Conjecture vs. hypothesis vs. law vs. theory
Mathematics and science both have words for statements that are proposed, tested, or established, and the words are often confused. A conjecture is a statement believed true but not yet proved, and it belongs to mathematics, where statements are settled by proof. In science, where statements are tested by evidence, a hypothesis is a testable proposal, and a theory is a well-supported explanation of many observations. A law describes a pattern that holds in every tested case, often as an equation such as $F = G m_1 m_2 / r^2$, without explaining why the pattern holds; explaining it is the job of a theory. In everyday speech, “theory” means a guess, but in science a theory is an a principle or body of principles that explains observed data and phenomenon.
Definitions
Missing definition: conjecture
A hypothesis is a guess about how something works that can be checked with an experiment.
A hypothesis is a proposed explanation or prediction that can be tested by observation or experiment, and that the evidence could show to be false.
Examples
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Before an experiment: “Bean plants grow taller with more hours of light each day”
“Bean plants grow taller with more hours of light” is a hypothesis, because it is a prediction that an experiment can test and could show to be false.
Non-examples
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Goldbach’s conjecture
Goldbach’s conjecture is not a hypothesis, because checking more even numbers cannot establish it; only a proof can.
- Newton’s law of universal gravitation, $F = G m_1 m_2 / r^2$
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The theory of evolution by natural selection
Evolution by natural selection is not a hypothesis because it has be demonstrated via experiments.
A scientific law is a statement, often an equation, that describes a pattern that holds in every tested case, without explaining why.
Examples
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Newton’s law of universal gravitation, $F = G m_1 m_2 / r^2$
Newton’s law of gravitation is a law because it is an equation that describes how strongly masses attract.
Non-examples
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Before an experiment: “Bean plants grow taller with more hours of light each day”
The hypothesis “Bean plants grow taller with more hours of light each day” is not a law, because it has not been observed to hold in every tested case.
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The theory of evolution by natural selection
Evolution by natural selection is not a law because it explains why species change rather than describing one pattern.
Properties
- A law describes what happens, and a theory explains why. A theory does not become a law by gaining more evidence.
A scientific theory is a well-tested explanation of a broad range of observations, supported by a large body of evidence and used to make predictions.
Examples
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The theory of evolution by natural selection
Evolution by natural selection is a theory, because it explains a broad range of observations (fossils, genetics, the distribution of species) and is supported by a large body of evidence.
Non-examples
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“I have a theory about who ate the cake”
“A theory about who ate the cake” is not a scientific theory, because it is a guess with little evidence.
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Before an experiment: “Bean plants grow taller with more hours of light each day”
The hypothesis “Bean plants grow taller with more hours of light each day” is not a theory, because no body of evidence supports it yet.
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Newton’s law of universal gravitation, $F = G m_1 m_2 / r^2$
Newton’s law of gravitation is not a theory, because it does not explain why masses attract; general relativity, a theory, does.
Properties
- A theory is not a hypothesis that is waiting to be proved. Instead, it is an explanation for existing data and observations. Theories may be revised as new evidence is collected.
Examples
| Example | conjecture | hypothesis (in science) | law (in science) | theory (in science) | Why |
|---|---|---|---|---|---|
| Goldbach’s conjecture | ✓ | ✗ | – | – | |
| Before an experiment: “Bean plants grow taller with more hours of light each day” | ✗ | ✓ | ✗ | ✗ | |
| The theory of evolution by natural selection | – | ✗ | ✗ | ✓ | |
| Newton’s law of universal gravitation, $F = G m_1 m_2 / r^2$ | – | ✗ | ✓ | ✗ | |
| “I have a theory about who ate the cake” | – | – | – | ✗ | In scientific terms, a “theory” about who ate the cake is closer to a hypothesis. |
Notes
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A conjecture is settled by proof and stays a conjecture no matter how much evidence supports it, while a hypothesis is supported or refuted by evidence and is never proved.
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Scientific laws and theories are not ranked: a theory does not become a law with more evidence.
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In mathematics, a “hypothesis” usually means an assumption of a theorem, and a “theory” is a body of results, such as group theory.