For those of you who don’t know (and shame on you if you don’t), David Hilbert was one of the giants of 19th-20th century mathematics. Despite his very English-looking name, he was German by birth and by upbringing and lived almost his entire life in Königsberg and later Göttingen. Although Hilbert wrote instrumental papers in dozens of fields of mathematics and physics, he is most famous for proposing a list of 23 unsolved mathematical problems that Hilbert thought were critical to the future. Today, eleven of Hilbert’s problems have been solved unequivocally and a further eight have been partially resolved or resolved but not to the universal satisfaction of mathematicians. Just as Hilbert anticipated, the solutions of the problems, even the partial and controversial solutions, have been central to the evolution of modern mathematics.

Now you may be wondering why I am bringing up David Hilbert. The answer is in this rather waffly piece by Peter Wood entitled “How Our Culture Keeps Students Out of Science.” Given that this essay is all in favour of  encouraging school students into science, you might think I would agree with it. You would be wrong. I wanted to agree with it. But then I made the mistake of reading it. Now I’m not going to punish you by following Wood’s meandering trail of unsupported assertions and blithe asides that bring nothing to the argument. I am, however, going to take issue with this statement:

A society that worries itself about which chromosomes scientists have isn’t a society that takes science education seriously. In 1900 the mathematician David Hilbert famously drew up a list of 23 unsolved problems in mathematics; 18 have now been solved. Hilbert has also bequeathed us a way of thinking about mathematics and the sciences as a to-do list of intellectual challenges. Notably, Hilbert didn’t write down problem No. 24: “Make sure half the preceding 23 problems are solved by female mathematicians.”

It is, I must confess, a mystery to me why a writer trying to encourage students to engage with science should make statements to the effect that women shouldn’t really bother. Given that the article is about the cultural barriers to science education, I would have thought that defending a rather, er, unnuanced view of female capability was counter-productive. Oh, I know, Wood’s point is that we should be putting more effort into teaching students to enjoy science than encouraging lots of ill-fated female applicants to join a field in which they are unlikely to excel. It’s a “let’s not waste effort” argument. Which might make sense if our mathematics and science faculties were brimming with women who were not producing much good work. I challenge Wood to support his intimation with some evidence. In fact, I’ll go one better. I hereby challenge Wood to explain his own choice of data. You see, as Wood points out,

The big problem? As of 2001, 80 percent of engineering degrees and 72 percent of computer-science degrees have gone to men.

Note the very careful choice of departments. Wood is only quoting figures for engineering and comp. sci. fields, which have traditionally borne a heavy masculine bias. But if Wood is correct, then women have not taken over these fields and therefore cannot be blamed for any dumbing down or lack of student interest. Wood is, of course, fretting about contemporary attempts to redress the gender balance. We should not, he argues, fritter away our energies trying to encourage women to become engineers or computer gurus because they just aren’t all that interested or good at it. This might be a sound argument if he could show that the influx of women into other more welcoming fields, such as the biomedical sciences, had caused disruption to research and teaching quality. I dare say Wood is going to find it hard to make that demonstration stick.

So back to David Hilbert, whom Wood misrepresents woefully. For one thing, Wood’s “24th” conjecture is rubbish. The reason why Hilbert would never have asked how to make half his problems be solved by women is that this is not a mathematical question. But even if we allow Wood his clumsy rhetorical device, it ought to be said that Hilbert would have been devastated to see this frippery attributed to him even in jest.

Back in the early twentieth century, a young mathematician of Bavarian stock came to the attention of David Hilbert. Her name was Emmy Noether. She went on to revolutionise algebra, field theory, and topology. Her first theorem, published in 1918, remains one of the pillars of modern physics. Whenever you hear physicists talking about symmetry, they are drawing on Noether’s First Theorem. If it had not been for Hilbert, she would probably never have found work in the German university system. Hilbert could not protect her completely and Noether suffered discrimination despite his constant support. Her outstanding mathematical publications were never rewarded with a senior position let alone tenure, and much of her work at Göttingen was in unpaid honorary positions (although in this case it was the university that was honored by her rather than vice versa).

So, you know, Mr Wood, if you want to change the culture of science to make it more attractive to school students, I have to wonder why you would spend such a large chunk of your essay telling the female half of the cohort that they are neurologically unsuited to maths and hard science and that efforts to encourage them will prove fruitless. You should not have put words in Hilbert’s mouth, especially words so antagonistic to Hilbert’s real beliefs. I would rather you had used Hilbert as an example of a great mathematician reaching out to support another great mathematician despite the many barriers that were placed in her way. (As well as suffering for the lack of a Y chromosome, Noether was a Jew and was cast out of the University of Göttingen during the Nazi sweep of academia—a dismissal that Hilbert fought against once more, this time unsuccessfully.) Instead of hijacking Hilbert’s 23 problems for a cheap jibe, you could have used Hilbert as an example of the sort of scientist we should be looking to put in positions of influence: one who will recognise and foster great talent wherever it lies, regardless of sex or race, and in the face of grave political and cultural discouragement. That’s the sort of culture change that would help science.

The best thing Hilbert ever said on the subject of women in science was this: When Noether’s appointment to the University of Göttingen was being blocked by stubborn faculty members, one of them complained to Hilbert that the students would resent learning “at the feet of a woman.” Hilbert replied that it should not matter. “We are a university, not a bath-house.”

Adjunct: It is one of my favourite quirks of history that Emmy Noether came to prominence around the same time that Einstein showed that her surname was a literal description of the structure of space and time.

Tags: david hilbert, education, emmy noether, Eureka!, Eureka!, peter wood, women