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Origin of Perron-Frobenius Operator

The Frobenius Perron Operator $P: L^1 \to L^1$ is defined by the integral equation $$ \int_A Pf(x) \mu(dx) = \int_{S^{-1}(A)} f(x) \mu(dx)$$ for some $\mu$-non singular map $S$. I found it in the book ...
Adam's user avatar
  • 377
12 votes
3 answers
3k views

Who first distinguished planets from the stars?

This is a pretty straightforward question, when the first observations of the night sky were being made, who was the first person to suggest that a planet, say Mars, was not a star, in the sense that ...
L.R.'s user avatar
  • 261
7 votes
1 answer
768 views

Why were hot-air balloons invented so late?

The first (documented) hot-air balloon was made in the late 18th century. The materials necessary (wood to burn, sheets for balloon) were around for thousands of years. Why didn't anyone think of ...
weeeeeeeeeeeeeeeeeeeee's user avatar
6 votes
4 answers
657 views

First use of zero as a number

The first know use of $0$ as it's own number was in India, but what was the equation in which it was used? Also, what was the tablet/scroll/whatever about?
tox123's user avatar
  • 1,094
21 votes
3 answers
14k views

Who first measured the distance to the Moon? How was it done?

Who first measured the distance to the Moon? How was it done? I think it had to happen after Newton, but I am not sure.
Milkman's user avatar
  • 321
2 votes
0 answers
93 views

Motivation behind Euler Theorem in differential geometry [duplicate]

I am teaching a class on elementary differential geometry and I would like to know, for myself and for my students, something more about the history of Euler Theorem and Euler equation: the curvature ...
Giuseppe's user avatar
  • 183
6 votes
0 answers
42 views

Motivation behind Euler Theorem in differential geometry [duplicate]

I am teaching a class on elementary differential geometry and I would like to know, for myself and for my students, something more about the history of Euler Theorem and Euler equation: the curvature ...
Giuseppe's user avatar
  • 183
7 votes
0 answers
148 views

Who first discussed the Lorentz force with respect to special relativity?

The fact that a Lorentz force in a reference frame 1 can become a Coulomb force in another reference frame 2 has always astonished me, especially because the velocities involved are really small. I ...
Gerard's user avatar
  • 171
10 votes
2 answers
1k views

Was Euler's theorem in differential geometry motivated by matrices and eigenvalues?

I am teaching a class on elementary differential geometry and I would like to know, for myself and for my students, something more about the history of Euler Theorem and Euler equation: the curvature ...
Giuseppe's user avatar
  • 183
2 votes
1 answer
151 views

Invention of modular inverse

A question arose in my mind about modular inverse. We know that there is no division operator in modular arithmetic, so we figure out the modular inverse of the denominator. For example, if we want to ...
Shahed al mamun's user avatar
4 votes
3 answers
228 views

When in the history of physics did 'laws of nature' become the primary form of explanation?

Aristotle's natural philosophy was an inquiry into the causal principles of nature. He famously proposed the notions of formal, material, efficient and final causes. At the dawn of modernity, figures ...
kristof2014's user avatar
5 votes
1 answer
305 views

How did the notion of "time" come in the world of physics?

I was trying to figure out how people came to know about time then I realized that people started keeping track of time to know about sunset and sunrise. But I can't figure out how did time came into ...
Soham's user avatar
  • 175
17 votes
1 answer
3k views

How did Babylonians figure out that the evening star is the morning star?

Hesperus (Roman Vesper) is the name ancient Greeks gave to the evening star that appears in the sky for an hour after the Sun sets. Phosphorus (Roman Lucifer, sic!), was the name of the morning star ...
Conifold's user avatar
  • 74.9k
14 votes
3 answers
1k views

3 Poles and 3 Texans who had read "Principia Mathematica"

To quote Bertrand Russell, "My Philosophical Development", Simon and Schuster, N.Y., 1959, p. 86: I used to know of only six people who had read the later parts of the book [Principia Mathematica]...
Pasha Zusmanovich's user avatar
7 votes
1 answer
384 views

When was the term 'elementary function' first coined and who did it?

The definition of what an elementary function is is quite arbitrary (see what math.SE has to say about it) and it makes me wonder why hasn't the mathematical community added other rather natural ...
hjhjhj57's user avatar
  • 1,142
16 votes
3 answers
1k views

Why did mathematicians not see that $f_n(x)=x^n$ is a counterexample to Cauchy's "theorem" about limits of continuous functions?

In 1821 Cauchy claimed that the limit of a sequence of continuous functions is continuous. In 1826 Abel gave a complicated trigonometric counterexample. When we teach analysis courses, we usually give ...
Helmer.Aslaksen's user avatar
14 votes
1 answer
2k views

When was the vector notation in physics and other sciences first introduced?

The vector notation in physics is a very compact and easy way to write things down, and according to Feynman it also saves print. When exactly did scientists realize that they were summarizing things ...
Gonenc's user avatar
  • 775
38 votes
6 answers
4k views

What is so mysterious about Archimedes' approximation of $\sqrt 3$?

In his famous estimation of $\pi$ by inscribed and circumscribed polygons, Archimedes uses several rational approximations of irrational values; a typical example is that he states, without ...
Mark Dominus's user avatar
9 votes
1 answer
2k views

When and by whom was the term 'momentum' introduced?

We know that up to 1726, when the third edition of the Principia was published, the name for $m\vec v$ was: quantitas motus. Do you know who substituted that with another Latin word: 'momentum'?
user avatar
5 votes
1 answer
2k views

When/How were the product and chain rules first proved?

Pretty much every proof of the product or chain rules presented today revolve around the definition of the derivative as a limit (e.g. this post). However, when Newton/Leibniz were developing ...
chipbuster's user avatar
12 votes
2 answers
6k views

How did Stephen Hawking conduct research?

Stephen Hawking was highly prolific. Compared to a regular person, how quickly could he communicate language to the people assisting him with his research? (e.g. compared to the human average of 40 or ...
Josh's user avatar
  • 223
10 votes
3 answers
2k views

Why should February have 28 days?

According to the Gregorian calendar the second month i.e. February have 28 days and in a leap year 29 days. I am not sure what calculations(science) it takes to decide the total number of days in ...
Amit Tyagi's user avatar
  • 1,478
3 votes
2 answers
593 views

Two competing definitions at the birth of the unit "meter"

It might be famous that $\pi^2$ is a good approximation to the gravitational acceleration in the unit "meter per second squared". My explanation for this is the seconds pendulum, which was proposed ...
Hao Chen's user avatar
  • 355
12 votes
1 answer
615 views

How certain is it that Lucas invented the Towers of Hanoi puzzle?

Wikipedia is unequivocal: The puzzle was invented by the French mathematician Édouard Lucas in 1883. I have no reason to doubt this, but given the many legends surrounding the topic, I wonder if ...
Joseph O'Rourke's user avatar
18 votes
4 answers
3k views

Did the pioneers of nuclear physics and radioactivity eventually get sick from their experiments?

We read about nuclear physics and radioactivity in books and we know how to keep safe from their harmful effects, but the physicists who first discovered them didn't have that luxury. Did the pioneers ...
Craig Feinstein's user avatar
9 votes
1 answer
340 views

When was string theory first heralded as a theory of everything?

Today, string theory is considered one of the leading candidates - perhaps the leading candidate - for a theory of everything. I'm guessing it wasn't always that way, but I haven't figured out just ...
HDE 226868's user avatar
  • 8,413
4 votes
1 answer
405 views

Peano's Axioms: their real origin

It is well-known that Guiseppe Peano formalized the axioms that, to some extent, motivated mathematical induction. These are known as Peano's axioms. However, these axioms are often called trivial as ...
Ahaan S. Rungta's user avatar
12 votes
3 answers
527 views

Are Leibnizian infinitesimals thought to be logical fictions by Leibniz scholars?

Japanese scholar Hide Ishiguro published a book in 1990 entitled "Leibniz's philosophy of logic and language" (second edition). Of particular interest, as far as the history of mathematics ...
Mikhail Katz's user avatar
  • 5,476
11 votes
1 answer
1k views

Who came up with the "proof" that all triangles are isosceles?

"All triangles are isosceles" is a famous geometric fallacy (see below). Unlike many other fallacies its flaw is subtle and hard to spot, so it is often used as a cautionary example against ...
Conifold's user avatar
  • 74.9k
4 votes
1 answer
171 views

About Archimedes methods in the discovered palimpsest

I think Archimedes had some great non-infinitesimal methods for discovering the area and volume of shapes. Some very visual methods involving his method of exhaustion for the volume of a sphere for ...
201044's user avatar
  • 385
12 votes
1 answer
1k views

Are there any theorems that become "lost" and discarded over time?

I read that Descartes and some other mathematician figured out a 'double tangent' method (as I think it was called) for calculating a derivative of a conic or some curve without using the concepts of ...
201044's user avatar
  • 385
21 votes
1 answer
8k views

Why did angular momentum get the letter L

Note - this question was inspired by this questions on physics.SE. Many (most) physical quantities are denoted with a single letter - latin or greek. For many, the letter chosen makes sense: $t$ for ...
Floris's user avatar
  • 758
17 votes
1 answer
1k views

Who discovered smooth non-analytic functions of a real variable?

Some functions of a real variable are infinitely smooth (have derivatives of all orders) but are not analytic (at some points $a$, the Taylor series at $a$ does not represent the function at any ...
user avatar
8 votes
3 answers
2k views

Was the convolution product invented or discovered?

In analysis textbooks and classes I sometimes see the convolution product introduced as a sort of artificial tool - just a clever method for constructing functions that somebody smart came up with at ...
Jack M's user avatar
  • 3,119
1 vote
1 answer
189 views

How did scientists know how to build spacecraft before we got them into space?

Surely the scientists working on (un)manned spaceflight understood the concept of the earth having an upper level to its atmosphere, but how were they able to determine what exactly the physics of ...
galois's user avatar
  • 724
3 votes
1 answer
294 views

Reference needed about history of classical mechanics

Who discovered/ defined momentum and impulse? Please, I want suggestions about materials/ books on the development of Classical mechanics? Something like a history of experiments.
Eng_Boody's user avatar
  • 161
9 votes
3 answers
565 views

Are there any canonical books on history of science?

I was looking for some fundamental books on history of science. I picked Thomas Kuhn book "The Structure of Scientific Revolutions" but it's not exactly about history of science - it's more on ...
Sergey's user avatar
  • 199
13 votes
2 answers
4k views

When was the cogwheel gear invented?

Can someone tell me what year was the cogwheel gear invented? I tried searching it up but the answers were too complicated.
user573's user avatar
  • 131
19 votes
2 answers
1k views

Who invented the way we write exponentiation?

Why do we write $a^n$ instead of $^n\!a$ for exponentiation? What benefit is there to writing the base before the exponent? With addition and multiplication order doesn't matter since $a + b = b + a$, ...
Frank Vel's user avatar
  • 301
4 votes
2 answers
522 views

Historical Instances of Set Theory

Context: I've been reading a lot about Set Theory lately, and how it suddenly sprung onto the mathematical scene in the late 1800's, thanks largely to Cantor. But it seems strange to me that no one ...
Michael Blakeman's user avatar
10 votes
2 answers
1k views

Why was the Vienna Circle so important?

As far as I know the Vienna Circle was very relevant to science in the twentieth century. Why? What was the importance of the members' philosophy in science? Would science be too different from what ...
hjhjhj57's user avatar
  • 1,142
14 votes
3 answers
1k views

What famous laws were named by their discoverer

A question posed on academia.SE prompts this follow-up question: Is there an example of a famous physical law, constant, equation, theorem etc that was named after its discoverer by the discoverer ...
Floris's user avatar
  • 758
6 votes
2 answers
518 views

How many papers on general relativity did Marcel Grossmann author or co-author?

Marcel Grossmann is perhaps best known for helping Einstein learn the Riemannian geometry necessary to formulate general relativity. He was instrumental in its early development. Wikipedia states: ...
HDE 226868's user avatar
  • 8,413
24 votes
1 answer
1k views

Why were geometers dissatisfied with the parallel postulate?

Euclid himself already treats it with gloves, it has an unusually precise formulation, and is not used in the first 28 propositions of the Elements. Why? Did he doubt it? It's not like Euclid was a ...
Conifold's user avatar
  • 74.9k
21 votes
1 answer
4k views

What cipher(s) did Isaac Newton use?

A number of sources including this one assert that Isaac Newton used encrypted messages to communicate some of his scientific discoveries, and as a way of establishing priority. What cipher(s) did he ...
A E's user avatar
  • 315
5 votes
1 answer
172 views

What's the origin and meaning of the adjective "free" in mathematics?

It's pretty common to call a group, ring or module free when it has a 'basis', but unlike other mathematical definitions whose names can be easily related to the concept they describe (e.g. the ...
hjhjhj57's user avatar
  • 1,142
7 votes
2 answers
497 views

What mathematician or scientist has published the most peer-reviewed articles on chess problems?

This question involves not only those provided by the link, but also those "chess-themed" mathematics and computer science problems which are not included in the link. Who has published the most peer-...
Paul Burchett's user avatar
22 votes
3 answers
16k views

Why were 20th Century German scientists so impressive?

German (and Austrian) scientists of the late 19th - early 20th centuries seem to have been the backbone of most of modern physics - namely quantum theory/mechanics. The following are a few predominant ...
galois's user avatar
  • 724
19 votes
5 answers
2k views

What led to the rise of Göttingen?

this is a counter part to my other question: What led to the fall of Göttingen?. Göttingen was a major university in which many famous physicists and mathematicians lived. It was located in ...
tox123's user avatar
  • 1,094
15 votes
2 answers
483 views

Was there any exact science or mathematics in the Eastern Roman Empire?

I mean in the Byzantine empire, from the transfer of the capital to Constantinople till its conquest by the Turks, spanning about 12 centuries. Unlike the Western Roman Empire, this one was never ...
Alexandre Eremenko's user avatar

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