An analogy is an inference that an unknown result is true, based on its similarity to a result already known to be true. In the hands of a skilled mathematician, analogy can be a very powerful tool for suggesting new and extending old results. However, subtleties can render results obtained by analogy incorrect, so rigorous proof is still needed.
Analogy
See also
Gauss's Formulas, Mathematical Induction, Napier's AnalogiesExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Analogy." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Analogy.html