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Questions tagged [mathematical-physics]

For questions regarding the mathematical aspects of physics.

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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 ...
1
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0answers
23 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 ...
3
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1answer
123 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 ...
2
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1answer
88 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 ...
2
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1answer
121 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 ...
0
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2answers
198 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 ...
1
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1answer
129 views

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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0answers
83 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 ...
4
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3answers
187 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 ...
0
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1answer
105 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 ...
0
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1answer
120 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.
3
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1answer
121 views

A Peculiar Quote from an Engineer

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?
2
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1answer
137 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 ...
0
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1answer
58 views

existed Ph D thesis programs in the past ? which was the first Ph D thesis in math , physics?

where Ph D thesis at those time of Galileo and Newton ? did newton make a Ph D thesis and Galileo? due to the poor level of science (before calculus and so on ) were Ph D thesis made in math and ...
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0answers
57 views

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 {\...
5
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1answer
187 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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0answers
203 views

History of PDE's in the 19th Century 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 ...
1
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2answers
233 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 mechanics, in ...
2
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2answers
436 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. I was wondering if anyone knows of any useful sources I could use?
3
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2answers
226 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 ...
3
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4answers
134 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? ...
4
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3answers
272 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 ...
6
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2answers
223 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) ...
3
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1answer
80 views

Who wrote down the equations governing gravity in a field language for the first time?

In his paper The search for unity: Notes for a history of quantum field theory [Daedalus 4, 106 (1977)], Steven Weinberg writes: The first successful classical field theory was based on Newton's ...
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39 views

Origin of diagrammatics illustrating the relation between cumulants and moments?

The exponential-log transformation of exponential generating functions (see OEIS A036040 and A127671) relate the classical cumulants to their associated moments. Who were some of the first to ...
5
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1answer
107 views

Who was the first person to describe the 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 ...
6
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1answer
322 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?
7
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1answer
192 views

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 ...
3
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1answer
97 views

when did polynomial coefficient matching start for solving equations?

Coefficient matching feels rather natural when solving equations and checking dimensions, however in footnote 2 to "Two alternative derivations of Bridgman's theorem" (Berberan-Santos M N, Pogliani L, ...
4
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1answer
212 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?
7
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5answers
343 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 ...
0
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1answer
141 views

Who introduced the Green function method into quantum mechanics?

Its power is amazing. For a Hamiltonian, you define the Green function as $$G = \frac{1}{\lambda E-H} .$$ Who first come up with this definition? What was the motivation?
3
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3answers
454 views

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

In this video about the Banach-Tarsky paradox the host stipulates that the history is full of examples of abstract mathematical theories that were later found to be applicable to the physical world. ...
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2answers
812 views

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 ...
6
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3answers
306 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 ...
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2answers
339 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 ...
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1answer
166 views

Is Vedic Science true? [closed]

I somewhere read that ancient Indian science was so advanced even in 2000 B.C. (or may be even before this) that Indian scientist and mathematicians calculated the value of distance between sun and ...
3
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1answer
97 views

Origin of the term “operator spectrum” and its relation to spectrum in physics

I believe i have been looking in the Internet once for the origin of the term "spectrum" in functional analysis and saw that the term was proposed by someone (by Hilbert?) with no relation to physics, ...
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0answers
21 views

History of the delta potential barrier in Quantum Mechanics [closed]

I'm interested in finding something out about the history of the problem of the delta potential barrier in QM. Who was the first to propose this problem, and perhaps any particular motivation for it. ...
4
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2answers
136 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 ...
3
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1answer
219 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 ...
2
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116 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 ...
5
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1answer
349 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 ...
5
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2answers
299 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 ...
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0answers
62 views

Who was the first pointing out the $U(1)$-gauge theories common structure?

It is well-known that in each $U(1)$-gauge theory one can define, in analogy with electromagnetism, a 1-form connection and an associated 2-form of curvature on an appropriate (principal) bundle, ...
6
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1answer
306 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\...
10
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1answer
532 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, ...
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3answers
556 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?
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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. ...