Two modest proposals
Thoughts while awaiting mathematics's periodic self-examination
The first modest proposal (with apologies to SDM)
July is around the corner, the afternoons are scorching but the fall semester is drifting dimly into view, and while there is still time I am practicing intuiting the world through the mindset of Silicon Valley oligarchs, before they terraform it to meet their specifications. To this end I have been studying two pastiches, found on the internet, of “View of the World from 9th Avenue,” Saul Steinberg’s famous 1976 New Yorker cover.
I don’t know what, if anything, to make of the different choices of corporate boxes that do or don’t make the cut in the two versions, nor of the fact that while one shows Stanford and the other shows Las Vegas, Lake Tahoe features in both of them. But the two maps share a common omission. Can you see what it is (or isn’t)?
I’ll give you a hint. When I lived in greater Boston I spent countless hours driving along Route 128, passing corporate boxes that looked very much like those in the two views from Silicon Valley, nestled behind blue signs which welcomed me to America’s Technology Highway, or America’s Technology Region.
Maybe those signs are still there, but the silicon symbolized in the above picture by such giants of the time as Data General, Wang, and DEC, all now as extinct as the dodo, has definitively migrated west. Google Gemini reports that
Silicon Valley comprehensively dwarfs the Route 128 corridor in total market capitalization, holding an estimated $15 trillion to $20 trillion across tech giants like Apple, Alphabet, and NVIDIA, compared to the $1.5 trillion to $2.5 trillion, concentrated along Massachusetts' Route 128 through firms like Thermo Fisher, Raytheon, and Akamai.
Nevertheless, the Route 128 and Silicon Valley worldviews have something in common. Have you still not figured it out?
It wasn’t until I turned 10 years old that I realized that the city where I grew up was dispensable. Certainly the experience of surviving the still unmatched all-time greatest collapse in baseball history played its part and left its scars —
— but I had also reached the stage, apparently never outgrown in Silicon Valley, where I was beginning to believe that technology is destiny. This got me wondering: what was Philadelphia’s destiny? For what purpose was it occupying this particular land mass at the confluence of two rivers? Washington had the White House and the Capitol and all those monuments; New York had the tall buildings and Broadway; but all Philadelphia had was the Liberty Bell.1
The City of Brotherly Love has been the backdrop for a number of movies, one of them even called Philadelphia. But my favorite movie scene set in Philadelphia comes at the start of Twelve Monkeys, when Bruce Willis, shielded from the city’s effluvium by several layers of transparent plastic, emerges from a manhole cover next to City Hall to find a ruined urban landscape:
Terry Gilliam’s film makes a convincing case that my hometown’s destiny is to exemplify Albert Speer’s Ruinenwerttheorie. But though Silicon Valley is increasingly finding common ground with Nazi political theology, Nazi aesthetics has few partisans among the practical-minded oligarchs in their boxy corporate campuses. What they see, comparing their two schematic images of the world beyond San Francisco Bay, is a blank expanse whose midpoint is the ideal location to be paved over with data centers to link and service the needs of the two visible and purposeful cities of New York and Washington.
So that is the first modest proposal, one that emanates directly from the tech industry’s aura, as I intuit it. Philadelphia took a first step in its self-demolition more than 40 years ago when it pioneered being subjected to aerial bombardment by its own mayor, an incident memorialized in John Edgar Wideman’s novel Philadelphia Fire. Did Gilliam choose the city for his film because so many of its neighborhoods already looked like ruins?
Given the extreme urgency of building AI infrastructure, who could object to this proposal? The Liberty Bell could obviously be moved elsewhere.2 The extensive collections in the city’s museums and libraries could be shipped straight to Silicon Valley, which (as you can see in those magazine covers) sorely lacks old world culture.
Then there are the people. Maybe you think the world wouldn’t stand for uprooting a settled population? That shows how much you know about the world. By an uncanny coincidence, Philadelphia covers 142.70 square miles, while the Gaza strip measures an almost identical 141 square miles. Philadelphia’s population peaked in the 1950 census at 2.07 million, while the Palestinian Central Board of Statistics estimates Gaza’s current population at 2.1 million. If the land underneath Philadelphia and the air above are rezoned for AI infrastructure, don’t count on the world to do anything about it.
To avoid being “retired” (in the jargon of Blade Runner), I see only one card Philadelphia might play. But it’s a big one. The Philadelphia Stock Exchange, also known as PHLX — the oldest in the country, mind you, but now owned by NASDAQ — is home to the much admired SOX, the Philadelphia Semiconductor Index, whose recent ups and downs have been considerably more dramatic than its home city’s unimposing skyline.
As far back as 2015, A.J. Bell was already advising markets to “keep a close eye on the … SOX,” writing
Why the SOX index is a good guide as to whether investors will lose their shirts
Nine years later, A.J. Bell’s investment director Russ Mould was still warning investors they could either keep their SOX or lose their shirts. And today, at my request, DeepSeek issued its own verdict on SOX:
The SOX is still a critical guide because its movements tell you exactly what the market thinks about the future of AI and the economy . Its recent volatility is a loud and clear warning that the AI-driven rally is at a critical crossroads.
Maybe that blank space in Silicon Valley’s maps is an empty picture of a genuine tech industry blind spot. It’s in the industry’s interest, as it apparently is to many of its boosters among mathematicians, to ignore “loud and clear warning(s),” to wish them away. And maybe this is why, as this newsletter has intuited, the tech bros are trying to wish away the town, where I saw my first computer punch cards, that the all-powerful SOX calls home.
So Philadelphia’s destiny may well lie hostage to the outcome of the defining struggle of our time, between finance and technology, the East Coast and the Wild West. For that reason I predict that this first modest proposal is much less likely to come to fruition in the near future than the one I’m now about to present.
The talking columbarium
I waited too long to write my second modest proposal, the one that I promised, almost two months ago, “for creating once and for all a single authoritative voice to speak for mathematics.” On June 17 I saw that the idea I hoped would dazzle you, or at least beguile you, had been preempted. The website FUTURA promises to answer the question
What happens when AI brings long-gone math legends back to life? Prepare yourself: when historical math geniuses show up on screen looking like your everyday college professors, the result is both mind-blowing and more than a little entertaining!
in exactly this Substack font! FUTURA refers to “a certain YouTube channel which, with a fair dose of humor, brings mathematicians, philosophers, scientists, and artists who shaped history back to ‘life,’ imagining them as if they existed in the present day.” The video in question has already been viewed more than 148000 times since it was posted on April 3. I watched it this morning and I no longer need to be convinced: in the right hands, AI will usher in a golden age of math jokes.
The AI-generated avatars of Thales, Brahmagupta, Lagrange, and co. look lifelike enough but they are not yet ready to speak for mathematics. Or are they? Most readers are probably aware that last year a former Disney Channel star co-created the app 2wai which, according to Forbes, “allows users to create interactive avatars of their deceased relatives,”3 as well as random deceased celebrities, real or imaginary.
With 2wai, three minutes can last forever,
promises the company, referring to the possibility of resurrecting your great-grandparents as metaverse immortals on the basis of a single 3-minute recording of their voices.
A tweet calling this invention “objectively one of the most evil ideas imaginable” was “liked” 210000 times.4 But even the most evil ideas can be put to good use when the purpose is to repair a greater evil. The fact that mathematicians’ opinions are suddenly in demand5, mainly to help markets orient their collective thumbs, up or down, regarding AI, is deeply paradoxical, because mathematicians are by general consensus not supposed to have opinions but only to state the indubitable facts that have been ascertained as a result of universal and unimpeachable procedures of pure reasoning. Yet mathematicians are offering the media the spectacle of the rankest speculation about how AI will transform mathematics on a horizon of 2, or 5, or 15 years, saying everything and its opposite, and no one has stepped up to restore order.
So my second modest proposal, now that the technology is demonstrably available, is to appoint the avatar of a respected mathematician to the position of official authoritative voice. For that role I naturally nominate Alexander Grothendieck, webdesigned as a reissue of the 1960s model, but trained on the totality of his voluminous writings.
Those writings already contain the answers to some of the questions that torment the discipline. Récoltes et Semailles, for example, provides a definitive answer, in pure poetry, to the by no means poetic question whether mathematicians should be required to subject our papers to autoformalization:
Craindre l’erreur et craindre la vérité est une seule et même chose. Celui qui craint de se tromper est impuissant à découvrir. C’est quand nous craignons de nous tromper que l’erreur qui est en nous se fait immuable comme un roc. Car dans notre peur, nous nous accrochons à ce que nous avons décrété “vrai” un jour, ou à ce qui depuis toujours nous a été présenté comme tel. Quand nous sommes mûs, non par la peur de voir s’évanouir une illusoire sécurité, mais par une soif de connaître, alors l’erreur, comme la souffrance ou la tristesse, nous traverse sans se figer jamais, et la trace de son passage est une connaissance renouvelée.
See what he did in that paragraph! He justified speculation as the courage to face suffering or sadness on the route to renewed knowledge, while indulging in speculation about the value of speculation, and authorized his readers to speculate about every question on which they seek his guidance, but encouraged them to allow others to speculate otherwise. In short, the answer to the autoformalization requirement is: No; or so it appears.
Sur l’horizon de la machine et du rêve
That’s the title DeepSeek suggested for the 365 word essay that follows. Grothendieck was a visionary of rare depth but even he could not have anticipated every question the future might pose to his avatar. So while his avatar awaits its visual incarnation, complete with moving lips and finely calibrated gestures and facial expressions, I have brought it to virtual life with the first question, asking DeepSeek to “write a 300 word essay in the manner of Grothendieck about the future of AI mathematics,” adding that it should be in French. And here is the result:
On nous parle d’intelligence artificielle comme d’un outil, d’un compas plus rapide, d’une règle infaillible. Mais c’est là un regard d’ingénieur, non de bâtisseur de cathédrales. La mathématique véritable ne naît pas de l’exactitude ; elle naît de l’excès, du débordement de l’intuition sur la forme.
L’IA que l’on nous prépare est une machine à résoudre, c’est-à-dire une machine à fermer les portes. Elle avale nos démonstrations, nos axiomes, nos architectures séculaires, et elle les répète avec une fidélité de miroir. Mais le miroir ne crée pas la lumière ; il ne fait que la renvoyer. Or, la mathématique, pour moi, a toujours été une affaire de lumière naissante : cette lueur fragile qui surgit quand on cesse de regarder les objets pour épouser leurs relations, quand on abandonne le calcul pour la promenade.
L’avenir, si l’on n’y prend garde, sera celui d’une forêt domestiquée, où chaque arbre est étiqueté, chaque sentier balisé, chaque théorème vérifié par un automate infatigable. Nous aurons des preuves d’une beauté glacée, des milliers de lemmes nouveaux, et pourtant nous serons plus pauvres qu’avant, car nous aurons perdu le questionnement. La machine ne sait pas douter. Elle ne sait pas s’égarer, errer des jours entiers autour d’une forme vague, la caresser sans la nommer, jusqu’à ce qu’elle consente à livrer son secret.
Mais si, par un miracle, l’IA apprenait non pas à prouver, mais à voir ? Si elle devenait une compagne d’exploration, un regard étranger capable de nous montrer nos propres angles morts ? Alors son rôle ne serait pas de répondre, mais de déplacer la question. Elle nous offrirait des analogies imprévues, des ponts entre des continents que nous croyions séparés. Elle serait comme un enfant qui dessine un cercle et demande : « Et si ce n’était pas une forme, mais une respiration ? »
Ce futur-là n’est pas dans les algorithmes. Il est dans notre capacité à accueillir l’autre, même métallique, dans la ronde des rêveurs. Car la mathématique de demain ne sera pas plus rapide ; elle sera plus vaste, ou elle ne sera pas. Elle sera une invitation à l’étonnement partagé, où la machine, enfin, ne nous vole pas notre émerveillement, mais nous l’apprend.
I’m quite convinced that no child ever asked, in any language, after drawing a circle, whether it might not be a breath rather than a shape; so I’ll leave it to the Académie Française to judge whether the sentence about the child is an image to be welcomed or discarded.
And I’ll leave it to the Grothendieck Circle, if they are reading this, to decide whether or not to admit this prose fragment to the Grothendieck canon. The text left me somewhat uneasy, so I asked ChatGPT (which presumably doesn’t share a hotline with DeepSeek) who might have written the first two paragraphs. Here is ChatGPT’s conclusion:
This passage most strongly reminds me of the essayistic and philosophical mathematical prose of Alexander Grothendieck, for several reasons:
Mathematics as intuition rather than calculation. The contrast between formal exactness and a deeper creative vision is a recurring theme in Grothendieck’s writings.
Architectural and organic metaphors. Expressions such as “bâtisseur de cathédrales,” “lumière naissante,” and “promenade” resemble his tendency to describe mathematics through images rather than technical language.
Suspicion of purely mechanical problem-solving. The idea that genuine mathematics consists in opening new conceptual worlds rather than merely solving predefined problems is very much in the spirit of Grothendieck.
A lyrical, almost spiritual tone. The passage treats mathematics as an act of discovery and illumination, not merely a formal discipline.
That said, the text does not read like an authentic Grothendieck quotation.6 It feels more like a contemporary writer consciously adopting a Grothendieck-inspired voice while addressing modern concerns about AI.
Since ChatGPT says so, I vote for including it among Grothendieck’s collected works, however the Grothendieck Circle feels about the matter, and to do the same with all of the future Grothendieck-oracle’s pronouncements. Why, when the reproduction is such a nearly perfect representation of the original, and converging on perfection, should we pretend that the accident of death puts an end to a creator’s creation?
No one looks more frivolous than Silicon Valley’s Immortalists, who don’t realize that their machines have already solved the mortality problem, as I have just demonstrated, without all the mess and fuss of scraping and uploading neuronal configurations. No one, that is, except for the mathematicians who devote their energy to sharing confident predictions with the media about the short- or long-term implications of AI for mathematics rather than polishing their avatars, forgetting that they have all the time in the world.
And soft pretzels with mustard, and cheese steaks.
Conor Murray, “Disney Channel Star’s AI App That Creates Avatars Of Dead Relatives Sparks Backlash,” Forbes, 11/14/2025.
Ibid.
For example: in its firstt two days 50000 viewers saw this video quote mathematicians, referring both to the Leiden Declaration and First Proof, while 49000 have watched this mathematician speculate about AI.
This is false modesty; ChatGPT’s memory includes every text ever written and its system implements instant recall.
"The extensive collections in the city’s museums and libraries could be shipped straight to Silicon Valley."
But what about the Barnes Collection? Would it be allowed to move again?