Questions tagged [mathematical-physics]

For questions regarding the mathematical aspects of physics.

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

Consider a fundamental concept in maths that was created to 'solve' a problem that simply couldn't be solved by any other approach (or maybe for some other reason). Now let's assume that this concept ...
Adil Mohammed's user avatar
29 votes
2 answers
2k views

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

In theoretical physics, the modern perspective on gauge theory is that it is most elegantly described in the 'language' of differential geometry. I am interested in the history behind these ideas. ...
Danu's user avatar
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18 votes
4 answers
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Why isn't Feynman's path integral taught more widely and earlier in today's academic physics curricula?

Anyone who has studied Feynman's path integral will know that it makes quantum mechanics more like classical mechanics. A student who has learned about the Lagrangian will easily understand the ...
Ooker's user avatar
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16 votes
5 answers
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What was the motivation for Minkowski spacetime before special relativity?

If I understand correctly, the concept of a Minkowski space/metric was already known before Einstein's paper on special relativity. Was there any physical motivation for studying this type of metric ...
Prastt's user avatar
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14 votes
1 answer
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Notation for Christoffel symbols

In Christoffel's 1869 paper in which he introduced the Christoffel symbols on the 3rd and 4th pages, they are written as $\left[\substack{ij \\ k}\right]$ and $\{\substack{ij \\ k}\}$. The notation $...
KCd's user avatar
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13 votes
2 answers
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When were vectors invented?

Encyclopedia Britannica says, In their modern form, vectors appeared late in the 19th century when Josiah Willard Gibbs and Oliver Heaviside (...) independently developed vector analysis to express ...
Joseph O'Rourke's user avatar
10 votes
3 answers
918 views

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

How come do we attribute general theory of relativity to Einstein when David Hilbert published first?
superAnnoyingUser's user avatar
10 votes
1 answer
3k views

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

The $\dagger$ symbol is often used in quantum mechanics,and also often in general mathematics to represent the conjugate transpose operation.For Hermitian matrices we can write $$A^\dagger=A$$Who ...
Manas Dogra's user avatar
10 votes
1 answer
862 views

How were vector calculus nabla ∇ identities first derived?

(Math Stack Exchange suggested that the same question I posted there be migrated here; The one at Math Stack Exchange was thus deleted. The recommendation message of migration can be found here, ...
Secret's user avatar
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9 votes
1 answer
197 views

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

I am a playwright working on a play about Sophie Germain. When Sophie was competing for the prix extraordinaire to find effective formulas to describe the vibrations of elastic surfaces, she believed ...
Brenda Kenworthy's user avatar
9 votes
1 answer
350 views

Is Hermann Weyl's book “Space, Time, Matter” (1923) on General Relativity still relevant?

I really liked Hermann Weyl's mathematical books and would like to get accustomed to general relativity from his perspective, but wonder if it's still relevant after almost 100 (!) years? Can this ...
Slaus's user avatar
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8 votes
3 answers
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Origin of operators in quantum mechanics

Historically, where did the concept of operators in quantum mechanics come from? How did people first understand that momentum operator should be of the form of $i \hbar \frac{{\rm d}}{{\rm d}x}$? ...
user157588's user avatar
8 votes
1 answer
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What was the real need of divergence and curl operators?

As I'm advancing my study in Electromagnetism I'm getting introduced to more mathematical operators which are exclusively used in Electromagnetism and Fluid Dynamics only. Let me try to explain myself ...
Knight wants Loong back's user avatar
8 votes
2 answers
1k views

What is Heaviside's version of Maxwell's equations?

I have read, in many places, statements like this: Heaviside was able to greatly simplify Maxwell's 20 equations in 20 variables, replacing them by four equations in two variables. Today we ...
Harry Weston's user avatar
8 votes
1 answer
575 views

History of complex analysis

Does anyone know of a good book on the history of imaginary numbers and complex analysis and its role in physics?
user3880994's user avatar
8 votes
2 answers
373 views

Has there been debate between relationship of philosophy of mathematics and physics?

Did there exist and does there still exist a debate over which school of mathematical thought (i.e. formalism, logicism, intuitionism, etc.) had the most affinity or application for physics? In ...
user278039's user avatar
7 votes
5 answers
836 views

Were matrix theory and functional analysis well-known to physicists before the invention of matrix mechanics?

Were matrix theory and analysis well-known to physicists circa 1920-1925? Did physicists make extended use of this theory in that period? The question is related to the discussion in How did ...
Frobenius's user avatar
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7 votes
1 answer
626 views

Who named the fugacity, who coined the variable name and did it already relate to complex analysis?

In Riemanns monumental paper, he expresses a prime counting function as an inverse Mellin transform of the log of the function he analytically continued into the complex plane $$\Pi(x) = \frac{1}{2\...
Nikolaj-K's user avatar
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6 votes
3 answers
433 views

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

The direction in which leading research is heading in these subjects (Math, Physics) is very much different and don't seem to be in tandem. Is this something that developed in more recent times? This ...
Wave Metric's user avatar
6 votes
2 answers
359 views

Notational change with Integrals

A little over 50 years ago I took my first Calculus class and learned the conventional form of an integral as: $$ \int f(x)\,\, \textrm{d}x $$ That is, the integral sign (definite or indefinite) ...
K7PEH's user avatar
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6 votes
1 answer
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Was Von Neumann and Birkhoff's original formulation of Quantum Logic related with projective geometry?

I was looking at how did von Neumann and Birkhoff formulate their Quantum Logic formalism back in 1936. To solve some questions, I contacted via email a philosopher who studied this topic. I thought ...
vengaq's user avatar
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6 votes
0 answers
118 views

What is the origin in the discrepancy between engineers' and physicists' notation of waves?

my question is very simple. Physicists use this notation in order to write a (for example) plane wave: $$ \xi(z) = \xi^+ \mathrm{e}^{+\mathrm{i}kz} + \xi^- \mathrm{e}^{-\mathrm{i}kz}, $$ where $\xi^+$ ...
gunix12's user avatar
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5 votes
3 answers
333 views

The Greeks did not discover "a single scientific law"

The title is drawn from a sentence in a Jim Holt article, "The Dangerous Idea of the Infinitesimal," now a chapter in his book collection.1 I found this a striking claim, and perhaps true, as the ...
Joseph O'Rourke's user avatar
5 votes
3 answers
769 views

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

In this video about the Banach-Tarski paradox the host stipulates that history is full of examples of abstract mathematical theories that were later found to be applicable to the physical world. Is he ...
daniel.sedlacek's user avatar
5 votes
2 answers
507 views

Who pioneered the study of the sedenions?

I found lots of background information about the discovery of both imaginary and complex numbers, and enough information about the first two types of hypercomplex numbers; quaternions and octonions (...
Mr. J. Larios's user avatar
5 votes
1 answer
666 views

How were negative numbers first used in physics?

The use of negative numbers in most of today's calculations is natural. But how did the use of negative numbers began in physics? What physical quantity required the introduction of negative numbers ...
Big Brother's user avatar
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5 votes
2 answers
434 views

On the development of Newtonian Mechanics

Having borrowed from the library an English translation of Newton's Principia (Motte's), I read the begining sections, Part 1 and the Systems of the world, and noticed that Newton did physics ...
Cicero's user avatar
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5 votes
1 answer
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Who originally derived the general force law equation of force between current elements?

Wikipedia credits this to Maxwell. This derivation can be found in Maxwell's Treatise on Electricity and Magnetism vol. 2, part 4, ch. 2 (§§502-527). I went through the derivation and found two self ...
Joe's user avatar
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5 votes
1 answer
185 views

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

Here I found that: Sixty years later, Russian mathematician Andrey Kolmogorov furthered our mathematical understanding of turbulence when he proposed that energy in a turbulent fluid at length $R$ ...
Paula's user avatar
  • 173
5 votes
1 answer
533 views

What did Lagrange do with his quantity (the Lagrangian in classical mechanics)?

When I was learning classical mechanics, I was quite baffled by the Hamilton's principle, since it involves a quantity named after Lagrange. So, it seems that the principle was not discovered by ...
kaiser's user avatar
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5 votes
0 answers
106 views

Were pictorial notations like Feynman diagrams for integrals used before Feynman?

In the book Mathews, Walker: Mathematical Methods of Physics, Addison-Wesley(1969), there is a pictorial notation of the solution found by Fredholm about an integral equation.p.304, p.305This circle ...
user avatar
4 votes
4 answers
180 views

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

What are some examples of big results in mathematics and or physics that took a long time to be considered groundbreaking? What was the length of time from the original publication to the recognition? ...
user162520's user avatar
4 votes
3 answers
325 views

Examples of Physical Discoveries with no Counterpart in Mathematics

Throughout the history of mathematics and physics, there has been many examples where mathematics was discovered first prior to its application in physics. Consider $i=\sqrt {-1}$ as an example, among ...
Josh's user avatar
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4 votes
3 answers
745 views

Best books/papers on Newton and his mathematical physics

In your opinion, what are some of the best books/papers on Newton and his work that accurately cover the connections between his geometric proofs in the Principia and his development of the calculus ...
Tom Copeland's user avatar
4 votes
1 answer
3k views

Collection of open problems in Partial differential equations

Except Navier-Stokes equation, are there any other interesting open problems in partial differential equations? I want to know the collection of problems, which are easy to understand but ...
Manoj Kumar's user avatar
4 votes
2 answers
678 views

What were the criticisms against the introduction of "vector analysis"?

Frequently, 19th century physicists—e.g., Helmholtz or Maxwell—did not use modern-day vector notation, which Gibbs contributed in large part to. For example, Helmholtz in his famous paper on the ...
Geremia's user avatar
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4 votes
2 answers
2k views

Who discovered the wave equation?

https://link.springer.com/chapter/10.1007/978-1-4684-5772-8_2 says: Using Newton's recently formulated laws of motion, Brook Taylor (1685–1721) discovered the wave equation by means of physical ...
user45664's user avatar
  • 173
4 votes
2 answers
244 views

History of delta barrier in quantum mechanics

I'm interested in finding something out about the history of the problem of the delta potential barrier in quantum mechanics. Which was the first study to propose this problem, and perhaps any ...
Ed Wolf's user avatar
  • 71
4 votes
1 answer
507 views

Where in Gauss's works does he derive "Gauss's Law"?

Where in Gauss's works does he derive "Gauss's Law"? Or is "Gauss's Law" named after Gauss for a different reason?
Geremia's user avatar
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4 votes
1 answer
366 views

How has the definition of a tensor today changed compared to its original definition?

On page 71 of The Absolute Differential Calculus by Levi-Civita, a very clear definition of a tensor is given in terms of how the coefficients of a multi-linear form transform, such that the product ...
Larry Harson's user avatar
4 votes
0 answers
151 views

Did Rayleigh or Ritz prove the Rayleigh–Ritz theorem?

The maximum eigenvalue of a real symmetric (or complex Hermitian) matrix is given as the maximum of the associated the quadratic form: $$ \lambda_{\rm max}(A) = \max_{\|x\| = 1} x^*Ax. \tag{1} $$ This ...
eepperly16's user avatar
4 votes
0 answers
150 views

In which work was Gibbs' Inequality introduced?

Gibbs' inequality $$-\sum\limits_{i=1}^n p_{i} \cdot \log{p_{i}} \le -\sum\limits_{i=1}^n p_{i} \cdot \log{q_{i}}$$ is such a popular thing that I cannot find where it was introduced. My findings I ...
Charlie's user avatar
  • 149
3 votes
3 answers
329 views

Best history of Maxwell and his equations

I've done my B.S. in Electrical Engineering as well as mathematics but I'd like to get a proper, or complete history of Maxwell and the history of his derivation of the equations and the newness of ...
Elliot's user avatar
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3 votes
1 answer
631 views

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

I remember hearing once that the first "proof" that the angle to maximise projectile range gave the correct answer, 45 degrees, but was later found that the proof was wrong. I can't remember ...
twentyyears's user avatar
3 votes
1 answer
476 views

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

I've read a lot about the Magnus effect altering the trajectories of cannonballs and musketballs. Robins noticed it with Musket balls and Magnus with canonballs, but presumably they weren't the first ...
Tom Lancaster's user avatar
3 votes
1 answer
120 views

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

Ladyzhenskaya is famous for fluid dynamics and partial differential equations, both of which are beyond my pay grade. And she worked on the Navier-Stokes equations. Does this circle with the arrows ...
Jeff Lima's user avatar
3 votes
2 answers
935 views

History of PDE's in the 19th Century

I've been asked to write an essay on whether the work on PDE's in the 19th century belonged to applied or pure mathematics. Does anyone know of any useful sources I could use?
Bradley Hill's user avatar
3 votes
2 answers
351 views

When Was Kaluza-Klein Theory Appreciated?

As far as I understand, the Kaluza-Klein theory, despite its unprecedentedly profound and beautiful character, had a modest following in its early days. I guess that two of the many reasons might be ...
ACat's user avatar
  • 1
3 votes
1 answer
272 views

How did philosophers and scientists in the 18th century view mathematical explanation?

The 18th century saw a rise in the use of mathematical formalisms to account for natural phenomena. Works of Lagrange, Euler, d'Alembert, etc., were groundbreaking in the history of mechanics and ...
Rain's user avatar
  • 559
3 votes
1 answer
273 views

A peculiar quote from Oliver Heaviside

The best result of mathematics is to be able to do without it. The above is a quote by Oliver Heaviside, an electrical engineer and mathematician. What does the quote really mean?
stoic-santiago's user avatar