# All Questions

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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 ...
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 ...
1 vote
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 ...
• 719
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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1 vote
60 views

### 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 ...
• 111
1 vote
49 views

### 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 ...
• 111
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 ...
1 vote
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. ...
• 335
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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### 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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### 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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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 ...
• 2,256
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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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 ...
• 632
1 vote
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 ...
• 247
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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### 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 ...
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 ...
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
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 ...
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 ...
• 545
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 ...
1 vote
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 ...
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? ...
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
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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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, ...
• 155
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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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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1 vote
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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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 ...
• 689
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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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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1 vote
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### 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 ...
• 834
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 ...
• 111
1 vote
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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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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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
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 ...
• 1,942
1 vote
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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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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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
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 ...
1 vote
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 ...
1 vote
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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### 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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