Snail image: Creative Commons licence courtesy of Te Papa; Clairaut’s love formula from Chapter 6 of MWA
My tireless editor Vickie Kearn at Princeton University Press has brought me the welcome news that Mathematics without Apologies will be coming out in a paperback edition next spring. I started this blog for two reasons, and one of them — to clarify my intentions in writing the book — will vanish when I add two or three pages to the preface of the new edition. The new pages — I have already written them — will devote one paragraph or so to each of four topics, provisionally under the headings charisma, memoirs, utility, and ethics; each paragraph will address some of the points raised by comments on this blog as well as in some of the more negative reviews.
My other reason for starting this blog was to find some outlet for the wealth of material that I was not able to incorporate in the book. Most of this material has remained untapped while I composed comments on current events or new findings, and I was idly wondering when I would get around to sifting through the 7 GB or so that is gathering nanodust on my computer’s hard drive. My Eureka! moment came when I realized that I had already devoted a considerable amount of my free time to writing the book during the better part of three years. Perhaps I didn’t really want to return to the old material? With the new preface, I can finally declare the book finished and move on to something else.
Will it be another book, maybe one that will win me the mythical seven figure advance? Or will there be another blog, or the same one under another name? That’s for the future to decide. Meanwhile, this one will remain visible, but with no new entries.
My thanks to the regular readers and occasional visitors who helped keep the blog from slipping into solipsism. And my special thanks to authors of comments who, by disagreeing, often sharply, with opinions expressed here, demonstrated that the meaning of mathematics is still a matter of controversy.
This was supposed to be the last entry, but I’m now thinking I should include part of the new preface material — or all of it, if PUP allows it. Meanwhile, in order not to let anything go to waste, here is the post on which I was working when I realized that this blog had reached the end of its natural life…
I Cunfirenti
This was originally going to be an appendix to the playlist near the end of Chapter 8: an exploration of the attitude to mathematics in the genre of organized crime ballads. The deeper meaning of Rick Ross’s 2009 single Mafia Music was exposed even before it was released, but I was unable to find an interpretation of the unexpected appearance of mathematics in the middle of this rap à clef:
I thought about my future and the loops I could pin.
Walked out on a gig and I turned to da streets,
Kept my name low key, I ain’t heard from in weeks.
I came up with a strategy to come up mathematically,
I did it for da city but now everybody mad at me.
Apart from Rick Ross, Gödel is the only person Google finds who can “come up mathematically.” My guess is that Ross’s strategy (unlike Gödel’s) involves money. But Ross is not really a gangster, and Mafia Music is not really a mafia song at all; in fact, by naming names the song breaks what I’m told is the most fundamental of all the rules of the Italian Malavita, namely the rule of omertà, the iron law of silence.
Now it struck me when I saw this that the mathematical profession has its own version of omertà, probably not very different from other forms of academic rules of silence, having to do with forms of behavior that straddle the line that divides the unpleasant from the unethical. The behavior protected by mathematical omertà differs from other varieties in that it tends to inspire less literary commentary. Instead it consists in scandalous rumors whispered in corridors when they are not being shouted across barroom tables, but that must under no circumstances be mentioned in public. (There was a scurrilous exception in a well known literary magazine a few years ago, but I will not dignify it with a link.)
I am particularly sensitive to this rule just now, because in the past few weeks I was shocked to learn of abuse of power by several colleagues I would not have believed capable of such behavior (and by a few others I can easily believe capable of anything). Whether being the repository of such confidences is one of the perks of my charisma, or whether it’s the abusers who feel newly entitled as a result of their own charisma, the mildest punishment I could expect if I chose to betray the dark secrets of the mathematical profession is not to be privy to such secrets in the future. Breach of Mafia omertà is treated more harshly than that. Many of the songs on the delightful album La Musica della Mafia are devoted to the many kinds of punishment the gangster ethic —
Laws that don’t forgive those/Who break their silence
reserves for traitors — cunfirenti, in Calabrian dialect. For example, the song entitled I cunfirenti promises that they will find “their final resting place in concrete walls” (‘Mpastati ccu cimentu e poi murati).
The album’s title is imprecise; it’s not a collection of songs of the Sicilian mafia but rather the ballads of their Calabrian declension, the ‘Ndrangheta, who deserve to be better known, and not only for their songs:
What I find most charming about this collection is the contrast between the lively rhythms of many of the songs and the uniformly grim, often bloody, content of the lyrics. For example:
Malavita, malavita
Appartegnu all’Onorata
Puru si c’impizzu a vita
Eu nun fazzu na sgarrata
Which means
Malavita, malavita!
I am one of the honorable society.
And even if it costs me my life,
I will never surrender.
If you’re looking for mathematical content you have to skip to the last verse:
Ed eo chi tingu sangu ´nta li vini
Su prontu d’affruntari mille infami
A chista genti ci rispunnimu
Pidi sunu pronti centu lami
Which means
And I who have blood flowing through my veins
Am ready to face 1000 traitors
As they know all too well
That 100 sharpened knives are ready for them.
Mathematics without Apologies, by Michael Harris 
“…opinions expressed here, demonstrated that the meaning of mathematics is still a matter of controversy”
That phrase was quite serendipitous for me as I’ve been thinking a lot about that very topic in the last 24 hrs. while reading an exchange between Ed Frenkel and Michael Baranyi on Twitter (you may or may not have followed it). I mostly agree with Ed (though was surprised by the harshness of some of his tweets), but find it interesting and telling that a field viewed by so many as dull and dry (as math), can still have such disputes over basic meanings (am tempted to write about the exchange for my own blog, but may not find the time and energy).
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Thanks for letting me know about that. I’m afraid my attention span is too long to follow a philosophical argument in 140 character segments, and I can’t figure out who said what.
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It’s ok, MH, I have a hard enough time following it myself, and I wrote a non-trivial portion of the tweets!
Hope you have a chance to compose some thoughts about it, SR. I’ve found the variety of reactions to my original Scientific American post quite revealing, with some big differences between public and private responses I’ve received.
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I read the Scientific American article when it came out and I wrote you to say that I wasn’t sure I agreed with your analysis, but it didn’t seem all that controversial to me. It makes some substantial claims, by implication, about the intentions of elite decision-makers, and these claims would have to be documented. I realize that there is no room for such documentation in a blog entry (much less in a tweet!) but I am not familiar with the literature on the topic. I have been interacting with the French educational system at all levels for more than 20 years and I am well aware that mathematics is a primary means, if not the primary means, of elite selection, but I still don’t understand why.
You have written about institutional support for mathematics in the postwar period, especially in the US, and while I’m not professionally qualified to judge the validity of your conclusions, I can certainly recognize that you have made important contributions to understanding how decisions were made. In my book I repeatedly express my belief that mathematicians need to be extremely modest in commenting on the conclusions of disciplines, in which they lack professional training, and this applies particularly to history of mathematics. Not all colleagues display the necessary modesty, and the problem may be compounded when they express themselves in what McLuhan called “hot media.”
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On the other hand, the use of the term “minorities” in connection with Enlightenment France looks anachronistic to me. Are you thinking of Italian immigrants?
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“Minority” was certainly a watchword in that period. E.g. it’s a central term in Kant’s “What is Enlightenment?” though you’re right the term had different connotations then vs now. But nation (and ethnicity), religion, gender, and other classifiers — then as now — could be associated with minority status.
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I will miss your blog!
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I am not in the same league as most of those who have participated in the very long interchange with Michael, however, I do wish that it were possible to save this entire dialogue (all 400 or so pages) just to permit a slow and careful read.
I have found it fascinating, enlightening, and encouraging.
Dick (aka oldrubbie)
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There is a website called Storify that allows you to organise tweets into a coherent and chronologically correct narrative (as opposed to whatever gunk Twitter threading churns out).
I think it would be incredibly useful and educational to see someone do that for this debate (I read some, and wish I could have gotten a better ‘view’ of it).
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Thank you, Michael, for running the blog, and engaging with the commenters. It has indeed helped clarify the book, as you saw in my review. I hope this site is not left to vanish like to so much digital ephemera — perhaps it could be donated into the Internet Archive.
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