I. A few days ago *MWA* was mentioned on MathOverflow in connection with a discussion introduced by Ryo with the following comment:

Many distinguished mathematicians, at some point of their career, collected their thoughts on mathematics (its aesthetic, purposes, methods, etc.) and on the work of a mathematician in written form.

Ryo invited users “to create a “`big-list`

” of the kind of works described in the above blockquote.” A few users obliged by proposing entries for a list that, for the moment, could hardly be called “big” (but maybe a “`big-list`

” doesn’t have to be physically big?).

Do you notice anything wrong with this list? Or maybe the question should be: do you notice anyting peculiar about the list, as it stands at present? (Take another look before reading ahead to see the answer.)

If you haven’t found the answer yet, please look back to this (meta)-discussion and to these observations by Izabella Laba, all dating to early 2011. That happens to be exactly when I began mining MathOverflow as a source of information about implicit assumptions about hierarchy and charisma (routinized and otherwise) in mathematics, with specific reference to this discussion.

A lot could be said about the MathOverflow discussion of the relative scarcity of women among active participants: for example, that it comes across as a sincere effort to address a genuine problem but that the effort was hampered by the absence of reliable empirical data and even more by the participants’ inability to agree on an appropriate methodology to begin asking questions that would lead to evaluate the scope of the problem (or even to realize that such a methodology is a necessary starting point); or that it was marred by what seems to me a misplaced display of tolerance of the defense of mathematical cultures where, to quote one user, “there are no such insubstantialy [sic] strong feminist views in women communities.” But I will just recommend that readers look over the comments and read Izabella Laba’s post carefully, and decide for themselves whether or not they have anything to do with the “`big-list`

” problem.

Many women mathematicians (including two mentioned in this post) have written and continue to write books for a broad public that speak *about* mathematics, the items on the “`big-list`

“, as I understand it, are meant to speak *for* mathematics, *in the name of* mathematics. I assume some MathOverflow users are familiar with essays (though not books) written in the genre of “distinguished women mathematicians speaking *in the name of women in mathematics*,” which is a respected and necessary genre but apparently not considered worthy of inclusion in the “`big-list`

“.

Maybe some readers of this blog will want to remedy this omission. [UPDATE: it has already been done on MathOverflow.] This post is concerned with what is wrong with the book to which the blog is dedicated; the question raised by the omission is whether, while purporting to speak *in the name of * mathematics as such, and indeed going so far as to announce the intention of doing so in its title, *Mathematics without Apologies *may instead be speaking *in the name of * a specifically male (not to say *laddish*) vision of mathematics. I will not go so far as to invoke standpoint epistemologies and instead mention what may be a typical example. Chapter 8 devotes a long discussion to the use of words like *philosophy*, *strategy*, and *tools* as metaphors for mathematical practice, and suggests a parallel with the trifunctional theory Georges Dumézil developed in his analysis of Indo-European mythology. But the trifunctional theory clearly reflects a society organized around the leading roles of *men* (in spiritual, military, and productive matters). Could *MWA* have focused on metaphors corresponding to female roles in the traditional division of labor? Indeed it could have explored how proofs are put together from *ingredients*; the *cleaning lemmas* that appear in fields as diverse as quantum computing, combinatorics, and singularity theory; and the domesticity of the *Weyl chamber*.

The suggestion is definitely NOT that it would somehow be more respectful to women mathematicians to stress that diverse sexually stereotyped metaphors occasionally appear on the dreary landscape of mathematical prose. It is rather to acknowledge that the standpoint underlying the choices made in the writing *MWA *may well not be that of the neutral voice speaking *in the name of* mathematics itself but is rather overdetermined by a history of male domination in mathematics that parallel the domination in the broader society. At the very least this undermines any claim that the author has (except in Chapter 9) systematically avoided introducing autobiographical elements except where they can be construed as representative of the mathematician in its purity that is ideal-typical, and presumably neutral with respect to gender as well as any other natural or social category.

II. Much evidence is presented in *MWA* to support the contention that pure mathematicians pursue our vocation in search of pleasure — or, as Stefaan Vaes explained to the Queen of Belgium, *omdat wij dit graag doen. *In the interest of honesty, however, more attention should have been given to mathematics as a source of *pain*, which may take the form of *anxiety*, *dread*, *grief*, or even *despair*. I would guess that nearly all the mathematicians reading this blog know perfectly well what I have in mind, and that the impossibility of conveying to a non-mathematician what it entails makes the experience all the more painful.

*MWA *records the exhilarating moment when, in the words of Marie-France Vignéras, “one direction becomes more dense, or more luminous.” But frustration may be the more universal experience of mathematicians. It’s common enough for mathematicians to report that most of their working time is spent getting nowhere. Occasionally something about the mathematician’s experience is so painful that it can only be relieved by suicide. The word “suicide” occurs exactly once in *MWA* (not counting the ritual *hara-kiri* performed in the film *Rites of Love and Math*) but I have been aware of suicide among mathematicians and students of mathematics since my earliest days as a student. Four of my fellow students had killed themselves by the time I had obtained my Ph.D. I didn’t know them well enough to understand their motivations, but at the time it was assumed that they gave up out of a sense of failure. Two of them had been forced to take jobs in places where they did not want to live, with no prospect of leaving unless they left mathematics. Their suicides may have made them *martyrs*, but not *madmen* — the two roles typically reserved for mathematical characters in popular culture.

In a peculiar way, the incidence of suicide among mathematicians — I don’t know how it compares to other professions, but it is certainly not negligible — confirms the model proposed by *MWA* that mathematics is a *relaxed field*. Some may feel that mathematicians are being immature when we insist on the pleasure principle at the expense of the reality principle; but frankly, what’s so great about reality when it consists in subordinating one’s freedom of action to projects that outsiders are able to assign to us simply because they are Powerful Beings, and whose goals we may find profoundly distasteful. The other day a graduate student in the common room was saying that he wanted his life to be organized in such a way that his work was his hobby. A second student found that perfectly natural. That is the purest possible expression of mathematics as a relaxed field, and nothing is more characteristic of the vocation than the willingness of its practitioners to suffer extraordinary levels of frustration, even pain, rather than submit to the reality principle that reigns elsewhere.

(Future posts will treat some of the many other things that are wrong with *MWA* but that have been neglected by the occasional hostile reviewer.)

David Roberts(I haven’t read all the post yet, but an initial comment)

“relative scarcity of women” make that “relative scarcity of women using female usernames”. It may be that some female mathematicians are pseudonymous/anonymous users for self-preservation reasons. Certainly in the ‘top’ users as ranked by reputation are almost all using their own names, and all of these are men. Given the origin of the platform in programming, and the overwhelming preponderance of men in that area, it wouldn’t be surprising to me that the mechanics of the site are geared towards male motivations (Competition, badges etc)

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mathematicswithoutapologiesPost authorYes, I assumed readers would figure that out by reading the discussion on MathOverflow, but it’s important to stress that distinction, even if no one knows what it means in practice.

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bf1) “Self-preservation reasons”: maybe we should do something so that this is no longer necessary, instead of viewing it as an unavoidable fact of life?

2) “all of these are men” possibly because becoming a top user requires investing a lot of time on the site – a more precious commodity for women that, on average, have larger duties outside mathematics.

3) “the mechanics of the site are geared towards male motivations”: Don’t know. I found that when you can compete fairly, women can enjoy competition quite as much as men. E.g., I certainly enjoyed getting consistently higher marks than my classmates in college ;). But reputation at mathoverflow is a mix of wasting time and peer evaluation, and the latter is heavily male-skewed.

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David RobertsThanks, bf. I heartily agree with 1). I would also humbly suggest that, in 2), male mathematicians may (I stress *may* – I have no evidence) have to ‘prove themselves less’, so can even divert time on MO that would otherwise be spent eg writing papers.

The points+badges system is is such that I know male mathematicians have voiced their aversion to it, knowing its essential silliness and propensity to become self-serving.

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NameYou misspelled the word negligible.

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mathematicswithoutapologiesPost authorDo you mean négligeable?

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mathematicswithoutapologiesPost authorI’m happy to open this up to a continuation of the exchange that took place last year on MathOverflow, and I will filter out comments I find offensive or culturally inappropriate. Let me stress, though, that the purpose of this post was to point out a few of the numerous flaws of

Mathematics without Apologies, specifically flaws that the occasional hostile reviewers missed. I brought up MathOverflow because the recent proposal for a “big-list” unintentionally highlighted an asymmetry, in the literature of mathematicians writing about mathematics; the earlier MathOverflow discussion, extended by Izabella Laba’s comments, is one of the few occasions on which the context for this asymmetry was treated with some of the attention it deserves.LikeLike

mathematicswithoutapologiesPost authorUPDATE: As of 16 hours ago, a new text by Mathilde Marcolli has been added to the MathOverflow “big-list,“ repairing the omission mentioned in the post:

http://mathoverflow.net/questions/220052/essays-and-thoughts-on-mathematics/220671#220671.

The text was published in an AMS book entitled

Art in the Life of Mathematiciansthat I somehow missed when it came out. It’s fascinating and thought-provoking and will undoubtedly be analyzed here at some point in the coming weeks. The first sentences suggest a relation to high art that is very different from the one hinted at in this posthttps://mathematicswithoutapologies.wordpress.com/2015/05/04/mathematicians-as-hackers-or-tricksters/

but at the same time the title is taken from the transcript of the obscenity trial for Allen Ginsburg’s

Howl(to which there is an allusion inMWA). So I don’t yet know what to think.LikeLike

Izabella LabaThank you for the shoutout to my blog. It might be useful to mention that Matilde’s essay (which I also found fascinating) is available online from her webpage, complete with illustrations. My own essay (also available online) is more specific to photography, except maybe for the first and last section. The contributions in that book are sort of all over the place: we had no guidelines as to what was expected, except that something about math be included. As I suppose you’ll see, different people aimed in very different directions.

You probably missed the book when it came out because the AMS did basically nothing to promote it. I’m not even sure if they know what “ARC” stands for. Anyway, I rather enjoyed your review of that exhibit in Paris a while ago, and I’m curious to know what you think of this book.

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mathematicswithoutapologiesPost authorThank you for writing. I’ve just read your essay, in the form on which you posted it on your blog, and I find its spirit, especially in the first section, to be very close to that of my book, in particular in your dissection of Hardy. If your essay is typical of the AMS book then everyone should get a copy.

Mathilde Marcolli’s first page, with expressions like “our house was frequented by a circle of…” practically begs to be parodied (and I did try to parody that kind of writing in my Chapter 2, though some critics thought it was the real thing). If you enjoyed my review of the Fondation Cartier exhibition in Paris you’ll understand what I mean. What I found most valuable in her essay, along with the fascinating images, was its discussion of

violence, as in the sentence “Violence, bullying, and intimidation exist and are practiced on a daily basis within the mathematical community, and there is a widespread ‘culture of cruelty’ among its practitioners, but it is incredibly difficult to even find a venue where such issues can be openly discussed.” There may not be muchphysicalviolence in mathematics, but I thoroughly agree with the sentiment and I think that the harshness of the judgment adds a valuable backdrop to the MathOverflow discussion.LikeLike

Izabella LabaI’m not sure that my essay, or Matilde’s, is that representative. The usual tropes about symmetries, tilings, golden means and the like make a few appearances; on the other hand, there were also some unexpected delights. Most of the contributors are both high-level mathematicians and also active practitioners of some kind of art, so you get less pontificating from the high chair (although there’s some) and more behind-the-scenes looks at how the sausage is made. Not all of the contributors are also writers practicing on a regular basis, and that shows. On the other hand, one of the less polished essays is also one of my favourites in the book, based on what the author has to say.

I agree with Matilde that the culture of academic mathematics has a deep layer of intellectual violence, and that this is especially true for women. I already write about sexism on my blog, so I did not want to replicate it yet again in my essay in AITLOM. (In fact, the first draft was just about photography, with mathematics hardly mentioned at all.) But my assessment would be similar, even if I might write about it differently.

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mathematicswithoutapologiesPost authorIzabella has convinced me to take up the topic of mathematical cruelty in my next post, which won’t be for a week. I can draw on a number of anecdotes as well as texts and I hope to hear more about other colleagues’ experiences of intellectual violence, especially the experiences of women.

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