What is proof?

A proof is a step‑by‑step logical argument that shows a statement is definitely true. It starts with facts you already accept (called premises) and uses clear reasoning to reach a conclusion that can’t be doubted. In tech, proofs are used to confirm that code, algorithms, or security protocols work exactly as intended.

Let's break it down

  • Premise: Something you know is true (e.g., “All numbers added together follow the rule of addition”).
  • Rule of inference: The logical rule that lets you move from one statement to the next (like “if A is true and B follows from A, then B is true”).
  • Step: Apply the rule to the premise to get a new statement.
  • Conclusion: After a series of steps, you arrive at the statement you wanted to prove. Think of it like a recipe: you start with ingredients (premises), follow the cooking steps (inferences), and end up with a finished dish (conclusion) that matches the picture on the box.

Why does it matter?

Proofs give certainty. They let developers and users trust that a program won’t crash, a cryptographic key can’t be guessed, or a blockchain transaction is valid. Without proofs, we’d rely on guesswork or trial‑and‑error, which can lead to bugs, security holes, and costly failures.

Where is it used?

  • Software testing: Unit tests act as tiny proofs that a function behaves correctly.
  • Formal verification: Mathematically proving that critical code (e.g., airplane control software) is error‑free.
  • Cryptography: Zero‑knowledge proofs, digital signatures, and hash functions rely on mathematical proofs of security.
  • Blockchain: Proof of Work, Proof of Stake, and other consensus mechanisms are proofs that participants followed the protocol.
  • Algorithms: Proving that a sorting algorithm always finishes in O(n log n) time, for example.

Good things about it

  • Provides absolute confidence that something works as intended.
  • Helps catch hidden bugs before they cause real problems.
  • Builds trust between users, developers, and businesses.
  • Enables secure systems like encrypted messaging and blockchain.
  • Encourages clear, disciplined thinking and better documentation.

Not-so-good things

  • Writing formal proofs can be time‑consuming and require specialized knowledge.
  • Complex proofs may be hard for non‑experts to read or understand.
  • Over‑proving simple features can waste resources that could be spent elsewhere.
  • Some proofs rely on assumptions that might later be shown false, requiring re‑work.
  • Automated proof tools can produce false positives or miss subtle errors if not configured correctly.