Too true. This is why Rudin's little book, Principles of Mathematical Analysis, normally takes a whole year to cover: one has to work through the proof line by line in order gain enough understanding to do the exercises. Programming gives you the false sense of ease with leaky "interfaces" and quantum-entangled "decoupling". LOL, one microservice in one separate git repo, and tested with mocks and Gherkin syntax BDD. Just LOL, I call this hyperreal programming. With "spec-driven" AI generated code that is reviewed and tested by AI, it is certain that "the programming did not take place". In this "brave new world", "the map has overcome the territory", and "the twelfth camel" was never returned. Programmers certainly don't need "the mythical man-ager" to go delulu and full ouroboros, i.e. "there is no big Other".
I've come to believe that democracy doesn't work because most citizens don't want to work it. Many of the legislations passed are harmful to the majority even when the intentions are good. Milton Friedman, Thomas Sowell, and Friedrich Hayek have been saying this for a century.
This was the sentiment for programmers well-versed in assembly languages (counting cycles, self-modifying code, story of Mel) when compilers came out, yet the advances in compiler technology enabled the creation of OCaml and Coq. What I think will actually happen is that a new breed of programmers with extensive mathematical background will start designing unprecedented software (or even digital circuits through high-level synthesis) that are almost correct by construction at a much faster rate with the combination of formal specification and AI coding. The field of computer aided design (CAD) will likely explode, and we will witness spaceships, nanobots, etc. being churned out at the rate of React websites. The whole computing field will become so high level that applied mathematics like optimal control, optimal transport, information geometry, etc. will become bread and butter for any programmer.
At the same time, there will be a new breed of artists that starts making games, movies, etc. with AI alone. We will witness a whole new form of artistic expression.
If developers are not using TLA+ or Lean4 etc. They are vibe coding. Nothing wrong with that. They just have to realize that they were never in control. Thinking logically is much harder than developers imagined. As Dijkstra observed, the whole field has adopted the mentra, "How to program when you cannot." I estimate that 80% of what developers do can be done once and for all for all of humanity, yet we don't learn. Be offended all you want, but I am fed up with this idiocy given all the usual rebuttals of deadlines etc.
No, formal specification helps from the get-go. You can iterate more reliably, thus faster. The successful development of mathematical theories depends on having rigorous definitions and proofs all the way from the start so that people can communicate effectively, point out caveats unambiguously, and modify the theory robustly. Without formal specs/proofs, refactoring will become too hard. It's actually a lot easier to capture the behavior of a program formally than by tests. Programmers need to gain some experience in math to see this. Listen to Hoare and Dijkstra, and start "thinking".
> Major flaws in a specification for one function are usually quickly picked up when the proof for another function relies on the missing specification properties
Great point! In a sense, it's testing by immediate use at compile time. I always imagine this to be the greatest productivity booster, even greater than AI. You'll notice things are wrong as you type.