Mathematics and the Undead

How Silicon Valley plans to "disrupt" mathematics

Zombie calculus teacher at the blackboard, imagined four times by Open AI’s DALL-E

The fact is, we couldn’t explain, not even in principle, anything to a zombie. This is because if one explains p to x, then x must grasp or understand p, but grasping or understanding requires being conscious. A rock will never grasp anything; it would be perverse to ask how we might explain dreaming to a slab of granite. Yet zombies are, by definition, no more “alive on the inside” than a rock.¹

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                        The intelligence of the corporate person is already artificial

The U.S. Supreme Court may oblige us to adhere to the doctrine of corporate personhood, but it can’t force us to contemplate engaging in social or any other kind of intercourse with the likes of Alphabet or Meta. When we ask ourselves why this is the case, we may or may not conclude with Marx that

Capital is dead labour, that, vampire-like, only lives by sucking living labour… If the labourer consumes his disposable time for himself, he robs the capitalist.²

but we certainly agree that a corporation is a peculiar kind of person, not the sort you’d like to take out to dinner. This is because, as Tony Smith writes, “capital as pure form is pure emptiness.”³ Philosophers have another name for a being of pure emptiness: they call it a zombie.

The usual assumption is that none of us is actually a zombie… The central question, however, is not whether zombies can exist in our world, but whether they, or a whole zombie world…, are possible in some broader sense.⁴

The philosopher’s zombie, according to the online Stanford Encyclopedia article where I found that quotation, is usually assumed to disguise its internal emptiness by looking and behaving like “one of us.” Although Silicon Valley behemoths like Alphabet and Meta and Open AI don’t “look like” anything, something about them disarms our critical faculties. How else to explain that their appropriation of the agenda for the automation of mathematics has been met with equanimity or indifference, has not provoked any objections whatsoever on the part of mathematicians, and indeed has been welcomed by many of the mathematicians most deeply invested in these questions?

                                “To learn about how AI is disrupting mathematics”

In my disjointed remarks at the October Fields Medal Symposium I expressed the concern that, even if human mathematicians were not displaced when a machine like Venkatesh’s א(0) is “let loose upon the world," the process might lead to a devaluation of the human experience of mathematics and, critically, a loss of autonomy on the part of human researchers. This point is often overlooked. Our universities and research centers may be run according to zombie principles, or are directed by literal zombies,⁵ but mathematicians, working collectively, have considerable freedom to determine our working conditions and the direction of our research. This immense privilege, which we share with academics in other disciplines, was acquired relatively recently,⁶ and is constantly under attack by the forces of reaction.⁷ Unlike our colleagues in other disciplines,⁸ mathematicians seem disinclined to argue that we are entitled to this privilege — on the grounds, for example, that it provides a model for the organization of society, to which everyone is entitled in principle.

One reason we may suspect that our academic freedom is an aberration that we are not entitled to defend is that no comparable autonomy is guaranteed to those who work for Silicon Valley’s vampire institutions. We should therefore be alarmed, rather than cheered, to learn that, within a few weeks of our conference on automation of mathematics, organized according to the standards of professional autonomy, the biggest names in the AI industry were heavily invested in two more conferences on the same theme. The 2nd MATH-AI Workshop at NeurIPS’22, whose scheduled speakers are split 50/50 between industry and academia, claims, without explanation, that

The machine learning community has contributed significantly to mathematical reasoning research⁹ in the last decades.

Meanwhile, just two weeks after the Fields Institute Symposium, Meta AI (Facebook) hosted a conference on Formal Languages, AI, and Mathematics at the Institut Henri Poincaré in Paris. A few mathematicians (including two from the Toronto event) were invited, together with representatives of Google, DeepMind (also Google), and Open AI, to show “how AI is disrupting mathematics.”

Whoever thought that Facebook — disrupter of privacy, of elections, of friendship, and of the word “like,” and “no more ‘alive on the inside’ than a rock”— would be a suitable vehicle to teach mathematicians the gospel of disruption has a sick sense of humor. This is not to say that disruption as such is always unwelcome. The strike by graduate student and other workers at the University of California system is the latest reminder that the organization of higher education, especially but not only in the US, is overdue for disruption, and not primarily by the deeply anti-union tech industry¹⁰. The American Mathematical Society recently published a study entitled “Towards a Fully Inclusive Mathematics Profession,” suggesting a need to disrupt the process that tends to reproduce the profession’s current skewed demographic characteristics.¹¹ And of course the substance and direction of research is periodically disrupted, more or less radically, to the point of what in other fields might be characterized as a "paradigm shift" in the sense of T.S. Kuhn.

But these disruptions all arise within the mathematical community. The only example that comes to my mind of disruption on the part of outsiders is the banning of the teaching of infinitesimals as “false and erroneous” by the Revisors Generals of the Society of Jesus:

The Jesuits …fought [this battle] because they believed that their most cherished principles… were at stake.¹²

Silicon Valley’s most cherished principle, we should never forget, is the defense of the bottom line: “Disrupt, then dominate.”¹³ Any human activity that does not contribute to their revenue stream is "false and erroneous."¹⁴ But the Valley has no need of the Inquisition’s thumbscrews and strappado. The tech industry's real stroke of brilliance is to make conformity feel hip, revolutionary, even disruptive. Technical expertise joins intellectual and ethical conformity to give birth to a collective zombie.

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                                        Who speaks for the future of mathematics?

“Modern techies have revived a technocratic sensibility,” Jaron Lanier wrote recently, “a belief that great engineers can and should guide society.”¹⁵ “They think that this is the future of information access, even if nobody asked for that future,” said Chirag Shah, speaking of the spectacular failure of Meta’s Galactica large language model for scientists. Meta promised that Galactica would “summarize academic papers, solve math problems, generate Wiki articles, write scientific code, annotate molecules and proteins, and more.” In practice “it just makes shit up.”

Readers of Silicon Valley press releases expect exaggeration and hype and understand that this is needed to keep attracting investment, which is the primary function of the AI industry, like every other form of undead labor. So when when the organizers of the imminent 2nd MATH-AI Workshop at NeurIPS bemoan the

large performance gap between models and top mathematicians

and set as their goal

to find out “when machines can surpass human experts in different mathematical domains?”

it’s fair to ask: did anybody ask for that future? This very quickly leads to the deeper question: who is entitled to be that “anybody”?

• Is it Mathematics, the universal heritage of humanity? In that case, maybe it’s up to UNESCO, guardian of world heritage, including Intangible Cultural Heritage.¹⁶ UNESCO staked its claim to speaking for Mathematics in November 2019 by declaring March 14 the International Day of Mathematics. UNESCO’s site, however, has chosen to focus exclusively on applications of mathematics, not the experience of mathematics as a heritage in its own right.

• Is it the mathematicians themselves, the “human experts,” welded into a community capable of speaking for itself through our professional organizations — of “living deliberately”? And if so, why on earth would we have asked this list of sponsors to design the future rather than designing it ourselves, as we have been doing throughout history?

• Is it mathematics, an abundant fossilized resource in an unguarded commons, free for the taking by the greatest of the great engineers, the miner with the most expensive shovel?

• Or is it the market… but when did mathematics become a commodity?

Asking the question “Who speaks for mathematics?” and its corollary, “Who sets the agenda for mathematics?” is, and always will be, the main purpose of this newsletter.

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                                              Hegemony and DeepPockets                                                            

The media are constantly bombarding each of us with stories about the desirability of self-driving cars, the convenience of smart homes and cities, the cleverness of crypto, the need to adjust to the inevitable replacement of large sectors of the human workforce by robots. It’s understood, as I already wrote, that this narrative is largely exaggerated and self-serving; it’s also indifferent to real or potential threats to privacy and to the environment. And it concretely affects the circumstances of our lives — at some point I’ll share what I learned when I was confronted with the installation of smart electric meters as a fait accompli, on which none of those most immediately concerned had been consulted, on the basis of often spurious claims.

Is artificial mathematics another example of manufactured demand? Ask yourselves why media like Nature print so many stories covering press releases by DeepMind or Meta AI or Open AI.¹⁷ Nature journalist Davide Castelvecchi publishes just a handful of articles about mathematics in any given year. Does anyone really believe that the results of the DeepMind collaboration with mathematicians, reported a year ago here but also widely in the press, qualify on their own merits, interesting as they undoubtedly are, among this year's 10 or 20 most significant developments in mathematics? Woul they have been considered newsworthy without AI in the title? Although Silicon Valley wasn't directly involved in Castelvecchi's June 2021 article on the successful resolution of Scholze’s Liquid Tensor Challenge, I found the choice of title and subtitle¹⁸ problematic as well, for the same reason — insufficient critical distance from the hegemonic narrative promoted by the tech industry.

It’s hard to escape the conclusion that we are caught in a symbiotic daisy chain of what Venkatesh called “construction of  value,” in which Nature (or Quanta, or New Scientist) runs an article about mathematics and AI because it is seen as exciting, and the development is seen as exciting because it was covered by the press. This whole circular process, vicious or virtuous depending on your perspective, is fueled by DeepMind's (or Open AI’s, or Meta AI’s) highly effective public relations apparatus, which I see as an epiphenomenon of Alphabet's (or Facebook’s) DeepPockets. Compare the resources of

1. Open AI:   $100000000 startup fund

2. Meta (for Meta AI):  Total assets US$166000000000+ (2021)

3. Alphabet (for DeepMind):  Total assets  US$359000000000+ (2021)

with the

4. Fields Institute:  (I should know the figures because I'm on the Scientific Advisory Panel, but I guess it's a few million per year).

Who is in a better position to establish and maintain the hegemonic narrative?

In short, I don't think Silicon Valley should be setting the agenda for (much less disrupting) mathematics. But nor do I think Silicon Valley should be perceived, by the media or by those directly concerned, as setting the agenda for mathematics. Academics are supposed to be critical thinkers, whereas engineers working for industry are primarily  concerned with the bottom line.  There is an extensive literature on how this tension has been handled in biotech. I think it's clear that a conference on the human genome where the speakers are academic researchers would look very different from one where some number of them were primarily working for the pharmaceutical industry. ¹⁹

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This newsletter doesn’t expect to resolve the tension between academic researchers and industry, but hopes rather to heighten it, to accentuate the differences so that they can be subjected to careful critical analysis. Although this essay is barely 2700 words long, Substack is warning me that it is approaching the email length limit. This particular theme will therefore be continued in a few days in the sequel, with the title Understanding vs. Reasoning.

1. Selmer Bringsjord, “In defence of impenetrable zombies,” Symposium on ‘Conversations with Zombies’ (1995).

2. Marx, Capital, Volume 1, Chapter 10, section 1.

3. Tony Smith, https://www.cambridge.org/core/journals/hegel-bulletin/article/hegels-logic-and-marxs-concept-of-capital/9F9E2411E0BBFE54CD0D4DC04B6DEBEB

4. “Zombies,” Stanford Encyclopedia of Philosophy.

5. When I was working in France, speeches I heard by certain higher education officials and government ministers convinced me that the possibility needs to be taken seriously.

6. The roots of academic freedom seem deepest in Germany. From the 1737 Statutes of the Göttingen Philosophical Faculty:

Alle Professoren sollen sich einer verantwortungsbewussten Freiheit der Lehre und der Überzeugung erfreuen, sofern sie Abstand halten von Lehren, die die Religion, den Staat und die guten Sitten verletzen; es soll ihnen frei stehen, die Lehrbücher und Schriftsteller auszuwählen, die sie in ihren Vorlesungen erläutern wollen.

Standards of academic freedom in the United States were formulated in a 1915 Declaration of Principles by the American Association of University Professors, without reference to possible injury of religion, the state, or good morals. This declaration served as the basis for the present codification of standards in the AAUP’s 1940 Statement of Principles on Academic Freedom and Tenure. This statement was endorsed by the Mathematical Association of America in 1965 and by the American Mathematical Society two years later.

7. … who now masquerade as defenders of academic freedom, as in this recent conference at Stanford, which gave a platform to climate deniers, proponents of Covid “herd immunity,” and the inevitable Peter Thiel.

8. See this blog post for an example. I will provide more documentation in a future essay.

9. By narrowly defining “mathematical reasoning” as the sort of process machine learning can handle, the claim of significance becomes more plausible, and the “different domains” mentioned in the next sentence — see below — come more clearly into focus.

10. See https://www.vox.com/recode/23282640/leaked-internal-memo-reveals-amazons-anti-union-strategies-teamsters. A speaker from Amazon will participate in next February’s IPAM workshop on Machine-Assisted Proofs.

11. From a 2015 article by Christopher C. Jett, David W. Stinson and Brian A. Williams in The Mathematics Teacher, published by the National Council of Teachers of Mathematics:

…effective mathematics teachers of black male students disrupt mathematics broadly
as a white enterprise…

And here are some suggestions for “disruption” from the online chat during a recent AMS “paraDIGMS” conference:

We need to normalize the notion of mathematical experience and growth over the framework of "mathematical talent" which poisons graduate education.

They have tended to focus on fixing the person and not the system.

Accreditation: "the action or process of officially recognizing someone as having a particular status or being qualified to perform a particular activity."

When have these places been qualified to support Black and Brown students?

(answer): Never!!

It is widely believed that the Association for Mathematics Research was created specifically to resist this kind of disruption.

12. Amir Alexander, Infinitesimal, New York: Farrar, Straus, and Giroux (2014), p. 174. The murder of Hypatia in 415 A.D. may also qualify as a disruption of mathematics by outside forces.

Wherever money changed hands, enterprising technologists and MBAs were bound to follow. The word "disruption" proliferated, and everything was ripe for or vulnerable to it: sheet music, tuxedo rentals, home cooking, home buying, wedding planning, banking, shaving, credit lines, dry cleaning, the rhythm method.… The endgame was the same for everyone: Growth at any cost. Scale above all. Disrupt, then dominate.

13. Anna Wiener, Uncanny Valley, p. 4, p. 136. The word “disrupt” appears on 11 pages in this excellent book.

14. Open Shoshana Zuboff’s The Age of Surveillance Capitalism to nearly any page if you think I exaggerate beyond the limits of poetic license. For example, from Chapter 14:

Like human experience, society is subordinated to the market dynamic and reborn as objectified computational behavioral metrics available to surveillance capitalism’s economies of scale, scope, and action in the pursuit of the most-lucrative supplies of behavioral surplus.

15. For example:

[Adam] Neumann … rambles on about ‘superpowers’, describes his life’s work as to ‘prepare for the the arrival of the messiah’, and treats WeWork as though it is not so much a machine for getting rich, as a vehicle for the spiritual transformation of the human race.

Daniel Kalder, WeWork’s mad messiah. Lanier quotation from New York Times, November 11, 2022.

16. … an expression that could have been invented to describe mathematics. Mathematics qualifies in at least two of UNESCO’s “intangible heritage domains”: as “Social practices, rituals and festive events” and as “Knowledge and practices concerning nature and the universe.” But I suspect UNESCO’s officers classify mathematics under the E and the S and overlook how it fits in C.

17. Most recently this one in Quanta.

18. The article itself is fine; my objection is to the claims that “Mathematicians welcome computer-assisted proof” (which mathematicians?) and that the verification “reveal[s] a bigger role for software in research.” I especially recommend Johan Commelin’s talk at the Fields Medal Symposium about this project — which he led — for a more nuanced perspective.

19. Daniel J. Kevles and Leroy Hood’s The Code of Codes, a collection of essays on the human genome project that grew out of a 1989-90 lecture series at Caltech, is a classic example of critical thinking applied to technological developments whose implications were already understood at the time to be transformational. Significantly, the Humanities and Social Sciences Division and the Biology Division of the NSF jointly cosponsored the lectures. The contributors presented “a balanced cross-section of views” on the topic, according to the review of the book in Nature. All contributors were academics; none (directly) represented the pharmaceutical industry.