33 votes
Accepted

Has physics ever given a physical significance to a mathematically abstract idea?

Physics cannot help giving physical significance to things. But, yes, the first item on your list should have been Lie Groups. Developed as a mathematical "sudoku" game generalizing ...
Cosmas Zachos's user avatar
29 votes

What was the motivation for Minkowski spacetime before special relativity?

Not quite. Minkowski had the idea of representing special ralativity as geometry in 1907 under the direct influence of Einstein's 1905 paper, and he developed it in Raum und Zeit (1907) and Zwei ...
Conifold's user avatar
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21 votes
Accepted

When were vectors invented?

This question was actually discussed on this site several times, for example here: When was the vector notation in physics and other sciences first introduced? It indeed looks strange to modern people ...
Alexandre Eremenko's user avatar
21 votes

Has physics ever given a physical significance to a mathematically abstract idea?

fractal The so-called Cantor set was described by Georg Cantor, 1884 (or H. J. S. Smith, 1875?) Sets with "fractional" dimension were described by Felix Hausdorff, 1918 Investigated ...
Gerald Edgar's user avatar
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18 votes

Has physics ever given a physical significance to a mathematically abstract idea?

The following quote is from C. N. Yang, delivered at a 1979 symposium dedicated to the geometer Chern: "When I met Chern, I told him that I finally understood the beauty of the theory of fibre ...
Mark Yasuda's user avatar
  • 1,538
12 votes
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The Greeks did not discover "a single scientific law"

It is a strange idea that scientific laws can be only expressed with algebraic means. The Greek did discover several scientific laws. The oldest one is attributed to Pythagoras himself: it relates the ...
Alexandre Eremenko's user avatar
11 votes

Did Sophie Germain find a flaw in Euler's equations for elastic vibrations?

There were two episodes with Germain and Euler's mistake in elasticity, but neither one of them is of Germain discovering Euler's mistake. The first one is from 1811 when she was starting to work on ...
Conifold's user avatar
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10 votes
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What was the real need of divergence and curl operators?

These operations arose from the study of quaternions see e.g. Thomson and Tait's Treatise on Natural Philosophy, that should probably have information on the sort of math. Stokes's theorem originated ...
Sam Gallagher's user avatar
10 votes

Who introduced the "dagger"symbol as conjugate transpose in quantum mechanics?

In a now-deleted comment, Consigliere ZARF listed a number of papers published in Zeitschrift für Physik in the late 1920's that used this notation. The earliest was Pascual Jordan's 1927 "Über eine ...
kimchi lover's user avatar
  • 2,535
10 votes

Examples of Physical Discoveries with no Counterpart in Mathematics

Potential theory (Green's formulas, Green's function etc.) was discovered by George Green who was doing physics. His work was called "An Essay on the Application of Mathematical Analysis to the ...
Alexandre Eremenko's user avatar
9 votes

Example of abstract math theory that was later found to be applicable to physical world?

Group theory. A story I heard (perhaps enhanced over the years): In 1910, Princeton was about to begin a major in physics. The physicists sat down to decide what would be required for those ...
Gerald Edgar's user avatar
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9 votes
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Notation for Christoffel symbols

Well, the history is not too simple, even though you have traced some correct events. It was Albert Einstein on November 4th, 1915 in his paper "Zur allgemeinen Relativitätstheorie" (Königlich ...
DanielC's user avatar
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9 votes
Accepted

How were negative numbers first used in physics?

Ancient Greeks painstakingly avoided negative numbers, although they could have come handy in astronomical calculations and number theory, among other places. Brahmagupta in Correctly Established ...
Conifold's user avatar
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9 votes
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Collection of open problems in Partial differential equations

This is a collection of open problems concerning various areas in function theory, functional analysis, theory of linear and nonlinear partial differential equations. Seventy Five (Thousand) Unsolved ...
Vatsal Limbachia's user avatar
9 votes

Who made the first derivation of the angle to maximise projectile range, which turned out to be wrong?

This probably refers to Galileo's "derivation" of Tartaglia's observation that cannon balls achieve maximal range when fired at 45°. Tartaglia's theory of projectile motion was wrong, he ...
Conifold's user avatar
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8 votes

What was the motivation for Minkowski spacetime before special relativity?

Minkowski space time was considered by mathematicians before Einstein and before Minkowski. Of course the name "space-time" was not used. The reasons were purely mathematical, not physical. The most ...
Alexandre Eremenko's user avatar
8 votes

Origin of operators in quantum mechanics

From where did the concept of operator in quantum mechanics came, historically? This was a gradual development started by Heisenberg's insight. He invented (infinite) matrices (without any prior ...
Alexandre Eremenko's user avatar
8 votes

Who originally derived the general force law equation of force between current elements?

Ampère did. Ampère's force law (not to be confused with one of Maxwell's equations, "Ampère"'s circuital law, which Ampère never wrote down, as Ampère didn't deal with the field concept), written in ...
Geremia's user avatar
  • 5,289
8 votes

The Greeks did not discover "a single scientific law"

Euclid wrote an Optica (300 BC) — surely “Visual rays proceed in a straight line indefinitely” ranks with the best physical laws. So did Ptolemy (160 AD), and Hero wrote a Catoptrica (50 AD). ...
Francois Ziegler's user avatar
8 votes

Does anyone know of any examples of the Magnus effect in a real battle?

I am afraid nobody noticed it, because nobody could have noticed it. A deviation is only a deviation when one has something that it is a deviation from. To "notice" the Magnus effect one has to ...
Conifold's user avatar
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8 votes

Has physics ever given a physical significance to a mathematically abstract idea?

Abelian and non-abelian group theory -> quantum chromodynamics Noneuclidean geometry -> general relativity Sorry, I cannot write you any equations as examples.
niels nielsen's user avatar
8 votes

Has physics ever given a physical significance to a mathematically abstract idea?

I don't know if this can be counted for as physics, but to my knowledge the radon transformation was mostly something mathematicians thought about without any application. Now, it is widely used (and ...
Eulenfuchswiesel's user avatar
8 votes
Accepted

The abstraction of mathematics from physics

You are right, this happened in ancient Greece, and is credited to Thales and Pythagoras. Unfortunately, too little of their early work survived (nothing written by Thales or Pythagoras). The main ...
Alexandre Eremenko's user avatar
7 votes
Accepted

Who was the first person to describe turbulence in mathematical terms?

Systematic study of turbulence originates with a series of experiments conducted by Osborne Reynolds starting in 1870s. His mathematical theory was developed in On the dynamical theory of ...
Conifold's user avatar
  • 75.2k
7 votes

History of complex analysis

I would say that there is no good book which satisfies your description. The Book of Bottazzini and Grey mentioned in the comments is OK, but it certainly does not cover the role of complex analysis ...
Alexandre Eremenko's user avatar
7 votes

Time for big results to become widely recognized in the scientific community

There is no point in giving examples on the second question, because for most truly groundbreaking results this time is really short. On the first question, one can mention almost all results of ...
Alexandre Eremenko's user avatar
7 votes

Time for big results to become widely recognized in the scientific community

Discovery of non-Euclidean geometries in 19th century, it took about 40-50 years for them to get accepted.
Moishe Kohan's user avatar
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7 votes

Example of abstract math theory that was later found to be applicable to physical world?

Essentially the same question was asked on Math Overflow: https://mathoverflow.net/questions/116627/useless-math-that-became-useful/116653#116653 , and many examples were given. Such examples are ...
Alexandre Eremenko's user avatar
7 votes

Does the “O” in the google doodle for Olga Ladyzhenskaya have anything to do with her work?

The equation in the picture is the Navier–Stokes momentum equation in convective form. The part inside the O looks like a cross-section of (the velocity field of) a flow between two rotating ...
Conifold's user avatar
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