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Here is a simple SQL query that should return 0.3: SELECT 0 . 1 :: FLOAT4 + 0 . 2 :: FLOAT4 ; In PostgreSQL, MySQL, and most relational SQL engines, the result is: 0.30000001192092896 If you calculate sales tax, loan interest, or wallet balances across 10,000,000 transactions a day , those tiny fractional drifts accumulate into real cash discrepancies during month-end ledger reconciliation. 🔍 Why Does Binary Floating-Point Drift Happen? Hardware Implementation: Modern computer CPUs represent FLOAT and DOUBLE PRECISION using binary floating-point numbers (IEEE 754 standard). Base-2 vs. Base-10 Math: In base-10, fractions like 0.1 (1/10) and 0.2 (2/10) look clean and simple. But in base-2 binary, 0.1 is an infinite recurring fraction : 0.000110011001100110011... (binary) Because hardware registers have finite bits (32-bit for FLOAT4 , 64-bit for FLOAT8 ), the value is truncated, introducing a tiny approximation error on every calculation. ⚙️ How PostgreSQL NUMERIC Works Under the Hood Unlike FLOAT , PostgreSQL's NUMERIC (or DECIMAL ) data type does NOT use IEEE 754 binary floating-point hardware representation. ┌────────────────────────────────────────────────────────────────────────┐ │ PostgreSQL NUMERIC Internal Memory Representation │ │ 1. Header (4 Bytes): Sign, weight, display scale, digit count │ │ 2. Digits Array: Stores exact base-10000 integer chunks (0000 to 9999) │ │ ➔ 100% Exact Arbitrary-Precision Base-10 Arithmetic │ └────────────────────────────────────────────────────────────────────────┘ It stores exact decimal digits in memory using base-10000 arithmetic . There is ZERO floating-point drift. 10.50 + 20.25 is always 100% exactly 30.75 . 💡 The Senior Data Engineer Production Standard When designing production DDL schemas for transactional, warehousing, or financial pipelines: Never use FLOAT , REAL , or DOUBLE PRECISION for: Product pricing ( unit_price ) Account balances ( wallet_balance , available_funds ) Tax & GST calculations ( tax_amount , discou

Standard chaos engineering assumes experiments stop cleanly, blast radius is knowable in advance, and production is fair game. Payment systems violate all three. Salim Adedeji describes ECS-specific failure modes from enterprise deployments: a 60-second DNS TTL that produced 93-second failover, retry logic amplifying database load 2.4x, and AZ rebalancing loops that generic tooling misses. By Salim Adedeji

If your pipeline isn't idempotent, it isn't production-ready; it’s just a fragile script waiting to ruin your weekend. Most engineers treat "idempotency" as an academic concept for distributed systems papers, but in the trenches of fintech and healthcare, it’s the difference between a minor blip and a regulatory filing. If you can’t run your job five times in a row with the exact same input and get the exact same state, you aren't doing data engineering—you're doing data gambling. I’ve spent six years cleaning up the messes left by "append-only" thinking. I’ve seen millions of dollars in duplicate ACH transactions and patient records corrupted by "just one more retry" logic. This guide covers the patterns I use to make sure that when the scheduler kicks off at 3 AM, I can sleep through the alarm because the system knows how to fix itself. 1. Stop relying on "Append" mode The biggest sin in data engineering is assuming that your destination table is a clean slate. When a job fails halfway through, you don't want a partial load sitting in your production warehouse. Never use INSERT INTO blindly. If you are using BigQuery, Snowflake, or Databricks, use MERGE or overwrite-on-partition. If you are using SQL-based ELT, write your transformations to stage data in a transient table before swapping it into production. Never push directly to the target. -- The wrong way: INSERT INTO target_table SELECT * FROM staging -- The right way: Use an atomic swap or a MERGE statement MERGE INTO production . transactions AS T USING staging . transactions AS S ON T . transaction_id = S . transaction_id WHEN MATCHED THEN UPDATE SET T . amount = S . amount , T . status = S . status WHEN NOT MATCHED THEN INSERT ( transaction_id , amount , status ) VALUES ( S . transaction_id , S . amount , S . status ); Photo by 🇻🇪 Jose G. Ortega Castro 🇲🇽 on Unsplash 2. Partitioning is your safety net If your pipeline runs daily, your data must be partitioned by that day. If you are loading data without a

Faker Doesn't Know Your Entities Are Related, So I Built Something That Does You've added a second entity to the schema, wired up a @ManyToOne , and gone back to your seed script to generate fifty more rows. Ninety seconds later, the app refuses to start: unique constraint violation, somewhere inside a loop you wrote three weeks ago at 11pm. You fix it. You restart. A different field breaks a different constraint. This is the exact moment every Spring Boot developer eventually meets the real limit of tools like Faker. They're brilliant at generating a name, an email, an address. They have no idea the Payment sitting in front of them needs a Counterparty to already exist. So you do what everyone does: hand-write the wiring. Create parents first. Hold onto their generated IDs. Wire them into children. Hope you didn't just violate a @NotNull somewhere in the process. It works, for a while. Then the schema changes, and the script quietly stops matching reality until the next 3am debugging session finds out the hard way. I hit this enough times that I stopped patching the script and looked at the actual problem: the information needed to seed this correctly already exists. It's sitting right there in the entity, in the annotations you already wrote. @ManyToOne , @NotNull , @Column(unique = true) , JPA already knows the shape of your data. Nothing should need to be told that twice. That became SynthForge . The core idea Instead of writing a script that generates data, you annotate the entity: @Entity @Seed ( count = 50 ) public class Counterparty { /* fields only */ } @Entity @Seed ( count = 200 ) public class Payment { @ManyToOne ( optional = false ) private Counterparty counterparty ; } Start the app in a dev profile. Both tables populate, correctly ordered, on every restart. No seed method. No calling code, anywhere. The entity is the seed script. What's actually happening underneath Entity scanning. SynthForge reads JPA-managed attributes through the jakarta.persisten

⚡ TL;DR Four things about controller mechanics are widely half-understood: what Reconcile receives, where its work comes from, what a periodic resync is, and what a predicate turns off. I built an operator, broke it five ways, and measured each mechanism directly. The reconcile function runs in 2.71ms mean, 77/77 under 25ms , a short resync period costs zero additional API requests , and GenerationChangedPredicate cut steady-state reconciles by 48.5% without touching live repair at all. That last combination is the one that matters at scale. Repo, raw data, and harness: kirPoNik/k8s-drift-operator . 🧩 The four barriers Everyone who runs Kubernetes knows the platform repairs itself. Delete a pod, it comes back. Scale a Deployment by accident, something puts it back. Almost nobody who relies on that property can say how it works, and the gaps are specific and consequential. I keep meeting the same four: People think a controller is told what changed. It is not, and the reason it is not is the single most important design decision in Kubernetes. People think a controller polls the API server. It does not, and knowing what it does instead tells you where your API load actually comes from. People think a resync is a re-check against the cluster. It is not, which is why a short resync period is nearly free — and why the number that is expensive sits somewhere else entirely. People treat a predicate as a pure optimisation. It is a filter with a silent cost, and the cost is not the one the documentation warns you about first. So I built the smallest system that has the self-healing property, broke it on purpose ten times per failure mode, and instrumented each of those four mechanisms until I could state what it does rather than what it is said to do. What I built. One CRD called Echo , holding an image, a replica count, and a greeting. A controller keeps three child objects in sync with it — a Deployment, a Service, and a ConfigMap holding the greeting — with owner referen

Why your settings don't live in your code Every application has settings that change depending on where it runs. The database URL on your laptop is not the one in production. The port the app listens on might be 8080 locally and something else inside a container. The API key you test with is not the real one. Externalized configuration is the simple idea that these settings live outside your compiled code — in a text file, an environment variable, or a command-line flag — so you can change them without recompiling. You write the code once; the settings travel separately and get slotted in when the app starts. You meet this the first time you deploy a Spring Boot app. It runs fine on your machine, you ship the exact same jar to a server, and it picks up a different database — without a single line of code changing. This article is about how Spring pulls that off, and the one question that trips everyone up: when the same setting is defined in two places, who wins? Spring's first job: build one big lookup table Before your code runs, Spring goes hunting for settings. It looks in files, it reads environment variables, it scans the command line — and it pours everything it finds into a single key/value lookup. Spring calls this lookup the Environment . Think of it as one flat dictionary: you ask it for a key like server.port , and it hands back a value like 8080 . Every setting your app could possibly care about ends up in here, no matter where it originally came from. The most common place to put settings is a file named application.properties , which Spring looks for automatically: server . port = 8080 app . greeting = Hello from the properties file Each line is one key and one value. Once Spring has read this file into the Environment, any part of your app can ask for those keys. Reading a value: the two ways in The quickest way to pull a value out is the @Value annotation. You put it on a field, and Spring fills that field in for you as it builds the object: @Compon

Picture, you join a new team working on a big system. Everybody who knew anything has left, either to find greener grass or to enjoy a well deserved pension. You and the team struggle to build new features for the system or to adapt functionality to match changes in legislation. Not to mention the trouble it is to figure out what to fix when things go wrong. At the same time, the business that you support is screaming for innovation and pushing for more and more changes. Recognize this situation? Ever experienced it yourself? A world full of legacy systems “Legacy. What is a legacy? It’s planting seeds in a garden you never get to see.” – Lin-Manuel Miranda, “Hamilton” Legacy, the thing that you are remembered for, typically the word has a positive meaning… how come that in tech the word “Legacy” has such a bad connotation? When we call out a legacy system, we usually mean: code without tests ( Michael Feathers ) or code you “got” from somebody else, or code that you’re scared to touch. However, there is a reason these legacy systems are still around. In almost all cases, that system still brings in money or is somehow still valuable. If it did not bring any value anymore, wouldn’t it be decommissioned? There must be something in these systems that makes them survive, where other systems did not. How systems become “Legacy” So legacy systems are those that have become hard or scary to change. In my experience, that not because something is wrong with the code or technology. The major contributing factor is usually that the knowledge about the system has left the organization. And then I don’t mean the documentation, but the people that built, maintained and ran the system. When those people are gone, you know that nobody else is going to be happy touching that thing. The value of software Code is like a mapping of desired real world behavior to a program that can be executed by a machine. So where is the value of a system, is that in that code? Over the past years I

In every project, someone says it sooner or later: "we have too much technical debt." Everyone agrees. Nobody asks how much. One day I tried to do the math for real. I learned very little about my code, and a lot about the metaphor. The bank statement If my technical debt were a loan, it would have the same structure: At the bank In the code The principal The shortcut taken to ship on time The interest The extra cost of every new feature Repayment Refactoring Bankruptcy A full rewrite So I listed my lines: a 3,000-line service with no tests, a framework three major versions behind, billing logic copied in four places, and one module everyone avoids. Every feature costs me about 30% more time. And the principal, the amount I would need to pay to reach zero, is measured in months of work that nobody will ever give me. The verdict: I am insolvent. And yet I ship every week, and I have been shipping for years. This is where the analogy breaks. Four reasons why it is not a debt I don't know the amount. A bank debt is a number written in a contract. Technical debt has no number, it has opinions. Ask three developers to rate the same module and you get three answers. I never signed anything. You choose to take a loan. Most of my technical debt arrived on its own: a library abandoned by its author, a business rule that changed, a project I inherited. Ward Cunningham, who created the term in 1992, was talking about a loan you take on purpose, to learn faster. He then spent twenty years repeating that he never meant "badly written code." The interest does not arrive every month. You only pay for the code you touch. I have terrible files that have not cost me a single minute in three years, because nobody goes there. And I have an 80-line file, changed twice a week, that is ruining me. There is no zero balance. The refactoring I do today will be out of date in two years. I never repay anything. I just trade one debt for another one with a better rate. The word itself is a prob

Humanistic Architecture Learning to See Problems Differently I had the opportunity to attend a class called “Humanistic Architecture” by Mr. Chakrit Riddhagni. The class was about applying humanistic principles to software development . Before talking about what I learned, I would like to share a little about my own perspective on software development. Personally, I have a quote and a belief about software development: it is both a science and an art. I see software development as something that has an artistic side, while being grounded in logic, with almost endless possibilities. “Crafting software requires artistry, guided by imagination, grounded in logic, endlessly enduring.” This quote has been one of my inspirations since I started working as a developer. What I mean by this is that I have always liked thinking about software development as a kind of literature . We are not simply writing code. We are solving problems. We are developing and creating something to solve a problem that either we or our customers are facing. Because of this, as a developer, I naturally work with problems every day. But… I never really thought much deeper about what a “problem” actually is. Usually, when we solve a problem for a customer or develop software for them, we receive an issue or a scope of work and then start working on it. We know that something is a problem, so we focus on solving it. But we do not always stop and ask What is the actual structure of this problem ? Is this really the problem? And does the solution we are building actually address the problem we are trying to solve? That changed when I attended the “Humanistic Architecture” class. One of the biggest things I gained from this class was a new perspective and a set of tools for defining what a “problem” really is. Anatomy of a Problem We can look at a problem through the Anatomy of a Problem , which consists of three parts: Current State — where we are now Gap — the difference between where we are and wher

A random game is easier to debug when the same inputs produce the same result. In HoopTrait, a browser basketball project, the Lab mode combines eight selected traits and generates a fictional career. The interesting engineering problem is keeping replay, sharing and validation consistent. This is a technical development note, not a claim that a game score predicts an athlete's real performance. Store the decisions, not just the result The Lab state records a seed, a dataset version and an ordered list of actions. An action is a pick or a reroll. Replaying those actions reconstructs the build. A seed alone is not a complete replay contract: changing the player pool or its order can change a seeded draw. A dataset version therefore matters alongside the random seed. For a future release, the same principle should apply to changes in the rules themselves. Test invariants across many runs The Lab test suite iterates through 1,000 seeds. For each seed it shuffles the order of the eight skills, uses the two allowed rerolls, and completes a build. It checks that: Eight distinct players were selected. All eight traits are present, and no player remains to be drawn after completion. The overall game score stays between 0 and 99 and matches the shared rating function. Packing and unpacking the share state returns the original state. Recomputing the fictional career returns the same output. The ten simulated seasons sum to the displayed career earnings. Those assertions catch different problems. A stable score does not prove that a shared link reproduces the same selections. A complete build does not prove that its season totals add up. Reject impossible histories A share payload is untrusted input, even in a client-side game. Negative or fractional seeds, duplicate skill picks, a third reroll, unknown action types, a mismatched dataset version and actions after completion are rejected. The tests also cover malformed encoded payloads and unexpected fields. Local state is usef

Adapted from my original Japanese article , with AI-assisted translation and editing. My manager: “Test this device.” (Doesn't really know the product or the technology.) Me: “Sure.” (Also doesn't really know the product or the technology.) If you've worked in infrastructure, that may sound familiar. I'm Goda, a network engineer sharing things I learned while figuring out the job. SNMP comes up in a lot of network device testing. For a while, my idea of an SNMP test was simple: Run snmpwalk . Watch a pile of OIDs and values scroll past. Mark SNMP as working. A screen full of output is reassuring. It certainly looks like something is being monitored. Then I was asked to write a test plan for a device. I added an item along the lines of “Confirm that information can be retrieved using SNMP” and sent it for review. The feedback was: Which OIDs will you use for CPU and memory? The customer will probably ask. You should at least cover those. That was when it clicked: a successful walk and successful retrieval of the metrics we need are two different things. My other thought was, “Fine, you write the test plan, then.” But the feedback was fair. Getting something back is not the same as getting what you need. What did the successful walk actually prove? snmpwalk is useful. Net-SNMP's tool uses GETNEXT requests to walk through a subtree starting from a specified OID. Net-SNMP manual If it successfully returns values, you've established that you could read those values under those test conditions . That matters. It does not, by itself, establish that your CPU and memory monitoring requirements are satisfied, or that every required OID is available. I had been treating a successful command as a much broader result than it actually was. Break “SNMP testing” into specific checks Today, I'd separate at least these questions: Question What to check Can I communicate over SNMP? Whether the device responds to the intended request under the defined conditions Can I monitor CPU? The

A process supervisor can tell you that a process exists. It cannot, by itself, tell you that a Minecraft player can join. I work on ChunkCraft, a Minecraft hosting project. Here is a small state model that helps keep operational status separate from player-facing guidance. Separate three questions Is the process alive? The container or service manager owns this signal. Has the game finished starting? Startup logs or a game-level probe provide this evidence. Can this player join? Client version, edition, whitelist and network reachability still matter. A useful state model is stopped → starting → ready , with failure and unknown states represented explicitly. Avoid converting a failed probe into “stopped”: a timeout means the observation failed, not necessarily that the server died. Tie each state to a next action Observed state Useful guidance Starting Wait for world loading; show recent startup progress Ready Show the complete connection address and expected version Unreachable or unknown Show when the last successful observation happened and offer diagnostics Player rejected Read the actual join error; check version and whitelist The same principle applies to control buttons. A copy-address action is helpful when the address exists and startup has completed. Showing it as the only instruction during startup invites repeated failed joins. Do not confuse observation with proof Even a successful game-level probe does not prove every player can reach the server. Likewise, a positive player-count sample proves someone was connected at that sample time; it does not identify that person or establish uninterrupted availability. Store observation timestamps alongside values. When a collector fails, preserve historical observations but mark them stale. A freshly rendered dashboard is not evidence of fresh underlying data. A small review checklist Does every status describe an observation we actually have? Is an unknown state distinguishable from a confirmed failure? Does th

We shipped a filter that threw away bad GPS readings. Months later somebody asked whether it was working, and I could not answer. The evidence was gone. That question changed how I build anything that rejects data. The obvious version, and why it rots Mileage tracking depends on trustworthy distance, and GPS lies constantly. So the first version of our cleanup did what everyone's first version does: if (! fix . isPlausible ( previous )) return // drop it, move on accumulateDistance ( fix ) Clean data comes out the other end. It feels responsible. It is also a trap, because that return destroys the only record that could ever tell you whether the rejection was correct. Six months in, someone asked the reasonable question: is the filter right? I could not say how many readings we had dropped, on which journeys, or whether any of them had been a genuine drive through a tunnel rather than a glitch. We had built a thing that made a judgement call thousands of times a day and kept no record of any of it. Persist, then classify The rebuild flipped the default. Rejection stopped being a return and became a label. Only two cases are still deleted, because they cannot physically be real: // impossible coordinates if ( fix . lat ! in - 90.0 .. 90.0 || fix . lng ! in - 180.0 .. 180.0 ) return null // impossible accuracy: too precise to be true, or useless if ( fix . accuracyM <= 0.1f || fix . accuracyM >= 250f ) return null That is the entire delete list. Everything else is persisted and sorted into named accumulators: originalDistanceM += displacement // every metre we ever saw when { fix . isMock -> mockDistanceM += displacement abnormal -> { abnormalDistanceM += displacement if ( isHardSpike ) spikeDistanceM += displacement } accuracyGated -> { /* recorded, deliberately not counted */ } else -> cleanedDistanceM += displacement } Five numbers instead of one. The UI shows cleaned . The rest live beside it. And the row itself keeps its provenance: accuracy, provider, bearing, a

If you're prepping for a Business Intelligence (BI) Engineer, Data Analyst, Data Engineer, or Data Scientist role at Amazon, you probably already know SQL matters. It's a core part of the hiring bar. But Amazon isn't just checking your syntax. They want to see if you can think in sets, write clean queries under pressure, and reason about data the way the business actually uses it. Here's exactly how to prepare based on what the interview actually rewards. What the Interview Really Tests Amazon's SQL rounds usually show up in one of two ways. It's either a technical screen using a shared coding tool, or a whiteboarding case-study during the main loop. Either way, the interviewer is watching for a few specific signals. For starters, correctness always beats speed. A working query is far better than a clever one that fails. Communication is also huge. Do you talk through your logic before you even touch the keyboard? You'll often get a vague ask, like finding the "best" customers. You are completely expected to define what "best" means out loud before you start writing Common Table Expressions (CTEs). And watch out for messy data. Nulls, duplicates, and mismatched grain are almost always baked into the problem on purpose. The Core Topics to Master Focus your prep time on a few specific areas. Actually, it turns out this is where almost all the interview questions live. Joins Inside and Out You need to know your INNER, LEFT, RIGHT, and FULL OUTER joins cold. Be ready to explain exactly why row counts change after each one. A classic Amazon-style question is finding customers who placed orders but never left a review. That's just a LEFT JOIN with a NULL check. The interviewers want to see you reach for it right away. Window Functions Functions like ROW_NUMBER() , RANK() , DENSE_RANK() , and LAG() or LEAD() show up constantly. You might see a common pattern—like finding the second-highest order value per customer, or calculating month-over-month growth. If you're shaky he

Why building reliable AI features requires more than better prompts A few years ago, building an AI feature often looked surprisingly simple. Write a prompt. Send some text to a model. Look at the response. Improve the prompt. Repeat. Eventually, the output gets good enough and the feature ships. That approach still works for many things. It works especially well when the task is simple, the consequences are low, and a human remains responsible for the final result. But production software introduces a different set of questions. What context should the model receive? Which data is it allowed to access? Which tools can it use? What happens when it chooses the wrong tool? How do we know a model or prompt change didn’t make the system worse? How do we debug a failure that happened only once? What happens when the model produces valid JSON containing an invalid business decision? And perhaps the most important question: How much autonomy should we give a system whose behavior is probabilistic? These are not prompt engineering questions. They are engineering questions. That is why I think we are seeing a shift from prompt engineering toward AI engineering. I don’t mean that AI engineering is a completely new discipline. Much of it comes from software engineering, MLOps, LLMOps, distributed systems, security, testing, and platform engineering. What is changing is the combination. The model has become a new kind of software component — one that can interpret, reason, generate, and increasingly act, but cannot be treated like deterministic code. That changes the engineering problem. From Prompts to Systems Prompt engineering is useful because it addresses a real problem. A model needs instructions. The way we formulate those instructions can have a significant effect on the result. But a prompt is only one part of the system. Consider a CRM application that asks an AI assistant to recommend the next action after a customer meeting. A prompt might look like this: Review the

Agentic Methods: Coding With AI Agents, Designing For Agents TL;DR "Agentic methods" covers two distinct things colliding right now: AI agents that code alongside the team (read, write, run, verify, in a loop), and agentic architectures we design into our own systems (orchestrating autonomous agents on the product side). In both cases, the same principle applies: an agent is only useful if the contract around it is explicit — scope, errors, permissions, stopping points. The Tech Lead role doesn't disappear, it shifts: fewer lines typed, more specification, review, and governance. The underlying topic isn't tooling, it's clarity — exactly like a well-modelled business workflow. Table of Contents Introduction — one word, two meanings Coding with AI agents: what actually changes From autocomplete to the agentic loop The developer's role shifts toward review Explicit guardrails Designing agentic architectures An agent is a box with a contract Orchestration or autonomy: a choice, not a default Observability: if you can't replay it, you can't debug it Where humans remain irreplaceable A Tech Lead checklist for adopting these methods Conclusion — agents reveal a team's maturity Introduction — one word, two meanings "Agentic" has been everywhere for a few months, but it means two different things depending on who's talking: Coding with AI agents : a tool that reads code, writes diffs, runs commands, launches tests, and iterates until it reaches a correct result — instead of suggesting one line at a time. Designing agentic systems : a software architecture where autonomous agents (often themselves LLM-based) make decisions, call tools, and cooperate to accomplish a business task — a support chatbot that triggers refunds, a document pipeline that routes complex cases to a human on its own. These are two separate topics, but the same underlying principle runs through both: an agent — human, AI, or service — is only reliable when it operates inside an explicit frame. It's the s

This GIF shows what happens if you slightly stretch the data texture storing the BVH and triangle data. Child nodes storing triangles got misaligned addresses first, while AABB nodes lose them later.

While Oura has largely dominated the smart ring market for years, a growing number of rivals are now racing to dethrone it by trying all sorts of approaches to get an edge over it.

JupyterGIS is a GIS-focused extension for Jupyter notebooks. The recent 0.16 release enhances collaborative features, real-time editing, and support for large-scale data processing, including remote sensing. It introduces better visualisation tools and extends compatibility to R users. Community feedback highlights practical concerns and a desire for improved portability. By Olimpiu Pop

On September 4, Anthropic published something that sounds like a headline from a decade in the future: the first complete, computer-checked proof of Fermat's Last Theorem, written by a team of Claude agents working largely autonomously over 11 days. Thirteen million lines of Lean. Nearly 30,000 intermediate theorems. About six billion output tokens. I want to talk about a detail that most coverage will bury, because it is the only part that matters if you build software with agents instead of reading about them. The first attempts failed. Not because the model was too weak. The agents had early success, then lost track of the project's state and stopped collaborating effectively. What fixed it was not a smarter model. It was a shared directed acyclic graph acting as the team's memory. If you have ever run two AI agents on the same codebase and watched them trample each other's work, you already understand this failure. You just have not seen it dramatized at the scale of one of the hardest proofs in mathematics. What actually happened, in numbers First the facts, because they are dramatic enough on their own. Fermat scribbled his claim around 1637: no positive integers a, b, c satisfy aⁿ + bⁿ = cⁿ for any n greater than 2. Andrew Wiles proved it in 1995 after a 129-page proof, and even that is underselling the drama. He presented the proof in June 1993, a reviewer's question exposed a critical gap two months into verification, and Wiles spent a year, first alone and then with his former student Richard Taylor, fixing it. Formalizing that proof, meaning rewriting it so a proof assistant like Lean can verify every step algorithmically, has been a community project since 2024, led by Kevin Buzzard at Imperial College London. The blueprint for just the initial phase runs 86 pages. It was scoped as a multi-year effort. Then Tianyi Peng, an Anthropic researcher whose group at Columbia University builds AI formalization tools, tested whether Claude could make progress on i