A Fifty-Year-Old Critique of Mathematical Proof as an Anti-High-Modernist Manifesto: A Reflection on the Limits of Rationalism

In 1976—at what seems like the dawn of the software age—my colleagues Richard Lipton, Alan Perlis, and I wrote a paper that fractured the calm surface of computer science. Social Processes and Proofs of Theorems and Programs1 was a direct, unfiltered assault on the burgeoning formal program verification movement. At the time, the software engineering community was infatuated with a seductive promise: that complex computer programs could be mathematically proven “correct,” eliminating human error and systemic unpredictability once and for all.

Looking back now, nearly half a century later, Social Processes… seems larger than a technical critique. Viewed in retrospect, our paper was a reflection on the limits of rationalism, an anti-high-modernist manifesto that anticipated the exact failure modes of today’s automated governance and laid the philosophical groundwork for resisting what I now call the Sovereign Code Doctrine.

The High-Modernist Illusion of Absolute Verifiability

We did not use the phrase “high-modernism” in 1976, but we were fighting its purest expression. As the political sociologist James C. Scott later argued in Seeing Like a State,2 high modernism is characterized by an absolute, blind faith in linear progress, standardization, and top-down rational design. The high-modernist administrator looks at complex, organic human systems and sees only messy inefficiencies to be optimized away. The high-modernist’s instinctive response is to force reality into a simplified, “legible” grid that can be centrally monitored and controlled.

The program verification movement of the late 1970s was the ultimate manifestation of this hubris within the digital realm. Its architects believed that the messy, iterative, and deeply human process of software development could be entirely flattened into a centralized grid of formal mathematical specifications. Enamored by formal methods, they presumed that a computer program could exist as a closed system of pure deductive logic, completely insulated from the chaotic variables of real-world application.

We saw this ambition as a dangerous illusion. We argued that a formal verification is not a conduit to absolute truth, because a specification complex enough to describe a real-world program is inherently either unreadable or incomplete. Even if such a specification could be imagined, it is mathematically impossible to guarantee that the code at hand represents a flawless implementation of it. The formal methodists were trying to replace the rich, localized context of software execution with a hollow, stylized caricature of mathematical perfection.

The Defense of Metis and the Open Software Society

In place of this sterile, technocratic positivism, we championed what Scott terms metis—the practical, experiential, and localized human knowledge that allows communities to adapt to unexpected anomalies. We reminded the computing world that mathematics itself does not progress through a bloodless chain of formal logic. Instead, mathematics is a social process.

A mathematical proof is accepted not because an automated oracle validates its syntax, but because it survives a grueling, communal gauntlet of peer review, debate, assimilation, modification, and historical consensus. Proof is not a mechanical derivation. It is a conversation. There is no other way to explain why among the many thousands of published proofs of theorems, an infinitesimally small fraction of them live on in the collective mathematical consciousness. A proof is an organic ecosystem of minds interacting over time. Software, by extension, derives its reliability from the same open, empirical process: it is read, tested, contested, and corrected by human beings operating within a shared culture.

This defense of the social process aligns our 1979 argument with the political epistemology of Karl Popper. In The Open Society and Its Enemies, Popper argues that absolute verification is a myth; human knowledge is fundamentally fallible, and the only protection against authoritarianism is an environment of critical rationalism where laws, ideas, and state policies remain permanently vulnerable to public challenge and falsification.

By applying this Popperian framework to computer science, we were making an early argument for an Open Software Society. We declared that code can never be accepted as an unchallengeable truth. It must remain open to human scrutiny, iteration, and rejection. The moment software is insulated from this social process, it ceases to be a tool of human reason and becomes an instrument of dogmatic authority.

The Tragedy of the Invisible Failure Mode

High-modernist architectures possess a fatal structural flaw: because their designers harbor a blind faith in the perfection of their models, they systematically dismantle the practical safeguards required to survive unanticipated errors.

We issued a stark warning regarding this psychological trap. We foresaw that a dogmatic belief in code “correctness” would breed a reckless complacency among system designers. Believing their software to be infallible, engineers would abandon the messy, defensive, and redundant safeguards—the margins of safety—that analog practitioners had relied upon for generations to recover from systemic failures.

When you engineer the human element out of a system under the guise of optimization, you do not eliminate error; you merely ensure that when the system fails, the failure mode is invisible, silent, and catastrophic. The telemetry is instantly erased, the capacity for local human intervention is stripped away, and the individuals governed by the system are left entirely defenseless.

From 1976 to the Mechanized State

The warning markers we planted out nearly fifty years ago have reached their logical destination in the modern Mechanized State. What we debated as a technical problem in software engineering has mutated into the defining constitutional crisis of our time: the rise of Sovereign Code.

Today, across the core infrastructure of public administration, from automated risk assessments in criminal justice to unauditable voting architectures in federal courts to AI-driven targeting decisions on the battlefield, tech bureaucrats deploy opaque, self-executing algorithms that make life-altering decisions without the burden of public justification. When these systems are challenged, their high-modernist defenders invoke the same defense we exposed in 1976: the architecture is too complex to inspect, too technical to reconstruct, and too optimized to be questioned by ordinary human beings.

Social Processes was a warning that absolute efficiency is a euphemism for absolute capitulation. It reminds us that our institutions are not trusted because they are mathematically correct, but because they remain permanently open to human challenge. To preserve the Republic against the encroachment of Sovereign Code, we must reclaim the core thesis of our early manifesto: we must reject the false idol of automated perfection, embrace the essential, protective friction of human messiness, and insist that no machine can ever be permitted to rule where human reason has been optimized out of existence.


Richard DeMillo/May 22, 2026/Atlanta/


  1. DeMillo, Richard A., Richard J. Lipton, and Alan J. Perlis. “Social Processes and Proofs of Theorems and Programs.” In Ideas That Created the Future: Classic Papers of Computer Science, edited by Harry Lewis, 447–62: MIT Press, 2021. ↩︎
  2. Scott, James C. Seeing Like a State: How Certain Schemes to Improve the Human Condition Have Failed. Yale University Press, 1998. ↩︎

Why Fed 10?

Federalist No. 10 is ultimately about opacity and unaccountable power, the great threats to democracies.

At first blush, it may not seem like it, but this is a technology blog. See? Here is some technology to prove my point.


Those are voting machines (as imagined by DALL-E to look as imposing and impenetrable as possible).

I’m dismayed that the reality of exercising your rights as a citizen in Atlanta, Georgia, in 2024 is only slightly less imposing and impenetrable.

How this technology works, where it comes from, and who is in charge are questions that connect deeply to who we are as a nation.

The machinery of government when the U.S. Constitution was drafted by James Madison and others looked something like this:

It looks peaceful enough, but things went awry almost from the beginning.

The first formal vote by Virginia colonists was after the Susan ConstantGodspeed, and Discovery arrived at the Chesapeake Bay.

The London Company had appointed Christopher Newport as the commander of the three-ship expedition that left London in December 1606 and carried over 100 people planning to live permanently in Virginia, but Newport would return home and others would govern the colony after arrival. Once the ships reached Virginia, the sealed box with the names of the new leaders was opened.

The company’s instructions appointed John Smith as one of the seven people on the council that would govern the colony, but the other appointees immediately decided to block him from participating. Smith had been locked up for most of the journey across the Atlantic Ocean. Evidently he was not very gentle when expressing his point of view, and others on the ships were not experienced at working together as members of a team. Captain Newport even proposed to hang Smith while the expedition sailed through the Caribbean before turning north to reach Virginia in April, 1607.

Because Smith was blocked from participating in the first vote to choose a President of the Council, voter suppression began at the very start of colonization in Virginia. Smith was added to the council with the right to vote before Captain Newport sailed home in June, 1607, but the Council remained a dysfunctional group of leaders.

There was voting in Virginia from the beginning of English settlement, but the number of voters was always tightly constrained. Only existing members of the Council (or company officials in London) could select new members of the Council; the other colonists had no ability to choose their leaders. Only members of the governing council, or the political/military leaders later appointed by the company, were authorized to vote on managing the colony until the company created a representative assembly in 1619.

Two months after Newport returned to England, half the colonists were dead or dying. The members of the Council accused their President, Edward Maria Wingfield, of hoarding food. By a vote of the council, Wingfield was deposed.

Madison was a Virginian, and he would have known these events and others that unfolded over the century and a half between the founding of Jamestown and the constitutional convention in 1787. He would have known about human nature and the fragility of decision-making to balance competing interests and beliefs. Yet the constitution is nearly silent on how democracy works. Article One, Section Four says it is up to the States to decide. And that is all.

But that is not all we know about how democracy is supposed to work. Madison, Alexander Hamilton, John Jay (and probably others) pored over the roadmaps that have taken us from colonial Virginia to these times–which everyone seems to believe are times of unique peril–and told us what they were thinking.

We know considerably less about what these people are thinking:

Federalist Paper No. 10 is about factions—groups of individuals united by a common interest or passion adverse to the rights of others. Madison says factions are inevitable due to human diversity, especially in opinions, wealth, and property. It is also about information: since factions are unavoidable, accessibility to information that expands the public sphere is the only way to control them in a democracy. Complex rules and technology undermine society’s access to information. Opacity, misinformation, disinformation, and unaccountable power are the great threats. Madison’s spirit haunts the present.

TO W. T. BARRY. MAD. MSS.

Aug 4, 1822

Dr Sir, I recd. some days ago your letter of June 30, and the printed Circular to which it refers.

The liberal appropriations made by the Legislature of Kentucky for a general system of Education cannot be too much applauded. A popular Government, without popular information, or the means of acquiring it, is but a Prologue to a Farce or a Tragedy; or, perhaps both. Knowledge will forever govern ignorance: And a people who mean to be their own Governors, must arm themselves with the power which knowledge gives…

Check back with us soon as we discuss how the ideals of Democracy have been undermined by complex rules and technologies that neither policymakers nor technologists fully understand. As James Madison–author of Federalist 10 — said, a government without accessible information is a “prologue to a farce or a tragedy.”