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The Usefulness of “Useless” Knowledge (and Why AI Makes Flexner Even More Right)

I just finished reading The Usefulness of Useless Knowledge again, this time with the perspective of living through a period of rapid technological acceleration driven by AI. On an earlier reading, Flexner’s defense of curiosity-driven inquiry felt aspirational and almost moral in tone, a principled argument for intellectual freedom. On rereading, it feels more diagnostic. Many of the tensions he identified (i.e., between short-term utility and long-term understanding, between institutional incentives and genuine discovery) now play out daily in how we fund, evaluate, and deploy AI research. What has changed is not the structure of his argument, but its urgency: in a world increasingly optimized for immediate outputs, Flexner’s insistence that transformative advances often arise from questions with no obvious application reads less like an idealistic manifesto and more like a practical warning.

In 1939, on the eve of a world war, Abraham Flexner published a slim, stubbornly optimistic essay with a mischievous title: The Usefulness of Useless Knowledge. His claim is not that practical work is bad. It’s that the deep engine of civilization is often curiosity that doesn’t start with an application in mind, and that trying to force every idea to justify itself immediately is a reliable way to stop the next revolution before it begins.

Robbert Dijkgraaf’s companion essay (and related pieces written from his vantage point at the Institute for Advanced Study) updates Flexner’s argument for a world that is now built out of microelectronics, networks, and software; this is exactly the substrate on which modern AI sits. Reading them together today feels like watching two people describe the same phenomenon across two eras: breakthroughs are usually the delayed interest on “useless” questions.

Below is a guided tour of their core ideas, with a detour through the current AI moment, where “useless” knowledge is quietly doing most of the work.

Flexner’s central paradox: curiosity first, usefulness later

Flexner’s essay is a defense of a particular kind of intellectual freedom: the right to pursue questions without writing an ROI memo first.

Dijkgraaf highlights one of Flexner’s most quoted lines (and the one that best captures the whole stance): “Curiosity… is probably the outstanding characteristic of modern thinking… and it must be absolutely unhampered.”

That “must” is doing a lot of work. Flexner isn’t saying that applications are optional. He’s saying the route to them is often non-linear and hard to predict. He even makes the institutional point: a research institute shouldn’t justify itself by promising inventions on a timeline. Instead: “We make ourselves no promises… [but] cherish the hope that the unobstructed pursuit of useless knowledge” will matter later.

Notice the subtlety: he hopes it will matter, but he refuses to make that the official rationale. Why? Because if you only fund what looks useful today, you’ll underproduce the ideas that define tomorrow.

The “Mississippi” model of discovery (and why it matters for AI)

Flexner is unusually modern in how he describes the innovation pipeline: not as single geniuses striking gold, but as a long chain of partial insights that only later “click.”

He writes: “Almost every discovery has a long and precarious history… Science… begins in a tiny rivulet… [and] is formed from countless sources.”

This is basically an antidote to the myth that research can be managed like a factory. You can optimize a pipeline once you know what the pipeline is. But when you’re still discovering what questions are even coherent, “efficiency” often means “premature narrowing.”

AI is a perfect example of the Mississippi model. Modern machine learning is not one idea; it’s a confluence:

  • mathematical statistics + linear algebra,
  • optimization + numerical computing,
  • information theory + coding,
  • neuroscience metaphors + cognitive science,
  • hardware advances + systems engineering,
  • and now massive-scale data and infrastructure.

Much of that was, at some point, “not obviously useful” until it suddenly was.

Flexner’s warning: the real enemy is forced conformity

Flexner’s defense of “useless knowledge” is not only about technology; it’s about human freedom. He’s writing in a period where universities were being pushed into ideological service, and he argues that the gravest threat is not wrong ideas, but the attempt to prevent minds from ranging freely.

One of his sharpest lines: “The real enemy… is the man who tries to mold the human spirit so that it will not dare to spread its wings.”

If you read that in 2025, it lands uncomfortably close to modern pressures on research:

  • “Only fund what’s immediately commercial.”
  • “Only publish what’s trendy.”
  • “Only study what aligns with the current institutional incentive gradient.”
  • “Only build what can be shipped next quarter.”

And in AI specifically:

  • “Only do work that scales.”
  • “Only do benchmarks.”
  • “Only do applied product wins.”

Flexner isn’t anti-application; he’s anti-premature closure.

Dijkgraaf’s update: society runs on knowledge it can’t fully see anymore

Dijkgraaf’s companion essay takes Flexner’s stance and says, essentially: look around, Flexner won. The modern world is built out of the long tail of basic research.

He gives a crisp late-20th-century example: the World Wide Web began as a collaboration tool for particle physicists at CERN (introduced in 1989, made public in 1993). He ties that to the evolution of grid and cloud computing developed to handle scientific data, technology that now undergirds everyday internet services. Then he makes a claim that matters a lot for AI policy debates: fundamental advances are public goods (i.e., they diffuse beyond any single lab or nation).That’s an especially relevant lens for AI, where:

  • open ideas (architectures, optimization tricks, safety methods) propagate fast,
  • but compute, data, and deployment concentrate power.

If knowledge is a public good, then a society that starves basic research is quietly selling off its future, even if it still “uses” plenty of science in the present.

AI as a case study in “useful uselessness”

Here’s a helpful way to read Flexner in the age of AI:

A) “Useless” questions that became AI infrastructure

Many of the questions that shaped AI looked abstract or niche before they became inevitable:

  • How do high-dimensional models generalize?
  • When does overparameterization help rather than hurt?
  • What is the geometry of optimization landscapes?
  • How can representation learning capture structure without labels?
  • What are the limits of compression, prediction, and inference?

These don’t sound like product requirements. They sound like “useless” theory, until you realize they govern whether your model trains at all, whether it’s robust, whether it leaks private data, whether it can be aligned, and whether it fails safely.

Flexner’s point isn’t that every abstract question pays off. It’s that you can’t pre-identify the ones that will, and trying to do so narrows the search too early.

B) “Tool-making” is often the hidden payoff

Dijkgraaf emphasizes that pathbreaking research yields tools and techniques in indirect ways. (ias.edu)
AI progress has been exactly this: tool-making (optimizers, architectures, pretraining recipes, eval frameworks, interpretability methods, privacy-preserving techniques) that later becomes the platform everyone builds on.

C) The scary twist: usefulness for good and bad

Flexner also notes that discoveries can become instruments of destruction when repurposed. He uses chemical and aviation examples to make the point.

AI has the same dual-use character:

  • The same generative model family can draft medical summaries or automate phishing.
  • The same computer vision advances can improve accessibility or expand surveillance.
  • The same inference tools can find scientific patterns or extract sensitive attributes.

Flexner’s framework doesn’t solve dual-use, but it forces honesty: the ethical challenge isn’t a reason to stop curiosity; it’s a reason to pair curiosity with governance, norms, and safeguards.

A Flexnerian reading of the current AI funding wave

We’re currently living through a paradox that Flexner would recognize instantly:

  1. AI is showered with investment because it’s visibly useful now.
  2. That investment creates pressure to define “research” as whatever improves next quarter’s metrics.
  3. But the next conceptual leap in AI may come from areas that look “useless” relative to today’s dominant paradigm.

If you want better long-horizon AI outcomes (i.e., robustness, interpretability, privacy, security, alignment, and scientific discovery) Flexner would argue you need institutions that protect inquiry that isn’t instantly legible as profitable.

Or in his words, you need “spiritual and intellectual freedom.”

What to do with this (three practical takeaways)

1) Keep a portfolio: fast product work + slow foundational work

Treat research like an ecosystem. If everything must justify itself immediately, you get brittle progress. Flexner’s “no promises” stance is a feature, not a bug.

2) Reward questions, not only answers

Benchmarks matter, but they can also overfit the field’s imagination. Some of the most important AI work right now is about re-framing the question (e.g., what counts as “understanding,” what counts as “alignment,” what counts as “privacy,” what counts as “truthfulness”).

3) Build institutions that protect intellectual risk

Flexner designed the Institute for Advanced Study around the idea that scholars “accomplish most when enabled” to pursue deep work with minimal distraction.
AI needs its own versions of that: spaces where the incentive is insight, not velocity.

AI is not an argument against Flexner (it’s his exhibit A)

If you hold a smartphone, use a search engine, or interact with modern AI systems, you’re touching the compounded returns of yesterday’s “useless” knowledge.

Flexner’s defense isn’t sentimental. It’s strategic: a society that wants transformative technology must also want the conditions that produce it: freedom, patience, and room for ideas that don’t yet know what they’re for. Or, as Dijkgraaf puts it in summarizing Flexner’s view: fundamental inquiry goes to the “headwaters,” and applications follow, slowly, steadily, and often surprisingly.

Main Source: https://www.ias.edu/ideas/2017/dijkgraaf-usefulness

Tradeoffs Matter: On Developing Lower Bounds

As I write this blog post, I just received news that the U.S. is designating Nigeria as a ‘country of particular concern’ over Christian persecutions. I cannot think of any other country with such a large population but (almost) equal representation of Christians and Muslims. Since before I was born, this has caused a lot of friction but somehow the country has survived all that friction (thus far!). But the friction stems from tradeoffs of having such religious heterogeneity, a topic of its own discussion. But in this post, I’ll focus on the high levels of mathematical tradeffs.

There’s something deeply human about lower bounds. They’re not just mathematical artifacts; they’re reflections of life itself. To me, a lower bound represents the minimum cost of achieving something meaningful. And in both life and research, there’s no escaping those costs.

The Philosophy: Tradeoffs Everywhere

Growing up, I was lucky enough to have certain people in my family spend endless hours guiding me: helping with schoolwork, teaching patience, pushing me toward growth. Looking back, I realize these people could have done a hundred other things with that time. But they (especially my mum) chose to invest it in me. That investment wasn’t free. It came with tradeoffs, the time she could never get back. But without that investment, I wouldn’t be who I am today.

That’s the thing about life: everything has a cost. In 2022/2023, I could have focused entirely on my research. But instead, I poured my energy into founding NaijaCoder, a technical education nonprofit for Nigerian students. It was rewarding, but also consuming. I missed out on months of uninterrupted research momentum. And yet, I have no regrets! Because that, too, was a lower bound. The minimum “cost” of building something (hopefully) lasting and impactful.

Every meaningful pursuit (i.e., love, growth, service, research) demands something in return. There are always tradeoffs. Anyone who claims otherwise is ignoring the basic laws of nature. You can’t have everything, and that’s okay. The beauty lies in understanding what must be given up for what truly matters.

Lower Bounds in Technical Domains

Mathematicians talk about lower bounds as the limits of efficiency. When we prove a lower bound, we’re saying: “No matter how clever you are, you can’t go below this.” It’s not a statement of despair: it’s a statement of truth.

Lower bounds define the terrain of possibility. They tell us what’s fundamentally required to solve a problem, whether it’s time, space, or communication. In a strange way, they remind me of the constraints in life. You can’t do everything at once. There’s a cost to progress. To prove a good lower bound is to acknowledge that reality has structure. There’s an underlying balance between effort and outcome. It’s an act of intellectual honesty: a refusal to pretend that perfection is free.

Nowhere do these tradeoffs feel more personal than in privacy. In the quest to protect individual data, we face the same universal truth: privacy has a price. If we want stronger privacy guarantees, we must give up some accuracy, some utility, some convenience. In differential privacy, lower bounds quantify that tension. They tell us that no matter how sophisticated our algorithms are, we can’t perfectly protect everyone’s data and keep every detail of the dataset intact. We must choose what to value more — precision of statistical estimates or protection.

These aren’t technical inconveniences; they’re moral lessons. They remind us that every act of preservation requires some loss. Just as my mother’s care required time, or NaijaCoder required research sacrifices, protecting privacy requires accepting imperfection.

Acceptance

The pursuit of lower bounds (in research or in life) is about humility. It’s about recognizing that limits aren’t barriers to doing good work; they’re the context in which doing good becomes possible.

Understanding lower bounds helps us stop chasing the illusion of “free perfection.” It helps us embrace the world as it is: a world where tradeoffs are natural, where effort matters, and where meaning is found not in escaping limits but in working within them gracefully.

So, whether in mathematics, privacy, or life, the lesson is the same: there are always tradeoffs. And that’s not a tragedy; it’s the very structure that gives our choices value.

I hope these ideas shape how I live, teach, and do research going forward. In my work on privacy, I’m constantly reminded that (almost) every theorem comes with a cost and that understanding those costs makes systems more honest and human. In education, through NaijaCoder, I see the same principle: every bit of growth for a student comes from someone’s investment of time and care.

Developing lower bounds isn’t just a mathematical pursuit. It’s a philosophy of life, one that teaches patience, realism, and gratitude. The world is full of limits, but within those limits, we can still create beauty, meaning, and progress: one bounded step at a time.

When Influence Scores Betray Us: Efficiently Attacking Memorization Scores

tl;dr 👉 We just put out work on attacking influence-based estimators in data markets. The student lead (who did most of the work) is Tue Do! Check it out. Accurate models are not enough. If the auditing tools we rely on can be fooled, then the trustworthiness of machine learning is on shaky ground.

Modern machine learning models are no longer evaluated solely by their training or test accuracy. Increasingly, we ask:

  • Which training examples influenced a particular prediction?
  • How much does the model rely on each data point?
  • Which data are most valuable, or most dangerous, to keep?

Answering these questions requires influence measures, which are mathematical tools that assign each training example a score reflecting its importance or memorization within the model. These scores are already woven into practice: they guide data valuation (identifying key examples), dataset curation (removing mislabeled or harmful points), privacy auditing (tracking sensitive examples), and even data markets (pricing user contributions).

But here lies the problem: what if these influence measures themselves can be attacked? In our new paper, Efficiently Attacking Memorization Scores, we show that they can. Worse, the attacks are not only possible but efficient, targeted, and subtle.

Memorization Scores: A Primer

A memorization score quantifies the extent to which a training example is “remembered” by a model. Intuitively:

  • A point has a high memorization score if the model depends heavily on it (e.g., removing it would harm performance on similar examples).
  • A low score indicates the model has little reliance on the point.

Formally, scores are often estimated through:

  • Leave-one-out retraining (how accuracy changes when a point is removed).
  • Influence functions (approximating parameter sensitivity).
  • Gradient similarity measures (alignment between gradients of a point and test loss).

Because they are computationally heavy, practical implementations rely on approximations, which (one could argue) introduces new fragilities.

The Adversarial Setting

We consider an adversary whose goal is to perturb training data so as to shift memorization scores in their favor. Examples include:

  • Data market gaming (prime motivation): A seller inflates the memorization score of their data to earn higher compensation.
  • Audit evasion: A harmful or mislabeled point is disguised by lowering its score.
  • Curation disruption: An attacker perturbs examples so that automated cleaning pipelines misidentify them as low-influence.

Constraints:

The attack could satisfy a few key conditions but we focus on

  1. Efficiency: The method must scale to modern, large-scale datasets.
  2. Plausibility: Model accuracy should remain intact, so the manipulation is not caught by standard validation checks.

The Pseudoinverse Attack

Our core contribution is a general, efficient method called the Pseudoinverse Attack: (1) Memorization scores, though nonlinear in general, can be locally approximated as a linear function of input perturbations. This mirrors how influence functions linearize parameter changes. (2) We solve an inverse problem (specified in paper), compute approximate gradients that link input perturbations to score changes, use the pseudo-inverse to find efficient perturbations and apply them selectively to target points. This avoids full retraining for each perturbation and yields perturbations that are both targeted and efficient.

Validation

We validate across image classification tasks (e.g., CIFAR benchmarks) with standard architectures (CNNs, ResNets).

Key Findings

  1. High success rate: Target scores can be reliably increased or decreased.
  2. Stable accuracy: Overall classification performance remains essentially unchanged.
  3. Scalability: The attack works even when applied to multiple examples at once.

Example (Score Inflation): A low-memorization image (e.g., a benign CIFAR airplane) is perturbed. After retraining, its memorization score jumps into the top decile, without degrading accuracy on other examples. This demonstrates a direct subversion of data valuation pipelines.

Why This Is Dangerous

The consequences ripple outward:

  • Data markets: Compensation schemes based on memorization become easily exploitable.
  • Dataset curation: Automated cleaning fails if adversaries suppress scores of mislabeled or harmful points.
  • Auditing & responsibility: Legal or ethical frameworks built on data attribution collapse under adversarial pressure.
  • Fairness & privacy: Influence-based fairness assessments are no longer trustworthy.

If influence estimators can be manipulated, the entire valuation-based ecosystem is at risk.

Conclusion

This work sits at the intersection of adversarial ML and interpretability:

  • First wave: Adversarial examples. i.e., perturb inputs to fool predictions.
  • Second wave: Data poisoning and backdoor attacks. i.e., perturb training sets to corrupt models.
  • Third wave (our focus): Attacks on the auditing layer: perturb training sets to corrupt pricing/interpretability signals without harming predictions/accuracy.

This third wave is subtle but potentially more damaging: if we cannot trust influence measures, then even “good” models become opaque and unaccountable. As machine learning moves toward explainability and responsible deployment, securing the interpretability layer is just as critical as securing models themselves.

Our paper reveals a new adversarial frontier: efficiently manipulating memorization scores.

  • We introduce the Pseudoinverse Attack, an efficient, targeted method for perturbing training points to distort influence measures.
  • We show, supported by theory and experiments, that memorization scores are highly vulnerable, even under small, imperceptible perturbations.
  • We argue that this undermines trust in data valuation, fairness, auditing, and accountability pipelines.