32 votes
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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 ...
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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 ...
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  • 67.1k
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 ...
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  • 8,625
19 votes
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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 ...
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17 votes

When and how was the geometric understanding of gauge theories developed?

I will focus on the history before the Yang-Mills paper. The first harbinger was the introduction of the scalar potential for the gravitational field by Lagrange in 1773. In 1864 Maxwell introduced ...
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17 votes
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When and how was the geometric understanding of gauge theories developed?

I'll focus on the geometry of Yang-Mills theories specifically, but as Conifold's answer points out, gauge theories were studied geometrically long before the work of Yang and Mills. The foreward to ...
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  • 2,732
17 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 ...
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  • 1,258
15 votes

How come we attribute the general theory of relativity to Einstein?

This seems a bit of a naive question to me. Einstein had been working on this problem for several years (starting as early as 1907), and had developed much of the physics by 1912. He greatly struggled ...
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  • 3,681
12 votes
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Why isn't Feynman's path integral taught more widely and earlier in today's academic physics curricula?

I do not agree with the statement, that the lack of mathematical rigor is a major reason for not teaching the path integral formalism in quantum mechanics. The common physicist is normally not ...
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  • 491
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 ...
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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 ...
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9 votes

Nowadays I see a distinct "line" dividing people working in Mathematics and the Physical Sciences. Why?

You do not say what field of mathematics you are working in, and perhaps there are signs of separation there. Overall however, lively interaction between mathematics and physics is alive and well. ...
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9 votes

How come we attribute the general theory of relativity to Einstein?

First, to echo and elaborate on previous answers, Hilbert only appeared on the scene during the last few minutes of the last act, so to speak. Einstein made his first step towards the General Theory ...
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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 ...
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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 ...
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  • 352
9 votes
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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 ...
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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 ...
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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 ...
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9 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 ...
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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 ...
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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 ...
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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 ...
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  • 5,051
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). ...
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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 ...
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8 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 ...
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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.
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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 ...
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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 ...
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7 votes

Why isn't Feynman's path integral taught more widely and earlier in today's academic physics curricula?

I would like to add a slightly more technical answer to supplement the other (although it is a bit late). It may be helpful, I think, and it touches a broader issue which interesting. It's a conflict ...
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