24

By way of throat-clearing, what is Occam's razor? John Baez has a useful essay giving the history and some examples. William of Ockham's original formulation was Entities should not be multiplied unnecessarily. In other words, don't assume the existence of something unless there is good evidence for it. Again quoting Baez, "In physics we use the razor to ...


14

The two most famous paradigmatic examples of de-unification are phlogiston and ether. The Kaluza-Klein theory of gravity and electromagnetism did not get to spread as far and wide before faltering. The splitting of jade into two distinct minerals, nephrite and jadeite, is a small scale example. The phlogiston/caloric theory was able to unify chemical and ...


12

Hausdorff wrote many literary and philosophical works, including poems and a play, under the pseudonym Paul Mongré.


12

Bertrand Russell wrote many books and essays on philosophy and social justice, and was awarded a Nobel Prize in Literature. And the Persian mathematician Omar Khayyám wrote poetry: quatrains that have been translated into English as the Rubáiyát of Omar Khayyám.


12

Check out these mathematicians: A father, and two sons, all of whom co-authored papers in various combinations. David Borwein, father Peter Borwein, son Jonathan Borwein, son Peter's memorial to his brother Jonahan, in which he speaks of writing papers together with his brother.


11

Many mathematicians wrote their autobiographies, see the answers to https://mathoverflow.net/questions/102597/history-question-autobiography-of-mathematicians/102676#102676 Quite a few also have engaged in writing literary fiction. For example, Sofya Kovalevskaya (apart from memories about her childhood) wrote a novel: Nihilist Girl, translated by Natasha ...


11

In the 1960s the mathematical structure of Turing degrees was conjectured to be rather simple and homogeneous. This was consistent with what was known at the time. It later turned out that the opposite is true in a sense: the Turing degrees are as complicated as can be. Details in Ambos-Spies and Fejer, History of degree theory.


11

Probably the most famous conflict that satisfies your requirements is the conflict between "Ptolemy system" and "Copernic system", though few people understand this even today:-) This conflict became so famous because of the intrusion of a non-scientific authority, that is catholic church. From the point of view of astronomy, there are two aspects: a) the ...


10

Quite a famous example from modern physics deals with the inherent randomness of quantum theory. In the early years of quantum mechanics when the formulation in terms of wave functions was developed, the question of interpretation arose. Copenhagen interpretation, developed mainly by Niels Bohr and Werner Heisenberg became the most accepted of all the ...


10

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 ...


10

There are lots of references to cranks in A Budget of Paradoxes, by Augustus de Morgan (1806–1871), who calls them “paradoxers”. There, he writes […] I say something on my personal knowledge of the class of discoverers that square the circle, upset Newton, etc. I suspect I know more of the English class than any man in Britain. I never ...


9

Elie and Henri Cartan (father and son) published a paper together, in 1931 (Les transformations des domaines cerclés bornés).


9

Arthur Leonard Rubin co-authored at least two papers with his mother, Jean Estelle Hirsh Rubin, the first one below when he was 13 years old. Arthur L. Rubin and Jean E. Rubin, Extended operations and relations on the class of ordinal numbers, Fundamenta Mathematicae 69 #2 (1969), 227-242. Paul Howard, Arthur L. Rubin, and Jean E. Rubin, Kinna-Wagner ...


8

Leibniz and Newton never thought of manifolds outside of ambient space as far as I know, Newton is credited with forging the concept of absolute space, and Leibniz with reducing it to a relational fiction in the style of Aristotle. The most influential philosopher of science in 19-th century was Kant, specifically his "Copernican revolution" of ...


7

Indian mathematician Srinivasa Ramanujan claimed and is often said to have come up with theorems and questions in his dreams. For example: Ramanujan's Mock Modular Forms: Indian Mathematician's Dream Conjecture Finally Proven While on his death bed, the brilliant Indian mathematician Srinivasa Ramanujan cryptically wrote down functions he said came to ...


7

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 ...


7

Several mathematicians wrote excellent recollections about their own life. Some of them are of high quality as literature. My favorite ones are by Weyl, Rudin and L. Schwartz. David Ruelle (a famous mathematical physicist) wrote some philosophical fiction.


7

Brothers Marcel and Frigyes Riesz have a joint paper, Brothers Rolf and Frithiof Nevanlinna have 6 joint papers. Brothers Alexander and Alexei Zamolodchikov have 8 joint papers. Brothers David and Gregory Chudnovsky have 80 joint papers. This list can be made very long. Father-son collaborations are not so frequent but Herman Weyl has a paper and a book ...


7

Luis Alvarez and his son Walter, and two other chemists, co-authored this 1980 paper on iridium levels at the K/T boundary. The Alvarezes conjectured the now widely accepted impact hypothesis explaining that extinction event. Another example: Katharine Cook Briggs and her daughter Isabel Briggs Myers co-developed MBTI (I'll leave it to the reader to decide ...


6

The mathematician E. T. Bell (known for Bell numbers, and the first stirrings of umbral calculus) wrote many science-fiction novels under the name John Taine. Arthur C. Clarke considered John Taine one of his heroes. (According to Constance Reid's The Search for E. T. Bell: also known as John Taine, which is a wonderful work of history/biography.)


6

One possibility is Ted Kaczynski, the Unabomber. He has been described as a mathematical prodigy and Allen Sheilds, his doctoral adviser, told once the Kaczynski was the best doctoral student he ever directed.


6

Alexander Abian may fit the bill here. His most notable contribution to mathematics was proving consistency and independence of four of the Zermelo-Fraenkel axioms. source: Wolfram Mathworld. They are : Extensionality, Replacement, Power set, and "Sum-set" (i.e., Union). See, for example, Abian and LaMacchia's Original Paper. So far, so good. However, ...


6

number versus numeral (a distinction everyone learns in the third grade – except for those who played hooky that day) loss of unique-factorization as you move from the reals to the complex numbers – e.g., 26 = (2)(3) and 26 = (1 – 5i)(1 + 5i) for two distinct numbers, in the set of positive numbers “is to the left of” and “is farther from 0” are synonymous, ...


6

Ken Ono published a paper with his father Takashi Ono in 1996: ``Quadratic forms and elliptic curves, III'' in Proc. Japan Acad. Ser. A Math. Sci. 72 (1996), no. 9, 204–205.


5

The standard example of "complete opposite" was N. Wiener. Anecdotes: Wiener walking on campus is stopped by someone and they start a mathematical conversation. After the end of the conversation Wiener asks: "In which direction I was walking before I met you?" -"This direction." -"OK, this means I already had my lunch!" Wiener bought a new house. On the ...


5

The Romanian mathematician Dan Barbilian was better known as the modernist poet Ion Barbu. It's interesting that the English wikipedia page deals mostly with his mathematical research. Also it is worth mentioning that he was the first to introduce Modern Algebra (a la Van der Waerden) in Romania.


5

Another famous controversy was about the age of the Earth. It was found long ago that the temperature in the very deep mines increases with depth. Using the model that the Earth evolved from a hot state when the rocks were melted, and was cooling down ever since, one could estimate the age from the known temperature of melting of the rocks and the current ...


5

FamousScientists.org has a thread titled, "7 Great Examples of Scientific Discoveries Made in Dreams." http://www.famousscientists.org/7-great-examples-of-scientific-discoveries-made-in-dreams/ The examples include those already discussed as well as: Mendeleev and the Periodic Table AR Wallace and natural selection Descartes' scientific method Loewi and ...


5

The mathematician Jordan Ellenberg (University page, personal website, Wikipedia article, blog) wrote a novel called The Grasshopper King in 2003. Does this satisfy your criteria? "Acclaimed mathematician": child prodigy, two-time Putnam fellow, Guggenheim Fellowship (2015) "novels, poems, or other literary works not related to mathematics": The Grasshopper ...


5

Rudy Rucker writes science fiction. Some of his novels explore mathematical concepts such as infinity. Ian Stewart, who is best known for his popular science and mathematics books (including the Science of Discworld books), has also written a couple of science fiction novels with Jack Cohen.


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