Edited sentence: However, this doesn't apply to mathematics, which is not subject to such retractions of established results, notwithstanding nineteenth and early twentieth century discoveries in mathematical logic, which may be popularly misunderstood as having overthrown prior mathematics.More engineer-minded cranks could claim to have invented a magic compression algorithm or a perpetual motion / free energy machine.Rather, it is correct to say that mathematicians have gradually developed more encompassing abstractions, which do not  invalidate earlier mathematics but do often reinterpret them in new and expanded contexts.That is, previous mathematical knowledge has been enriched, not overthrown, by such discoveries as non-Euclidean geometry or Gödel's incompleteness theorems.The mathematical cases provide a baseline for application of the epithet, since the nature of mainstream or for that matter learned, scientific opinion can change over time; however, irrationally rejecting established mathematical truth is archetypical crankery.The term crank is often applied to persons who contradict rigorously proven mathematical theorems, such as the impossibility of squaring the circle by ruler and compass, or who deny extremely well established physical theories, such as the special theory of relativity, conservation of mass-energy, or a spheroid earth (See Flat Earth Society).Those who have studied the phenomenon of crankery agree that this is the essential defining characteristic of the  crank: being impervious to facts, evidence, and rational inference.Typically a crank is impervious to contrary evidence