It’s 1943. American bombers are returning from missions over Nazi-occupied Europe, and the engineers mapping the damage see a clear pattern: bullet holes cluster in the fuselage, almost none on the engines.
The military needs to know where to add armour. They have the maps. They have the data. They have men who have studied aerial combat their entire careers.
Where would you reinforce the plane?
Take a moment. Most people — including those engineers — land on the same answer.
That answer was about to get thousands of men killed.
The Man Who Looked for What Wasn’t There
The person who caught the error was Abraham Wald — a Romanian-born mathematician, driven from Vienna by the Nazis, now sitting in a classified Manhattan apartment working on reports he technically wasn’t allowed to read. He had never been near a cockpit. He barely cared about planes. What he cared about was the skeleton hiding under any problem once you stripped away assumption.
When Wald looked at the bullet-hole data, he didn’t see what the engineers saw. He saw what was missing.
The planes returning with fuselage damage had survived because fuselage damage is survivable. Those holes aren’t evidence of vulnerability — they’re proof of tolerance. But the planes that took engine hits? They were at the bottom of the Atlantic. They never came back to be counted. The absence of engine damage on surviving aircraft wasn’t evidence that engines were safe. It was evidence that planes hit there simply weren’t in the room.
The armour, said Wald, doesn’t go where the bullet holes are. It goes where the bullet holes aren’t.
If you said reinforce the fuselage, you were in excellent company. The engineers who got it wrong were experienced, intelligent, patriotic — with vastly more knowledge of aerial combat than Wald would ever accumulate. They weren’t careless. They were doing exactly what every human instinctively does: reading the data in front of them, and forgetting to ask about the data that never arrived.
Wald’s recommendations were adopted immediately and remained military doctrine through Korea and Vietnam. But the lasting damage wasn’t operational. He had exposed a flaw so fundamental to human cognition that Jordan Ellenberg, in How Not to Be Wrong, gives it a name: survivorship bias. The systematic error of building your understanding of the world from only the data that survived long enough to reach you.
Once you see it, it’s everywhere. And the next place it showed up was in your wallet.
The Prophet Who Was Just Good at Maths
A stockbroker in Baltimore sends you a newsletter. Week one: he predicts a stock will rise. It rises. Week two: fall. It falls. Ten weeks in a row — ten perfect calls. On week eleven, he asks for your money.
The odds of calling the market correctly ten times in a row by chance are 1 in 1,024. Would you invest?
Here’s what you didn’t see. He sent 10,240 newsletters simultaneously — half predicting rise, half predicting fall. After each week, he dropped everyone who received the wrong prediction. By week ten, ten people had received ten perfect calls. Not by genius. By elimination. You are one of those ten. You believe you’ve found a prophet. You’ve found a magician who quietly discarded every audience member who saw through the trick.
This isn’t just a parable. Investment firms routinely incubate dozens of funds simultaneously, let them compete internally, then launch only the winners — complete with a glowing multi-year track record and zero mention of the ones that quietly died. When you invest in a “hot fund with a 3-year record of beating the market,” you’re not seeing evidence of skill. You’re seeing the one survivor from a secret tournament you were never told existed.
We glorify the dropout who became a billionaire. We never count the thousands who made the identical bet and are doing freelance work to pay rent. Failure doesn’t publish its memoirs.
Survivorship bias doesn’t just distort data. It distorts what we believe is possible, what we think is earned, and who we decide we should become. We built our entire understanding of success on the testimony of the people who came back — and never once asked about the ones who didn’t.
Then we handed that same blind spot to our machines and asked them to be smarter than us.
What the Algorithm Never Learned
Every AI system in the world is trained on data. The smarter the system, the more data it needs. And for the last decade, we have been feeding these machines everything we could find — medical records, financial histories, human conversations, the accumulated text of the internet itself.
The question no one was asking: what did we leave out?
An AI built to predict surgical recovery outcomes, trained on hospital databases that only include patients who survived long enough to consent, learns nothing from those who died before reaching the threshold. It sees only the planes that came back. When deployed on the full population, it fails at exactly the cases that matter most — the critical ones, the edge cases, the people the original dataset never had room for.
Researchers studying AI cancer-detection tools found that systems trained on medical image databases performed brilliantly on lighter skin tones and dangerously poorly on darker ones — not from malice, but from absence. The training sets reflected who historically had access to dermatologists, whose cases got photographed, whose records got digitised. The bias wasn’t written into the code. It was baked into what the code never saw.
The same problem runs through every large language model now reshaping how the world communicates. These models are trained on text — but not all text equally. They learn from what was written down, published, digitised, and indexed. They inherit the silence of every voice that was never given a platform, every language that didn’t make it onto the internet, every perspective that existed only in conversation and was never transcribed. The model doesn’t know it’s missing anything. It was never told there were missing planes.
This is survivorship bias embedded in silicon. We built systems from incomplete data, optimised them on visible outcomes, and called the result intelligence. The machine is brilliant at answering questions about the world that the data describes — and completely blind to the world the data forgot.
Real mathematical intelligence — the kind Wald practised — doesn’t ask “what does the data show?” It asks “what is the data structurally unable to show, and why?” That question doesn’t get easier when the data is bigger. It gets more urgent.
And it doesn’t only apply to machines. It applies to every conclusion you’ve ever drawn from the evidence in front of you.
The Advice You’ve Been Acting On
Think about what shaped your understanding of success — the books you read, the people you admired, the lessons you absorbed about what it takes to make it. Most of us built those beliefs from people who got there: their interviews, their biographies, their hard-won frameworks.
Where did the people who followed the same advice and didn’t make it go?
They’re not keynote speakers. They’re not writing the books. They exist in a part of the dataset the dataset cannot see — the same Atlantic the missing planes fell into, the same silence where failed funds disappear without a press release.
This is not an argument that hard work is meaningless or that success is purely luck. It’s something more precise and more uncomfortable: we have built our entire model of what works from a systematically incomplete sample, and we’ve been optimising our lives against it without knowing the sample was broken.
Wald’s officers weren’t foolish. They were looking at data the way humans naturally do — from what arrived, from what survived, from what showed up to be measured. Wald did something different. He asked: what process created this data? What had to happen to everything that didn’t make it into this room? What would the data look like if my assumptions were false?
That is not a genius-level skill. It is a learnable one. And once you have it, it changes the texture of everything — every graph, every success story, every confident claim about what the evidence shows.
Which is why the last thing about Wald is the thing I keep coming back to.
The Missing Plane Who Found the Others
He was a refugee. Classified as inferior by a regime that used its own ideological data to justify it. He arrived in America stateless, technically classified as an enemy alien, not permitted to read the classified reports he was producing. He was, in the most literal sense, a person the official record had decided not to count.
And he was the one who saw the missing planes.
Not despite being excluded from the data — because of it. A lifetime of being the person the system wasn’t designed to see had sharpened in him an instinct the officers, deep inside the data, had completely lost: the instinct to ask who wasn’t in the room.
Mathematics didn’t teach Wald to notice absence. Absence taught him to do mathematics.
Mathematical intelligence is not fundamentally about equations. It is about honesty — the rigorous, uncomfortable discipline of asking whether the world you are optimising for is the world that actually exists, or just the world that was convenient enough to measure.
Optimisation built on incomplete data doesn’t solve problems. It solves the visible parts of problems, perfectly, at the expense of everything the data forgot to count — which tends to be exactly the part that matters most.
The planes, the funds, the algorithms, the advice — they’re all the same mistake at different scales. We look at what came back and call it the truth. We never ask what’s missing from the room.
So here is the only question that actually matters: What are the bullet holes in front of you evidence of — and what do the missing holes tell you about everything that never came back?
Disclosure
AI Assistance: This article was written with the assistance of Claude (Anthropic) for research structuring and drafting. All ideas, narrative framing, and conceptual interpretation reflect the author’s own perspective and intent.
Primary Reference: Jordan Ellenberg, How Not to Be Wrong: The Power of Mathematical Thinking (Penguin Press, 2014). The story of Abraham Wald, the concept of survivorship bias, and the Baltimore Stockbroker parable are drawn from this book.