Scientific method
Updated: 12/11/2025, 1:36:45 PM Wikipedia source
The scientific method is an empirical method for acquiring knowledge through careful observation, rigorous skepticism, hypothesis testing, and experimental validation. Developed from ancient and medieval practices, it acknowledges that cognitive assumptions can distort the interpretation of the observation. The scientific method has characterized science since at least the 17th century. Scientific inquiry includes creating a testable hypothesis through inductive reasoning, testing it through experiments and statistical analysis, and adjusting or discarding the hypothesis based on the results. Although procedures vary across fields, the underlying process is often similar. In more detail: the scientific method involves making conjectures (hypothetical explanations), predicting the logical consequences of hypothesis, then carrying out experiments or empirical observations based on those predictions. A hypothesis is a conjecture based on knowledge obtained while seeking answers to the question. Hypotheses can be very specific or broad but must be falsifiable, implying that it is possible to identify a possible outcome of an experiment or observation that conflicts with predictions deduced from the hypothesis; otherwise, the hypothesis cannot be meaningfully tested. While the scientific method is often presented as a fixed sequence of steps, it actually represents a set of general principles. Not all steps take place in every scientific inquiry (nor to the same degree), and they are not always in the same order. Numerous discoveries have not followed the textbook model of the scientific method, and, in some cases, chance has played a role.
Tables
| Mathematical method | Scientific method | |
| 1 | Understanding | Characterization from experience and observation |
| 2 | Analysis | Hypothesis: a proposed explanation |
| 3 | Synthesis | Deduction: prediction from the hypothesis |
| 4 | Review/Extend | Test and experiment |
References
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- Pólya (1957), p. 131 in the section on 'Modern heuristic': "When we are working intensively, we feel keenly the progress
- Huai-Dong Cao and Xi-Ping Zhu (3 Dec 2006) Hamilton-Perelman's Proof of the Poincaré Conjecture and the Geometrization Chttps://arxiv.org/pdf/math/0612069.pdf
- George Lakoff and Rafael E. Núñez (2000) Where Mathematics Comes From
- "If you can't solve a problem, then there is an easier problem you can solve: find it." —Pólya (1957), p. 114
- George Pólya (1954), Mathematics and Plausible Reasoning Volume I: Induction and Analogy in Mathematics.
- George Pólya (1954), Mathematics and Plausible Reasoning Volume II: Patterns of Plausible Reasoning.
- Pólya (1957), p. 142.
- Pólya (1957), p. 144.
- Lakatos (1976) documents the development, by generations of mathematicians, of Euler's formula for polyhedra.
- H.S.M. Coxeter (1973) Regular Polytopes ISBN 9780486614809, Chapter IX "Poincaré's proof of Euler's formula"
- Charles A. Weibelhttps://web.archive.org/web/20210906014123/https://faculty.math.illinois.edu/K-theory/0245/survey.pdf
- Henri Poincaré, Sur l'analysis situs, Comptes rendusde l'Academie des Sciences 115 (1892), 633–636. as cited by Lakatos
- John Stillwell, reviewer (Apr 2014). Notices of the AMS. 61 (4), pp. 378–383, on Jeremy Gray's (2013) Henri Poincaré: Ahttp://www.ams.org/notices/201404/rnoti-p378.pdf
- Lakatos (1976), p. 55.
- Mackay (1991), p. 100.