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In the comments on this question on Physics about the usefulness of expensive experiments such as the CERN, the following short discussion happened:

Has there ever been a major basic science result that did not lead to practical applications within the next couple of hundred years?


Isn't there a strong selection bias there? If something hasn't lead to anything much in the following couple of hundred years, we've probably forgotten about it, regardless of how big a deal it seemed at the time.

While the second argument is indeed sound, I wonder whether there is any good example for this. More precisely and with slight deviations from the inspiration, I am looking for the following:

  • A scientific result that can be considered basic science in the sense that it was not mainly about application to begin with.
  • This result was considered a breakthrough at its time by notable sources (in particular not by people gaining advantage from exaggerating something as a breakthrough).
  • Neither this result nor its successors are considered relevant today. There is no relevant technological application (nor has there ever been) and it does not appear in modern textbooks of any discipline.
  • The result was not a negative one, such as the falsification of the ether theory.
  • The result must be real, e.g., it should not have turned out to be due to experimental errors.
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    $\begingroup$ @Wrzlprmft I think you can not mix "no relevant technological application" and "[not] relevant (point)". A lot of discoveries in maths or astrophysics don't (won't?) have any technological application (=technologically not relevant) but are in textbooks. If you remove this last thing too, the result probably never was a real "breakthrough", by definition. $\endgroup$ – Peabody Nov 5 '14 at 11:32
  • $\begingroup$ @Peabody: I intentionally added the textbook criterion and thus I am really looking for examples that probably never were a real breakthrough, if you so wish, but were considered one at their time. $\endgroup$ – Wrzlprmft Nov 5 '14 at 11:38
  • $\begingroup$ @Wrzlprmft Indeed, that's in the title of your question "Considered a breakthrough at its time". In my mind a breakthrough does not depend on the epoch it was made but I see what you mean... although I have no answer to suggest! $\endgroup$ – Peabody Nov 5 '14 at 11:55
  • $\begingroup$ We hear daily about "breakthrough in HIV vaccination" that actually do not lead to anything... Would you consider this a valid answer? $\endgroup$ – VicAche Nov 5 '14 at 19:24
  • $\begingroup$ @VicAche: Those “breakthroughs” would be very close to application to begin with, but most importantly, I do not think that they are considered breakthroughs by somebody other than incompetent or calculatingly exaggerating journalists (but I am not an expert on this topic). Moreover, I cannot remember having heard any news on a breakthrough in HIV vaccination by reputable media my whole life. (I have specified the question regarding the notability of the breakthrough claim.) $\endgroup$ – Wrzlprmft Nov 5 '14 at 21:04
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I'll give it a try but strictly speaking your conditions exclude pretty much everything. Breakthroughs considered such by competent people not prone to exaggeration probably were "real" in some sense, in hindsight perhaps for wrong reasons. What was once considered "real" is not anymore, old models that were seen as advances and made sense in their time are viewed as errors today, due to obliviousness or poor measurement capabilities. Anything that described some phenomenon once would have a modern "successor" that describes that phenomenon, and modern textbooks usually have historical sections describing little known tidbits of times long gone. So examples below may not be what you are looking for.

Eudoxian model of homocentric spheres, first geometric model in astronomy that cleverly reconciled uniform circular motions (required by Pythagorians and Plato for heavenly bodies) with messy and retrograde motions of the planets. Was later supplanted by the epicyclic model of Apollonius that lasted until Copernicus.

Tusi couple that solved the problem of representing latitudinal motion without a longitudinal component in epicyclic astronomy. When a circle rolls without slipping inside another circle twice its size all points on its circumference oscillate along straight lines, there is a curious video presenting this as an "optical illusion". Tusi couple influenced Copernicus, but of course fell into oblivion along with epicyclic astronomy.

Stahl's phlogiston allowed to treat heat exchange and combustion quantitatively, but was eventually rejected when Lavoisier clarified the oxidation process.

Cuvier's catastrophism, a theory explaining apparent replacement of species in the fossil record prior to Darwin's evolution theory.

Gordan's construction of invariants of binary forms at the end of 19-th century earned him the title "the king of invariants". Unfortunately, his (constructive) methods could not be extended beyond binary forms. After (non-constructive) Hilbert's basis theorem the classical invariant theory, along with Gordan's result, fell into obscurity. "This is not mathematics; this is theology" is anecdotally attributed to Gordan.

All these examples have a common theme. A breakthrough is made in a framework later replaced by a more advanced one, into which it does not translate.

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Andre Weil's approach to algebraic geometry, set out in his book Foundations of Algebraic Geometry, was a breakthrough for its time because it was the first language for algebraic geometry that could handle abstract algebraic varieties that were not a priori subvarieties of affine or projective space (analogous to the distinction between submanifolds of Euclidean space and abstract manifolds). Weil's Foundations provided the terminology and viewpoint of the field for roughly 10 years in the mid-20th century.

Grothendieck's approach to algebraic geometry, based on schemes and not directly building on Weil's work, completely supplanted Weil's Foundations to the extent that Weil's Foundations are largely forgotten today and important papers from the 1950s and later written in the language of Weil's Foundations are very hard to read unless they can be translated into the modern language. See https://mathoverflow.net/questions/36979/some-arithmetic-terminology-universal-domain-specialization-chow-point for a discussion of this last point and chapter 8 of Reid's Undergraduate Algebraic Geometry (http://homepages.warwick.ac.uk/staff/Miles.Reid/MA4A5/UAG.pdf) for a comparison of the three main waves of rigor in algebraic geometry in the 20th century. While Grothendieck's approach could be considered a successor to Weil's, it was not a logical descendant and therefore I think this example fits the question.

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Rene Thom's Catastrophe Theory After Thom classified them, there was a frenzy of claims for how catastrophes were a universal model for abrupt changes in real life situations. The mathematical theorems are sound, but the prospect of applications died quickly, and today no one talks of catastrophes.

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Let us think of something more controversial: how about Freud's theory of the ego, super-ego and id; does anyone believe in this stuff any more?

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  • $\begingroup$ The first problem here is whether psychoanalysis is a science at all. This is strongly disputed and your use of the word believe supports this. Even if we accept psychoanalysis as a science and do not “believe in this stuff”, then this would be excluded by my last criterion (“The result must be real”). $\endgroup$ – Wrzlprmft Jan 23 '15 at 14:47
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    $\begingroup$ Psychoanalysis defines itself as a branch of medicine. Freud himself was a professor in the faculty of medicine. $\endgroup$ – fdb Jan 23 '15 at 15:06
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    $\begingroup$ Pardon my brusqueness, but: So what? $\endgroup$ – Wrzlprmft Jan 23 '15 at 15:12
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    $\begingroup$ Freudian psychoanalysis is possibly the worst example for work that has since been forgotten. Even most laypeople and children have some familiarity with it at this point. $\endgroup$ – Superbest Jun 10 '15 at 3:30
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"Has there ever been a major basic science result that did not lead to practical applications within the next couple of hundred years?"

Transfinite set theory.

It can be considered basic science in the sense that it was not mainly about application.

This result was considered a breakthrough at its time by notable sources like Hilbert and many other mathematicians.

Neither this result nor its successors are considered relevant today for any practical application in sciences like physics, chemistry, biology, technology.

There is no relevant technological application (nor has there ever been) and it does not appear in modern textbooks of any scientific discipline.

The result was not a negative one, but an invention of new notions.

Only the last condition is not satisfied.

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  • $\begingroup$ "...does not appear in modern textbooks of any scientific discipline" - one can easily find hundreds of examples of modern textbooks that discuss transfinite numbers. To pick a random example, Chaos: The Science of Predictable Random Motion by Richard Kautz, Chapter 14. $\endgroup$ – Will Orrick Oct 2 '17 at 10:26

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