Questions tagged [mathematical-physics]

For questions regarding the mathematical aspects of physics.

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Math concepts introduced by physicists and made rigorous later

I am looking for mathematical concepts (*) which have been introduced by physicists in a non rigorous way (e.g. without a formal definition, without rigorous proofs of the results, etc.) and used to ...
Weier's user avatar
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1 answer
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How did Schrödinger do quantum mechanics with wave functions?

On my way to learn about the very beginning of quantum mechanics and its different formulations, starting with Heisenberg infinite matrices and Schrödinger's wave functions, I can really not find till ...
user19358's user avatar
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Surface Integrals History

Can't find any information about who and when first used surface/surface area integrals. What was the original motivation? In it's modern form it depends on some relatively modern notations like ...
simd's user avatar
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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
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1 answer
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Did physics resulted in invention of maths or vice a versa [closed]

Did physics resulted in invention of maths or Maths resulted in invention of physics ??
πααρτθ Σαρθι's user avatar
2 votes
1 answer
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Why is $T_{\mu\nu}$ the Standard Notation for the Stress-Energy-Momentum Tensor

My question is simple: why do we use $T_{\mu\nu}$ to denote the stress energy momentum tensor, and when was the concept of the stress energy tensor first (or roughly the first) introduced (and by whom)...
spicy_potatoes's user avatar
2 votes
1 answer
267 views

The abstraction of mathematics from physics

When and how did mathematics come to be abstracted away from the physical world? At first, mathematics would originate in its simplest form of counting and addition as to keep track of certain ...
Joseph_Kopp's user avatar
1 vote
2 answers
147 views

What was the first physical theory to be mathematically expressed?

Newton's theory of gravitation is expressed as a mathematical relationship between distances and masses. It can be deduced from Kepler's equations (which are also mathematical). Are there even older ...
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1 vote
1 answer
148 views

Physical theories and Mathematics [closed]

I study pure mathematics. In pure mathematics, we begin from some axioms and obtain theorems. I am also interested in studying physics. I have some questions about the relationship between physical ...
S Ali Mousavi's user avatar
1 vote
0 answers
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Complex potential in E227?

I have a reason to believe that Euler introduced the complex potential in his Continuation des recherches sur la theorie du mouvement does fluides, published in 1757. However, I am having hard time ...
timur's user avatar
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2 votes
1 answer
139 views

Who first proposed the idea of "resolution of the identity"?

Who first proposed the idea of "resolution of the identity" as used in the functional calculus of self-adjoint operators? Was it von Neumann? In Japanese, it translates as "resolution ...
enjin2000's user avatar
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Who established the current standard demonstration of Euler-Lagrange equation in calculus of variations?

Who established the current standard(*) demonstration of Euler-Lagrange equations in calculus of variations, that is, $\displaystyle\frac{\partial f}{\partial y}-\frac{d}{dx}\frac{\partial f}{\partial ...
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Who first used complex analysis to account for singularities in field theory?

In 1925, Frenkel wrote a paper titled Zur Elektrodynamik punktförmiger Elektronen, which used complex analysis to treat an electron as a point, and its corresponding potential function as an isolated ...
Larry Harson's user avatar
32 votes
11 answers
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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
3 votes
3 answers
339 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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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
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1 answer
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Were Kepler's Laws of Planetary Motion the first formal definition of an ellipse?

It seems to me that Kepler's Laws necessitate some definition of an ellipse in terms of a coordinate system. I am wondering whether Kepler's Laws mathematically defined what an ellipse is, or if he ...
Clark Merala'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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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
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9 votes
1 answer
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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
2 votes
0 answers
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Background on the Stone-von Neumann theorem

I'm a mathematician. I'm required to give a lecture on the Stone-von Neumann theorem. I already have all the mathematical details figured out, but I wish to make the lecture more interesting by giving ...
Khal's user avatar
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How did we arrive at the rule of addition of vectors?

I wanted to ask about how they arrived to the rule of addition of vectors. How did they know that if we add the X's and Y's of two vectors they would get a third vector which has exactly the same ...
Manar's user avatar
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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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Finding sources for "computers will become so powerful that special functions will become obsolete" as a zeitgeist

In Why are special functions special [Physics Today 54, 11 (2007); eprint], Michael Berry makes the following observations: This continuing and indeed increasing reliance on special functions is a ...
Emilio Pisanty's user avatar
5 votes
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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
9 votes
1 answer
353 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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1 answer
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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
2 votes
0 answers
79 views

Who originally worked out the magnetic field produced by a solenoid and toroid?

Although, it seems very easy to find the magnetic field produced by a solenoid or a toroid, all we got to do is to make a suitable an Amperian Loop and take the $\mathbf B$ out of the integral and so ...
Knight wants Loong back's user avatar
6 votes
1 answer
376 views

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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10 votes
1 answer
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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
5 votes
2 answers
511 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
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
2 votes
0 answers
265 views

Where did Euler derive the wave equation in 3d?

Wikipedia claims that Euler was the first do derive the wave equation in 3d. In which of his writings can I find this?
Michael Bächtold's user avatar
8 votes
1 answer
1k views

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
3 votes
1 answer
478 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
5 votes
1 answer
676 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
208 views

What are the great works of Richard Phillips Feynman? [closed]

What are the prerequisites to read his book? Why Richard Phillips Feynman is so famous? What are great works of Richard Phillips Feynman?
Aakash Thoriya's user avatar
13 votes
2 answers
6k views

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
1 vote
0 answers
31 views

Introduction of shape parameters in the formulation of probability distribution

I'm familiar with the definition of location, scale, and shape parameters, and the type of distributions they parametrized. I'm interested in understanding how shape parameters became part of the ...
MMphysics's user avatar
3 votes
1 answer
274 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
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3 votes
1 answer
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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
2 votes
1 answer
763 views

Origin of the Heaviside function?

I have tried to find the actual origin of the Heaviside unit step function and could not. I've searched and searched, read one complete biography of Oliver Heaviside, skimmed another, but nowhere can ...
147pm's user avatar
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14 votes
1 answer
1k views

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
  • 5,597
0 votes
2 answers
282 views

Who used the symbol $S_n$ for "rotation reflection" as a symmetry operation?

I am looking for the origin of the symbol $S_n$ used by chemists to denote the symmetry operation consisting of a $\smash{\frac{2\pi}n}$ rotation ($C_n$) about an axis and a reflection in a plane ...
AChem's user avatar
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1 vote
1 answer
362 views

Who first solved the two-body problem in 3D?

Who first solved the two-body problem in 3-dimensions? Was it Laplace?
Geremia's user avatar
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1 vote
0 answers
105 views

Reference for Math-Physics history book

I am looking for a book on the history of mathematics that would also serve as a book on the history of physics. In the sense that the history of math is developed along with the developments in ...
user147168's user avatar
5 votes
3 answers
345 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
1 vote
1 answer
213 views

Why did Noether's theorem take so long to show up?

Obviously like they say hindsight is 20/20, but it seems to me that all the ingredients for Noether's theorem were in place more than a hundred years before its publication, and to be honest it is not ...
Javier's user avatar
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1 answer
185 views

Why was Courant's "Methods of Mathematical Physics" suppressed, by the Germans, during WW2?

In the preface to Methods of Mathematical Physics Richard Courant, the author, wrote that the book was suppressed by the National Socialist rulers(Nazi) of Germany. Hence, my question. Thanks.
user avatar
3 votes
1 answer
282 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