---
title: "Scientific method"
chunk: 13/13
source: "https://en.wikipedia.org/wiki/Scientific_method"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T03:43:09.265477+00:00"
instance: "kb-cron"
---

=== Science of complex systems ===
Science applied to complex systems can involve elements such as transdisciplinarity, systems theory, control theory, and scientific modelling.
In general, the scientific method may be difficult to apply stringently to diverse, interconnected systems and large data sets. In particular, practices used within Big data, such as predictive analytics, may be considered to be at odds with the scientific method, as some of the data may have been stripped of the parameters which might be material in alternative hypotheses for an explanation; thus the stripped data would only serve to support the null hypothesis in the predictive analytics application. Fleck (1979), pp. 38–50 notes "a scientific discovery remains incomplete without considerations of the social practices that condition it".

== Relationship with mathematics ==
Science is the process of gathering, comparing, and evaluating proposed models against observables. A model can be a simulation, mathematical or chemical formula, or set of proposed steps. Science is like mathematics in that researchers in both disciplines try to distinguish what is known from what is unknown at each stage of discovery. Models, in both science and mathematics, need to be internally consistent and also ought to be falsifiable (capable of disproof). In mathematics, a statement need not yet be proved; at such a stage, that statement would be called a conjecture.
Mathematical work and scientific work can inspire each other. For example, the technical concept of time arose in science, and timelessness was a hallmark of a mathematical topic. But today, the Poincaré conjecture has been proved using time as a mathematical concept in which objects can flow (see Ricci flow).
Nevertheless, the connection between mathematics and reality (and so science to the extent it describes reality) remains obscure. Eugene Wigner's paper, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", is a very well-known account of the issue from a Nobel Prize-winning physicist. In fact, some observers (including some well-known mathematicians such as Gregory Chaitin, and others such as Lakoff and Núñez) have suggested that mathematics is the result of practitioner bias and human limitation (including cultural ones), somewhat like the post-modernist view of science.
George Pólya's work on problem solving, the construction of mathematical proofs, and heuristic show that the mathematical method and the scientific method differ in detail, while nevertheless resembling each other in using iterative or recursive steps.

In Pólya's view, understanding involves restating unfamiliar definitions in your own words, resorting to geometrical figures, and questioning what we know and do not know already; analysis, which Pólya takes from Pappus, involves free and heuristic construction of plausible arguments, working backward from the goal, and devising a plan for constructing the proof; synthesis is the strict Euclidean exposition of step-by-step details of the proof; review involves reconsidering and re-examining the result and the path taken to it.
Building on Pólya's work, Imre Lakatos argued that mathematicians actually use contradiction, criticism, and revision as principles for improving their work. In like manner to science, where truth is sought, but certainty is not found, in Proofs and Refutations, what Lakatos tried to establish was that no theorem of informal mathematics is final or perfect. This means that, in non-axiomatic mathematics, we should not think that a theorem is ultimately true, only that no counterexample has yet been found. Once a counterexample, i.e. an entity contradicting/not explained by the theorem is found, we adjust the theorem, possibly extending the domain of its validity. This is a continuous way our knowledge accumulates, through the logic and process of proofs and refutations. (However, if axioms are given for a branch of mathematics, this creates a logical system —Wittgenstein 1921 Tractatus Logico-Philosophicus 5.13; Lakatos claimed that proofs from such a system were tautological, i.e. internally logically true, by rewriting forms, as shown by Poincaré, who demonstrated the technique of transforming tautologically true forms (viz. the Euler characteristic) into or out of forms from homology, or more abstractly, from homological algebra.
Lakatos proposed an account of mathematical knowledge based on Polya's idea of heuristics. In Proofs and Refutations, Lakatos gave several basic rules for finding proofs and counterexamples to conjectures. He thought that mathematical 'thought experiments' are a valid way to discover mathematical conjectures and proofs.
Gauss, when asked how he came about his theorems, once replied "durch planmässiges Tattonieren" (through systematic palpable experimentation).

== See also ==
Evidence-based practice – Pragmatic methodology
Methodology – Study of research methods
Metascience – Scientific study of science
Outline of scientific method
Quantitative research – All procedures for the numerical representation of empirical facts
Research transparency
Scientific law – Statement based on repeated empirical observations that describes some natural phenomenon
Scientific protocol
Testability – Ability to examine a theory by experimentation

== Notes ==

=== Notes: Problem-solving via scientific method ===

=== Notes: Philosophical expressions of method ===

== References ==

=== Footnotes ===

=== Sources ===

== Further reading ==

== External links ==

Andersen, Hanne; Hepburn, Brian. "Scientific Method". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. ISSN 1095-5054. OCLC 429049174.
Fieser, James; Dowden, Bradley (eds.). "Confirmation and Induction". Internet Encyclopedia of Philosophy. ISSN 2161-0002. OCLC 37741658.
Scientific method at PhilPapers
Scientific method at the Indiana Philosophy Ontology Project
An Introduction to Science: Scientific Thinking and a scientific method Archived 2018-01-01 at the Wayback Machine by Steven D. Schafersman.
Introduction to the scientific method at the University of Rochester
The scientific method from a philosophical perspective
Theory-ladenness by Paul Newall at The Galilean Library
Lecture on Scientific Method by Greg Anderson (archived 28 April 2006)
Using the scientific method for designing science fair projects
Scientific Methods an online book by Richard D. Jarrard
Richard Feynman on the Key to Science (one minute, three seconds), from the Cornell Lectures.
Lectures on the Scientific Method by Nick Josh Karean, Kevin Padian, Michael Shermer and Richard Dawkins (archived 11 May 2013).
"How Do We Know What Is True?" (animated video; 2:52)