way connected with them. This is what is meant by calling mathematics an abstract science” (Whitehead, 1948, p. 2). It is perhaps one of the reasons why the study of mathematics has attracted many people with Asperger Syndrome.
Hilbert seemed to lack tact in his relationship with “the flames” he pursued. He basically denied the existence of his son when he got ill. He couldn’t really relate to children, as we have seen, and would spend just a minute or so with them. This is not unlike Bertrand Russell.
While he had very intense relationships with mathematicians, these were exclusively focused on discussing mathematics, which is typical of Asperger Syndrome. He could also relate in a social way to students, but again, even at dinner, mathematics was the focus. The brutality with which he could dispose of someone who did not meet his standards was well known. Hilbert once told Norbert Wiener, later a famous mathematician himself, that his lecture was “the worst there ever has been!” (Reid, 1970, p. 170).
Despite being married himself, Hilbert was against scientists marrying. When Wilhelm Ackerman married, Hilbert was very angry and refused to do anything more to further Ackerman’s career. Ackerman, a gifted young logician, had to teach in a high school.
Nonverbal Communication Problems
From photographs, Hilbert appears to have had a peculiar, stiff gaze.
Motor Clumsiness
He was probably not clumsy because he was a good dancer. In very high-IQ Asperger Syndrome, clumsiness does not come into the picture. It is possible that in cases where clumsiness does come in, a somewhat lower IQ exists and maybe more severe brain pathology. (True Asperger Syndrome probably does not include clumsiness, which should therefore be excluded as a criterion for it — this may be the one item that Asperger himself got wrong.)
Anxiety/Depression
In 1908, Hilbert became depressed and spent time at a sanatorium. The breakdown did not seem to be triggered by any specific experience. Courant, in the Foreword to Reid’s (1970) book, wrote that “almost every great scientist I have known has been subject to such deep depressions.” He felt that this might be due to periods in the life of a productive person when he appears to himself to be losing his powers, which can come as a great shock.
Conclusion
David Hilbert meets the criteria for Asperger Syndrome, according to Gillberg (1996), with the exception of an absence of speech and language problems and motor clumsiness. However, neither of these features is essential for such a diagnosis, while their absence would suggest a diagnosis of Asperger’s disorder under the American Psychiatric Association (1994) classification. It is likely that Asperger Syndrome/disorder helped Hilbert to become as creative as he was in mathematics because it gave him the kind of exclusive focus that is necessary for major creativity.
- Michael Fitzgerald, Former Professor of Child & Adolescent Psychiatry
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