Author Archives for Daniel Alabi

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

From Postdoc Notes to a Full Textbook

During the 2024–2025 academic year, I decided to start writing detailed lecture notes on Topics in Information-Theoretic Cryptography (https://dacesresearch.org/infocrypto/). At the time, I was still thinking about research (e.g., in differential privacy, zero-knowledge, and information-theoretic security more broadly) while also preparing to transition into my faculty role at UIUC.

During that period, I started drafting early versions of the lecture notes that would eventually form the backbone of my Fall 2025 graduate course at UIUC. These weren’t intended to be a book (at least, not at first). They were simply my attempt to consolidate ideas I was using in my research (from fingerprinting lower bounds to statistical zero-knowledge to watermarking generative models) into a cohesive pedagogical narrative.

I experimented heavily with new ways to explain familiar concepts. I rewrote some proofs repeatedly. I paired classical topics (e.g., the One-Time Pad and Shannon entropy) with modern concerns such as data-market privacy risks, statistical attacks on machine learning models, and quantum-era cryptographic threats.

By the time I arrived at UIUC in Fall 2025, the notes had already grown into something far larger than a lecture packet. Teaching the course from these notes, and expanding them week after week, revealed that they could become more than supplementary material. Maybe these notes could become a full textbook?

This blog post is a reflection on that journey: how the material grew, what the book covers, and the many people and institutions who made it possible.

Reflections on the Process

1. Writing revealed connections I hadn’t noticed before.

Integrating ZK, DP, MPC, and quantum topics forced me to articulate the conceptual threads uniting them.

2. Student questions shaped the clarity of the exposition.

When multiple students struggled with the same definition, I rewrote it. Many of those improved explanations are now part of the book.

3. Compiling a textbook is a creative research act.

Several new lemmas, interpretations, and frameworks arose during the writing (simply from trying to explain concepts more cleanly).

Book Chapters

Compiling the textbook required reorganizing an entire semester’s worth of evolving lecture notes into a coherent structure that, I hope, could guide a reader from basics of probability to the frontiers of modern security. Below is a thematic overview of how the chapters came together.

1. Foundations

The book opens with a modern introduction to cryptography, revisiting the motivations, core goals, and roles of secrecy, randomness, and adversaries. It then transitions through a detailed review of probability (i.e., expectation, independence, conditional distributions) and into essential tools from information theory.

I believe this foundation anchors the rest of the text and supports the many advanced topics that follow.

2. Attacks That Motivate the Theory

A distinctive early feature of the book is its chapter on attacks, including:

  • reconstruction attacks
  • chosen-plaintext and side-channel attacks
  • valuation attacks in data markets

These examples provide students with an intuitive understanding of what must be defended and why theory matters.

3. Differential Privacy: From Basics to RDP and Hypothesis Testing

DP occupies several chapters, covering:

  • Laplace and Gaussian mechanisms
  • composition theorems
  • Rényi DP
  • DP-SGD
  • framing DP through the lens of hypothesis testing

This was one of the most extensive parts of the rewriting process, as I attempted to unify multiple strands of the privacy literature into one narrative.

4. Lower Bounds in Differential Privacy

Another major contribution of the book is its treatment of lower bounds:

  • packing arguments
  • fingerprinting codes
  • mutual-information-based bounds
  • connections to group privacy

These tools help readers understand the inherent limitations of privacy guarantees.

5. Statistical Estimation, Testing, and Machine Learning Under DP

Later chapters connect DP mechanisms to classical statistical tasks:

  • mean/variance estimation
  • linear regression
  • hypothesis testing
  • utility tradeoffs

Each topic demonstrates how information-theoretic reasoning guides algorithm design.

6. Privacy in Distributed Systems: LDP, Shuffling, MPC, FL

This chapter weaves together local differential privacy and secure multiparty computation—two topics rarely unified in a single textbook:

  • randomized response and k-ary LDP
  • shuffle model and ESA
  • MPC definitions and protocols
  • secure summation
  • federated learning with DP

7–10. Zero-Knowledge Proofs and Information-Theoretic Proof Systems

These chapters form a complete narrative arc:

  • classical ZK protocols (3-coloring, GI)
  • statistical zero-knowledge and SZK-complete problems
  • multi-verifier SZK
  • ZK over secret-shared data
  • linear PCPs and IOPs
  • polynomial commitments and inner-product arguments

11. Multi-Party Differential Privacy

A modern and emerging topic, combining cryptographic and information-theoretic privacy:

  • adversary models
  • distributed noise-addition protocols
  • MPC-based DP
  • simulation and composition theorems

This chapter, in my opinion, is one of the most forward-looking in the book. (I have some active research projects in this space.)

12. Quantum Cryptography

A full chapter on quantum mechanics and its cryptographic implications, featuring:

  • the photon-polaroid experiment
  • superposition, entanglement, and measurement
  • Shor’s algorithm
  • QKD (BB84)
  • pure vs. mixed states

This chapter offers both intuitive and formal perspectives.

13. Watermarking, Steganography, and AI Content

The final chapter bridges classical information hiding with generative AI:

  • perceptual models and robustness
  • spread-spectrum and QIM watermarking
  • deep-learning-based steganography
  • watermarking of large generative models
  • powered randomness used for sampling

This connects the field’s classical roots to current and future security challenges.

Acknowledgements

I developed the bulk of the course materials for the accompanying course during my postdoc, while supported by a Simons Junior Fellowship from the Simons Foundation (965342, D.A.). I am deeply grateful for this support; it gave me the intellectual space to design the course, think deeply about its structure, and begin drafting what would become this book.

This book would not have been possible without the support of my colleagues at UIUC, especially in the Department of Electrical and Computer Engineering. Many colleagues provided helpful feedback while I was developing the materials, attended some class sessions where I tested parts of the exposition, or offered valuable insights on how to structure complex topics such as zero-knowledge proofs, differential privacy, and information-theoretic analyses. Their encouragement and technical discussions greatly shaped the final form of the text.

I will, most likely, upgrade the textbook everytime I teach a subset of the topics covered!

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.