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22 views

Who superseded Peano's dot notation in symbolic logic and when?

Bertrand Russel gave an exhaustive treatment of creating mathematics from logic in Principia Mathematica (1910-1913), using the logical notation created by Frege and Peano. As monumental as this is, I ...
2
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0answers
19 views

When was the concept of probability density explicitly appear in mathematics?

I was reading the wikipedia article about the normal distribution and it's attribution by some historians of science to De Moivre(althought he lacked the concept of the probability density function) ...
3
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1answer
40 views

What are the sources for Democritus’ experiment of dividing a shell down to its atoms?

It is common to find accounts of Democritus explaining his thought experiment to demonstrate the existence of atoms by taking a piece of rock/shell/cheese, and breaking it in smaller and smaller bits ...
4
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0answers
42 views

How did Eratosthenes know the distance between Aswan and Alexandria?

In his well-known measurement of the Earth, and according to Cleomedes, Eratosthenes estimated in 5000 stades the distance between Aswan and Alexandria. Modern accounts state that he calculated the ...
5
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1answer
137 views

Why were equivalence classes named classes rather than sets?

If $R\subseteq A\times A$ is an equivalence relation (i.e., a relation that is reflexive on $A$, symmetric, and transitive), then for each element $x\in A$, the subset $[x]_R=\{y\in A: \langle x,y\...
7
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0answers
55 views

Apéry’s mysterious recurrence relation

A fairly detailed (14 page) account of Apéry’s original proof of the irrationality of $\zeta(3)$ is given in Julian Havil’s book The Irrationals which states that Apéry’s starting point is the ...
1
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1answer
37 views

which country launched N-95 mask for the first time?

I did every search about N-95 mask but couldn't find any clue about it's main country who launched it. Can anyone let me know which country really launched it ?
2
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0answers
76 views

Did Heisenberg ever accept Schrödinger's formulation of quantum mechanics or at least, did he relax his negative views about it?

Both Heisenberg and Schrödinger found each other's way of formulating Quantum Mechanics quite repellent. My question is: Did any of the two changed their views towards each other (specially ...
2
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1answer
85 views

History of exponential notation for the set of functions between two sets

It's well-known that if $A$ and $B$ are two sets, then the set of all functions from $A$ to $B$ can be denoted by $B^A$: explanations of this particular notation can be found in many places: https://...
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0answers
49 views

Why is a linear equation in 3 variables called 'linear'? [duplicate]

I have read that an equation of form 0=Ax+By+C is called linear because its graph is a straight line. But why is the equation 0=Ax+By+Cz+D also called linear even though its graph is a straight plane?...
2
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1answer
80 views

Portrait of Stephen Butterworth

Does anybody know of a portrait of Stephen Butterworth (1885 - 1958), a British physicist?
8
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1answer
809 views

How many important logicians did NOT receive doctoral degrees?

I can think of three. Saul Kripke quite famously could only be begrudged to finish his undergraduate degree at Harvard before being hired as a full professor. Donald Martin (the set theorist of Martin'...
4
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1answer
95 views

For many years, were Emmy Noether and Helene Braun the only female mathematicians to obtain habilitation at Göttingen University?

Emmy Noether was the first woman in Germany to obtain habilitation in 1919. But I remember to have heard in the debate concerning the situation of women in academic mathematics that took place on the ...
4
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0answers
61 views

Books on elliptic functions

In the end of his address to the Mathematical Association in 1933 titled "The marquis and the land agent: a tale of the 18th century", G. N. Watson says: My final task is to express my gratitude to ...
3
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1answer
87 views

Etymology of certain terms in the theory of elliptic integrals

In the theory of elliptic integrals, one encounters the terms "amplitude" and "modular angle" in relation to incomplete integrals of the first kind, which are two variables that denote the upper limit ...
5
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1answer
277 views

Did Ptolemy and other Greek scientists actually measure the distance to the Sun?

According to Subhash C. Kak: Early Theories on the Distance to the Sun: “Pancavimsa Brahmana states that the heavens are 1000 earth diameters, de, away from the earth. The sun was also taken to be ...
2
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0answers
59 views

Historical accounts of a oft-cited quip by astronomer Walter Baade

I am looking for any documented, historical reference to an oft-cited humorous reply by German astronomer Walter Baade (1893 – 1960). After having asked if other astronomers were familliar with the ...
5
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0answers
54 views

Why do Thai numerals look so different than Arabic numerals?

The Arabic numerals I am referring to are “1234567890”. I have read that Thai numerals, “๑๒๓๔๕๖๗๘๙๐”, are actually distantly related. Both descend from the numeral system invented by the Phoenicians, ...
2
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0answers
49 views

How much ground was prepared for Riemann so that he could conjecture Riemann hypothesis?

Although I do not doubt in Riemann˙s originality, I would like to know how much complex analysis was developed up to the day when Riemann conjectured what is today called Riemann hypothesis and how ...
3
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1answer
80 views

Question about Hermite's 1858 solution to the quintic equation using elliptic modular functions and it's relation to Gauss' and Jacobi's work

The general quintic equation cannot be solved by radicals and is shown in a landmark and far reaching work of Galois from 1832, which became a template of modern Group theory and Galois theory. ...
2
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0answers
24 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 ...
-1
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0answers
38 views

Where did the bracket notation for vectors come from and is using parentheses to represent vectors valid?

In class I learned that a vector can be represented using <>, a column vector, and unit vector notation. However, one of the old math books that I study from notes that a vector in unit vector form ...
1
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1answer
111 views

What is a spacetime continuum?

A very common expression I see in pop science is "the spacetime continuum". This expression isn't commonly used in modern discussions of general relativity, but looking at some older papers on the ...
6
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1answer
225 views

What is the first reference to a nondeterministic Turing machine?

I am looking for the first reference of a Nondeterministic Turing machine. There is no mention of them in the 1936 paper "On Computable Numbers."
4
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0answers
74 views

Why did Jordan introduce his canonical form?

Camille Jordan's famous canonical form for matrices over algebraically closed fields, is considered an important result nowadays, commonly taught to all students of mathematics in undergraduate linear ...
6
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0answers
85 views

When did computer pioneers realize that some problems were intrinsically hard?

In my theory computation class, I was told that early computer pioneers didn't realize that some problems were intrinsically hard---what we now call NP Hard problems. Instead, it took a while to ...
5
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1answer
118 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 ...
1
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1answer
42 views

Lawrence and Segre: Further information about relationship

There is a oft-repeated story (https://en.wikipedia.org/wiki/Emilio_Segr%C3%A8) about Lawrence, upon discovering that Segre was legally trapped in the USA, unable to return to Italy due to fascist ...
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0answers
62 views

Conjectures mentioned (and proposed) at International Congresses of Mathematics

I guess that every International Congress of Mathematics (Mathematicians) brings up some unresolved issues of various types but that also that at least some (if not all) ICM´s present some new ...
5
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1answer
174 views

Quotation about $\pi$ and the number of deaths

I read more than once a story which took place, if memory serves me well, in England, in the XIXth century. A statistician (or a mathematician) was making computations about life expectancy (or ...
1
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0answers
82 views

How did Cramer's work on permutations influence early pre-group theory (particularly the work of Lagrange and Vandermonde)?

In his Réflexions paper, Lagrange is using one of Cramer's results on the Elimination Theory for the proof of a theorem. It seems that Cramer did some early work on the permutations of variables in ...
3
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1answer
91 views

When was the problem of factoring integers explicitly considered, what was the oldest factoring algorithm?

I know Gauss made it clear that he wanted an efficient solution to the problem in 1801. In his Disquisitiones Arithmeticae he calls all factoring algorithms "laborious and prolix", surely a 19th-...
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116 views

Was it common for Lagrange to make his theorems so general to the point of ambiguousness?

In Harold Edward's book on the history of Galois Theory, there is the following theorem of Lagrange: From the previous theorems of Lagrange on pre-group theory presented in this book, this one seems ...
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2answers
186 views

Does the word “God” appear regularly in the works of Joseph Lagrange?

In the Religious opinions section of the Wikipedia article on Laplace, there is an excerpt from Antommarchi's "The Last Moments of Napoleon", in which it is written that the name of God appeared ...
3
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1answer
142 views

What is the etymology of “phase space” of a dynamical system?

The state space of a dynamical system is often called a "phase space". What is the etymology of this? (Note that I'm not asking about the history of the concept, but rather about the history of the ...
-1
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1answer
155 views

Was Tesla the only scientist whose possessions were confiscated by secret services?

Tesla, especially later in his life was constantly monitored by the FBI. When he died all his notes and other belongings were taken and for a very long time nothing was returned to his family. Has ...
2
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1answer
84 views

Did Weizsäcker's change his mind about time being a fundamental object?

I have some questions about von Weizsäcker's views in physics, which I find them generally interesting. One of them is that he thought that time was fundamental (he even thought that logic, which is ...
4
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1answer
112 views

Why do some people represent vectors with overbars while others use underlines?

When I was originally introduced to vectors, I was told to write them with an arrow above the variable, like so: $$\vec{x}$$ As soon as I began taking vector-heavy classes, I found that those ...
2
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1answer
109 views

When is the first use of Newton's method for root finding?

I saw this from Wikipedia. The name "Newton's method" is derived from Isaac Newton's description of a special case of the method in De analysi per aequationes numero terminorum infinitas (written in ...
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0answers
84 views

What do people really mean when they say how many prime factors a positive integer has? [closed]

I think that technically, one positive integer is a prime factor of another positive integer if it is prime and it is a factor of the other positive integer. The answer to the question of how many ...
1
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0answers
38 views

Where did the Delannoy numbers make their first appearance?

I am writing a short exposition on the central Delannoy numbers and would like to find the year which Henri Delannoy first introduced them in a formal setting. I believe Delannoy's initial ...
6
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2answers
135 views

Origin of $\ll$ notation

Vinogradov introduced the notation $$f(x) \ll g(x)$$ to denote that for some $C>0$, we have $|f(x)|\leqslant C\,g(x)$ for all $x$ under consideration; usually for all $x$ larger than a fixed ...
1
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2answers
224 views

Can you provide pages 7, 8, 25 of the 1969 edition of the Art of Computer Programming?

A paper published in 1975 references The Art of Computer Programming (then published in 1969), so it's probably the first edition. I can't even find this edition for sale anywhere. Would you be so ...
0
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2answers
106 views

Why is one meter as long as it is?

The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second Why is this so? Who decided that 1/299,792,458 of a ...
1
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1answer
67 views

How did Weibull derive the three parameter Weibull distribution?

How did Weibull or any other mathematician arrive at the above expression? I saw the 1951 paper, but it is not clear to me. In 1939 he had published a book called "A Statistical Theory of the Strength ...
2
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1answer
54 views

When was the Laguerre's method first used to approximate roots?

Is there a specific date when Laguerre published his root finding method? I found his 1880 note Résolution des équations numériques, but I am not sure if this is the source because I can not read ...
1
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2answers
229 views

The history of the equation $\boldsymbol {Et}-\boldsymbol {tE}=\frac{h}{2\pi i}$

Heisenberg already in 1927 quotes this equation as a "known equation".1 Then what is the origin of it? And what is its further history of it, ending in its death? 1 Über den anschaulichen Inhalt der ...
1
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3answers
102 views

What made Newton realize that the law of gravitation was 'universal'? [duplicate]

Newton's law of gravitation operative near the earth is the same law causes the earth and the other planets to go around the sun and other heavenly phenomena. Was it a giant leap of faith by Newton or ...
0
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0answers
30 views

Did pre-Galilean astronomy inspire Mach's principle?

Was Mach, in his formulation of "Mach's principle," influenced by pre-Galilean astronomy, such as that of Aristotle in On the Heavens, where heavenly bodies influence terrestrial ones?
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28 views

Did scientists at some point believe that *everything* is made out of atoms? [duplicate]

Did scientists at some point believe that everything is made out of atoms? Or were atoms always accompanied by other "elementary particles"? I myself did not realize that there existed other "...

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