The scientific method is usually taught as a fixed sequence: observe, form a hypothesis, predict, test, revise. That description is useful for beginners and does not survive contact with how science has actually developed.

The standard account and its problems

Observation is not neutral. What you record depends on what you take to be relevant, which depends on the theory you hold. There is no stage of pure data collection before theorizing begins.

Confirmation is weak. Instances agreeing with a hypothesis do not establish it — Hume's problem of induction. Any finite body of evidence is compatible with more than one general claim.

Tests are never isolated. A prediction follows from the hypothesis plus assumptions about equipment, background conditions and auxiliary theories. A failure tells you something in that bundle is wrong, not which part.

The main proposals

Popper replaced confirmation with falsifiability: make bold conjectures, try hard to refute them, keep what survives, and never claim proof.

Kuhn argued that the description should follow the history, which shows long stable periods of work inside a framework, interrupted by revolutions — see paradigm shift.

Imre Lakatos proposed research programs with a protected core and a belt of adjustable assumptions, judged over time by whether they predict new phenomena or merely absorb failures.

Paul Feyerabend argued that no methodological rule has gone unbroken by a successful scientist, and that insisting on one would have blocked several major advances.

What is left

No single procedure. What the accounts share is a set of commitments that hold across fields: claims answer to evidence rather than to authority, methods are stated so others can check them, results have to survive people trying to break them, and any claim can in principle be revised.

That is weaker than a method and is what does the work. See first principles and second-order effects.