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Exhaustion method blocked by religious aspects?

Eudoxus developed the exhaustion method for calculating areas that continued with Archimedes and then only in the 16th century with Stevin and Cavalieri. Why did it take so long? Was there any ...
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45 views

What is Weierstrass' "simple diagram" in the calculus of variations?

In An essay on the psychology of invention in the mathematical field Hadamard said this about Weierstrass: The two German mathematicians whom Poincaré compares are Weierstrass and Riemann. That, as ...
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60 views

Claims that fully formal proofs are impossible to write down

It is sometimes asserted that human-readable mathematical proofs that we construct and publish are just informal approximations to the gold standard, which is a completely formal proof in a formal ...
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3 votes
0 answers
43 views

In which work was Boltzmann's entropy originally introduced?

I get an impression from this enyclopedia entry that the primary source of the Boltzmann entropy equation $S = k \log W$ might be 1866, Über die Mechanische Bedeutung des Zweiten Hauptsatzes der ...
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Who was G. H. Hardy's Tripos coach?

There is conflicting opinion as to who was Hardy's Tripos coach. The Wikipedia page on Hardy claims it was R. A. Herman, a claim that appears to be backed up by Leonard Roth in his article "Old ...
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Simultaneous independent or semi-independent solutions to problems

This is a request for help (with examples, as described below) with a talk I giving to graduate students regarding the dynamics of mathematical research among mathematicians and the development of key ...
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0 votes
1 answer
68 views

Did thinkers we now regard as mathematicians call themselves philosophers prior to the 19th century?

Recently, a teacher of mine stated that, since the institutional division between philosophy and other fields of academic enquiry, especially the natural sciences, happened somewhere along the 19th ...
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1 vote
2 answers
136 views

Simplest of the many proofs the prime harmonic series diverges

Over the history of mathematics, some key facts have had multiple and different proofs developed for them. Sometimes these different proofs provide a unique insight or understanding of those facts. ...
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2 votes
0 answers
75 views

Computing Gravitational constant G from Cavendish's data

I'm trying to compute the value of G from Cavendish's own observations. I get $G_{Cav}=5.27501×10^{−10}$ which is 8 times bigger than the accepted value of $G_{True}=6.67430×10^{−11}$. Do you see ...
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76 views

Was Nikola Tesla aware of Maxwell's equations?

Was Nikola Tesla aware of Maxwell's equations or Heinrich Hertz's experimental proof of the former when he worked on his radio device invention?
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4 votes
0 answers
87 views

Who first proved that there is no five-digit perfect number?

A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. The first five perfect numbers are 6, 28, 496, 8128, and 33550336. Nicomachus ...
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0 answers
86 views

Seeking quotes rejecting early forms of the Dirac delta

Question Why is Dirac delta named after Dirac when the concept was already over two centuries old? notes the Dirac delta function effectively appeared centuries before Dirac. This was long before the ...
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1 answer
147 views

What exactly did Lagrange do, historically?

I'm tying to understand, historically, what lead to Lagrangian mechanics (LM). What did Lagrange actually do? In the time (year 1788), when Lagrange published his work (that we nowadays call "...
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  • 119
2 votes
2 answers
118 views

How were the values of permeability and permittivity derived?

Do you know how the values were measured and if they where determined by particular conditions/ restraints? They can be put to 1 (or to any values, I suppose); what escapes me is why 1/ε × μ must be ...
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1 vote
0 answers
36 views

What is the earliest use of the $\perp\!\!\!\!\perp$ symbol in statistics to denote statistical independence?

The symbol $\perp\!\!\!\!\perp$ in statistics is a way to denote statistical independence of a collection of random variables. I have seen two forms of it. The first is highly suitable in writing ...
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  • 247
3 votes
1 answer
85 views

Source of a Quote by M. Stone on Poincaré and Bourbaki

The quote in question is the following: For Bourbaki, Poincaré was the devil incarnate. For students of chaos and fractals, Poincaré is of course God on Earth. The common reference for this quote ...
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0 answers
78 views

How did Niels Bohr arrive at the second postulate of his atomic model?

Niels Bohr's second postulate of the Atomic Model states that the electron revolves in specific orbits in which the electron's angular momentum is an integral multiple of $\large\frac{h}{2π}$. Since ...
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46 views

To what extent did d'Alembert want to avoid the newtonian concept of force?

The context of this question: In everyday life we use push and pull all the time to get things moving, to move ourselves. To ride a bicycle: our feet push the pedals to get moving. To accelerate we ...
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58 views

What is the historical significance of Riemann’s discovery of non-flat metrics?

From a perspective of math history, what discoveries resulted directly from Riemann’s discovery and codification of non-flat metrics on Riemannian manifolds? After Albert Einstein modeled the Universe ...
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2 votes
1 answer
142 views

Reference for "A manifold is a topological space which satisfies a long series of axioms."

In On teaching mathematics, Vladimir Igorevich Arnold states "What is a smooth manifold? In a recent American book I read that Poincaré was not acquainted with this (introduced by himself) notion ...
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1 vote
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82 views

Did Felix Bloch really discover Bloch oscillations?

A 1929 paper by Felix Bloch, Über die Quantenmechanik der Elektronen in Kristallgittern, is widely cited as having predicted the phenomenon of Bloch oscillations: The oscillatory motion of an electron ...
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4 votes
1 answer
130 views

Hilbert's problem list did not include Fermat's last theorem. Why?

Fermat's Last Theorem was open for more than 350 years until Andrew Wiles proved it in 1995. Are there possible (historical or other) reasons why David Hilbert did not include this famous open problem ...
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  • 545
2 votes
1 answer
178 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 ...
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1 vote
0 answers
103 views

The original Dirac equation

In the original 1928 paper (pdf) the Dirac equation appears on page 615 in equation (9) as $$ [p_0+\rho_1\left(\boldsymbol{\sigma},\boldsymbol{p}\right)+\rho_3mc]\psi=0\qquad(1) $$ Using the ...
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2 votes
0 answers
83 views

When did we have first calculations of moon phases?

I'm interested in knowing more about the history around lunar tables and calculation of moon phases. When did we have first (reliable) calculations of moon phases and first (reliable) lunar tables? ...
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7 votes
1 answer
427 views

Who was D.A. Millin, the eponym of the Millin Series?

The Millin series is defined as: $$\sum_{n \mathop = 0}^\infty \frac 1 {F_{2^n} }$$ where $F_n$ denotes the $n$th Fibonacci number. It can be shown to equal $\dfrac {7 - \sqrt 5} 2$. But who was the D....
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1 vote
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47 views

What contributions from Glavieux & Thitimajshima were "merged" into Claude Berrou's now-famous 1993 talk "Near Shannon limit error-correcting coding"?

At 01:15:13 in the delightful video The Bit Player | Claude Shannon | Father of Information Theory | IEEE Information Theory Society Andrea Goldsmith recounts ...
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2 votes
0 answers
81 views

Bureau human computing services

Prior to the development of electronic computers, human computers were used and computer departments consisted of a room with humans at desks performing calculations. Large scientific organizations, ...
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14 votes
3 answers
4k views

What does this cover of a 1508 German book on arithmetic depict?

In a 1508 German book on arithmetic for merchants, this image appears on the cover (high resolution and context here): What is this depicting? Who are these people and what are their roles? In ...
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  • 401
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0 answers
66 views

What concept did pre-modern people have about thermodynamic phenomena?

How did people before the advent of modern science in the 17th century conceive thermodynamic phenomena? I want to know how people in Ancient Mesopotamia, Egypt, Greece, Rome, China and in the Middle ...
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  • 149
1 vote
1 answer
109 views

Fermat et l'équation de Pell

Does any of you happen to own and electronic copy of the paper "Fermat et l'équation de Pell" by A. Weil? If I understand correctly, this paper can be found on pages 413-419 of the third ...
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5 votes
3 answers
188 views

First attempt to measure speeds using distance divided by time?

Did the ancient Greeks, for example, speaks of number of paces per heartbeat? I could see them only saying, something moved with the speed of an arrow or a running horse or a running man but that they ...
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2 votes
1 answer
205 views

How did mathematics come to use $\log(x)$ and not $\ln(x)$

Question: How and why did the discipline of mathematics come to use $\log(x)$ and not $\ln(x)$ in its writing - papers, books, teaching? Clearly $\ln(x)$ is unambiguously $\log_e(x)$, but $\log(x)$ is ...
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  • 335
-1 votes
0 answers
39 views

What notation historically has been used for rings with two alternative multiplications?

Suppose one has a ring with two alternative multiplications, like "$\times$" and "$\cdot$". Each one rises a set of analytic functions that can be applied to the elements of the ...
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  • 596
1 vote
1 answer
100 views

What problem was Borel trying to solve?

I may be mistaken but I understood that Borel developed his sigma algebra before Lebesgue developed his measure. If correct, then Borel can't have been trying to find a collection of sets in $\mathbb{...
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  • 141
0 votes
0 answers
57 views

Were 3-dimensional split-complex numbers ever described in literature?

Basically, if you add two complex dimensions to reals, say $i$ and $j$, you automatically get a fourth dimension $ij$ because this number cannot be expressed using only the three dimensions. The ...
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  • 596
3 votes
2 answers
197 views

Marx economics theory

Before Marx, economic theory had two big names: Adam Smith and Ricardo. It is well known that Marx used their work. When at school I was told without much specific that Marx had substantial ...
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0 votes
0 answers
74 views

Origin of Catalan numbers and original intuition of the first interpretation and proofs

I was reading about Catalan numbers and how they provide the number count in a variety of situations. I found it very interesting how the main proof is about the underlying common patterns and ...
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1 vote
1 answer
92 views

The housing of the Cavendish Experiment

[I posted this to History, but it was suggested that History of Science and Mathematics would be a better choice. So I'm posting it here too.] I’m working to build the Cavendish experiment of 1798 ...
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  • 31
2 votes
1 answer
90 views

How has the modelling of classical electrodynamics changed since Maxwell?

Maxwell published his Treatise on Electricity and Magnetism in 1873, 150 years ago; before the discovery of quantized charges, special relativity, quantum field theory etc. How has the mathematical ...
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0 votes
0 answers
74 views

Cantor's later life

I saw this on Wikipedia: In June 1917, he entered a sanatorium for the last time and continually wrote to his wife asking to be allowed to go home. Georg Cantor had a fatal heart attack on January 6, ...
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1 vote
0 answers
61 views

Upon which incorrect equation of Euler did Sophie Germain rely in her work that won a prix extraordinaire from the Paris Academy of Sciences?

Wikipedia's Sophie Germain; Work in elasticity; Subsequent attempts for the Prize says: Germain had derived the correct differential equation (a special case of the Kirchhoff–Love equation),31 but ...
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1 vote
0 answers
89 views

First example of regularization

Background: I like to think of L'Hospital as one of the earliest authors of least-squares regression. L'Hospital, G. (1696). L'analyse des infiniment petits pour l'intelligence des lignes courbes. I'm ...
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9 votes
1 answer
2k views

Context behind Planck's "A new scientific truth does not triumph by convincing its opponents...but rather because its opponents eventually die..."?

The open access paper Lehtola & Karttunen (2022) Free and open source software for computational chemistry education (found in this answer) contains the following paragraph: 2 FREE AND OPEN ...
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2 votes
0 answers
32 views

How was adiabatic expansion seen from the caloric theory perspective?

Nowadays we say that during the adiabatic expansion stage of the Carnot Cycle the internal energy due to the temperature of the gas gets transformed into work, but Carnot himself supported the caloric ...
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1 vote
0 answers
45 views

Can anyone recommend sources on the standardisation of research methods in modern (20th-21st c) science?

I’m interested in learning more about how statistical methodology and research design has changed over the course of the 20th and 21st century. I’m particularly interested in ways in which research ...
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1 vote
0 answers
48 views

Published expository account of Franklin's work on electricity?

Is there a good (or even mediocre) published expository account of Benjamin Franklin's work on electricity? From what I have read and heard, it appears that Franklin may have been the first to ...
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1 vote
0 answers
94 views

partly a LANGUAGE question - uncia (Latin one-twelfth) is the source of both Inch and Ounce. Does anyone know the Greek or pre-Roman equivalent?

Much as per question - Uncia is the Latin for one-twelfth and thence is used for coin (As),length (Pes),weight (Libra), area (Jugerum) etc from whence derives inch and ounce. I can find nothing much ...
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0 votes
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56 views

Formal logic as a synonym to syllogistic logic, or as a name for the study of logic?

On page 443, section 1.1 Expanding to Contradiction, in José Ferreirós' A Road To Modern Logic - An Interpretation, the following is written: Philosophical conceptions of logic have been complex and ...
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0 votes
0 answers
75 views

Did Kary Mullis actually invent PCR as he claimed?

I remember learning that the inventor of polymerase chain reaction (PCR) was Kary Mullis, who was awarded the Nobel prize in chemistry in 1993. I recently learned that there is some controversy about ...
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