Mathematical Language · Siblings

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

hypothesis (in science)

Elementary

A hypothesis is a guess about how something works that can be checked with an experiment.

High school

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
Non-examples
  • Goldbach’s conjecture: every even integer greater than $2$ is the sum of two primes
    Goldbach’s conjecture is a conjecture, because it is a mathematical statement that is believed true but has no proof. It is not a hypothesis, because checking more even numbers cannot establish it; only a proof can.
  • Newton’s law of universal gravitation, $F = G m_1 m_2 / r^2$
    Newton’s law of gravitation is a law because it is an equation that describes how strongly masses attract. It is not a theory, because it does not explain why masses attract; general relativity, a theory, does.
  • 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. It is not a law because it explains why species change rather than describing one pattern. It is not a hypothesis because it has be demonstrated via experiments.

law (in science)

High school

A scientific law is a statement, often an equation, that describes a pattern that holds in every tested case, without explaining why.

Examples
Non-examples
  • 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. It is not a theory or a law, because no body of evidence supports it yet, and it is not a conjecture, because experiments, not proofs, decide it.
  • 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. It is not a law because it explains why species change rather than describing one pattern. It is not a hypothesis because it has be demonstrated via experiments.
Properties
  • A law describes what happens, and a theory explains why. A theory does not become a law by gaining more evidence.

theory (in science)

High school

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
  • 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. It is not a law because it explains why species change rather than describing one pattern. It is not a hypothesis because it has be demonstrated via experiments.
Non-examples
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: every even integer greater than $2$ is the sum of two primes ✓✗–– Goldbach’s conjecture is a conjecture, because it is a mathematical statement that is believed true but has no proof. It is not a hypothesis, because checking more even numbers cannot establish it; only a proof can.
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. It is not a theory or a law, because no body of evidence supports it yet, and it is not a conjecture, because experiments, not proofs, decide it.
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. It is not a law because it explains why species change rather than describing one pattern. It is not a hypothesis because it has be demonstrated via experiments.
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. It is not a theory, because it does not explain why masses attract; general relativity, a theory, does.
“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. In scientific terms, it is closer to a hypothesis.

Notes

  • 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.

  • Scientific laws and theories are not ranked: a theory does not become a law with more evidence.

  • In mathematics, a “hypothesis” usually means an assumption of a theorem, and a “theory” is a body of results, such as group theory.

See also

All distinctions · All definitions