Questions tagged [mathematical-physics]

For questions regarding the mathematical aspects of physics.

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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 ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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3 answers
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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2 votes
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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 ...
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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 ...
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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 $\xi^+$ ...
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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 ...
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5 votes
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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 ...
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9 votes
1 answer
279 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 ...
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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 ...
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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 ...
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6 votes
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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 ...
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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 ...
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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 (...
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1 answer
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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 ...
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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?
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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 ...
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5 votes
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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 ...
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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?
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13 votes
2 answers
4k 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 ...
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1 vote
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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 ...
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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 ...
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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 ...
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2 votes
1 answer
471 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 ...
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13 votes
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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 $...
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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 ...
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1 vote
1 answer
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Who first solved the two-body problem in 3D?

Who first solved the two-body problem in 3-dimensions? Was it Laplace?
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1 vote
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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 ...
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5 votes
3 answers
265 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 ...
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1 answer
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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 ...
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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.
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3 votes
1 answer
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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?
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2 votes
1 answer
162 views

Did Euler or did D'Alembert incorporate initial conditions into the solution to the 1D wave equation?

My question is: Who is responsible for incorporating the initial conditions into the one dimensional wave equation solution? References or technical information would be appreciated, especially ...
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1 answer
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Which were the first PhD thesis in Mathematics and Physics?

Were there PhD thesis in the time of Galileo and Newton? Did Newton and Galileo make a PhD thesis? Due to the poor level of science (before calculus and so on), were PhD thesis made in math and ...
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0 votes
0 answers
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Why is the angular momentum written as JJ in quantum mechanics?

Why is $\textbf{J}$ called angular momentum operator? Can anyone explain why the expectation value of J is angular momentum? Here is how $J$ is defined: The rotation operator $$ U(\alpha)=\exp(-i {\...
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5 votes
1 answer
326 views

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 ...
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History of PDE's in the 19th Century (part 2)

This is a follow up to this question: History of PDE's in the 19th Century The question I have been given to answer is: The history of partial differential equations in the 19th Century belongs ...
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3 votes
3 answers
636 views

Math development and under-appreciation of Maxwell's Equations

Freeman Dyson expresses the opinion in his 1972 essay titled "Missed Opportunities" that Maxwell's equations could have played a much bigger role, one that is comparable to classical ...
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8 votes
3 answers
728 views

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 $i \hbar \frac{{\rm d}}{{\rm d}x}$? ...
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