# All Questions

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### What mathematician is Paul Graham's father?

From Paul Graham (programmer) - Wikipedia: Paul Graham (/ɡræm/; born 1964)[3] is an English computer scientist, essayist, entrepreneur, investor, and author. He is best known for his work on the ...
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### What was the role of Schmidt in derivation of the Gram-Schmidt process?

When reading the section related to Gram-Schmidt process in the book Linear Algebra and Its Applications by Gilbert Strang, I found a foot note that says: If Gram thought of it first, what was left ...
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### Are adjoint operators historically related to integrating factors?

Birkhoff and Rota, in their book Ordinary Differential Equations (4e), claim on p.55 that: The concept of the adjoint of a linear operator, which originated historically in the search for integrating ...
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### How do we explain the lack of activity in the study of Latin mathematics?

A full professor teaching the history of mathematics at Masters level recently told a friend of mine that there was nothing of interest left to explore in the mathematics written in Latin over the ...
76 views

### Who first considered signed area?

Who first suggested that the area enclosed by a closed path and the area enclosed by that same path traversed in reverse could be regarded as equal in magnitude but opposite in sign? Cauchy must have ...
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### solving polynomials the hard way, need help ASAP [closed]

So i have two questions that seems crazy to me, and i need help understanding them. 1) Let P(x) = x^2 + mx +n such that the discriminant of P(x) < 0 (less than zero), show that there exist A(x), B(...
50 views

### History of Pfaff's problem and integrability conditions

I'm curious about Pfaff's problem and all the various mathematicians who have worked on it. From Wikipedia articles I was able to gather the following timeline of events. In the modern language: Pfaff'...
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1 vote
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### A collection of the fragments of Eudemus of Rhodes?

I am looking for a complete collection of fragments of Eudemus of Rhodes. He is considered to be the first historian of science. His fragments have given us a glimpse of how Greek mathematics ...
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1 vote
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### How did the Ancient Greeks conceive of the Platonic solids?

Now we generally think of the Platonic solids as being the regular convex polyhedra. And while the Ancient Greeks were aware of this solids as being particularly special, I don't believe that it is ...
207 views

### Implications of several unpublished "binomial congruences" of Gauss

In article 23 of his first memoir on biquadratic residues, Gauss gave the first example of a binomial-type congruence, which is apparently a quite "deep" result - many authors relate it to ...
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### Negative coefficients in the barycentric calculus

The barycentric calculus of Möbius involves formal sums of expressions of the form $mP$ where $m$ is a real number and $P$ is a point, where $mP$ is to be thought of as $m$ units of mass located at $P$...
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### What is the opinion of famous mathematicians about academic research compared to mathematical competitions and olympiads? [closed]

I wonder what the quotes from mathematicians are about their views on academic research vs. math competitions. I can't find much, but I have found one: Math competitions are to research what spelling ...
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951 views

### Did Caroline Herschel know about the discovery of Neptune?

I was reading about the discovery of Neptune when I realised that Caroline Herschel was still alive at the time. Neptune was discovered in September 1846. Caroline died in January 1848, more than a ...
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### Who first stated the "uncertainty principle" for Fourier transforms?

My question is clearly related to this one, but my interest is not specifically in Heisenberg's result. To quote from Wikipedia. A nonzero function and its Fourier transform cannot both be sharply ...
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### Who are the youngest mathematicians that published an original research article in a peer-reviewed journal?

There is a lot of interesting information about young mathematicians, but I cannot find any information about the youngest mathematician that published an original research article in a peer-reviewed ...
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### What is Cardano trying to say in this passage of his Ars Magna Arithmeticæ?

It is well known that Cardano considered the problem of "dividing 10 into two parts the product of which is 40" in his Ars Magna. This problems leads to the complex solutions $5+ \sqrt{-15}$ ...
210 views

### How did the concept of pH originate and develop?

Background & My research To begin I did some research to find a few articles on the history of pH namely "The Symbol for pH" - William B. Jensen, "One-Hundred Years of pH" - ...
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480 views

### What are some famous named groups of scientists?

Scientists are often associated together and get famous group names. In physics, I know of Via Panisperna boys (Enrico Fermi and co. working in Rome in nuclear physics) Princeton string quartet (...
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### Dirac’s debt to Hamilton

According to Tobias Hurter’s popular exposition Too Big for a Single Mind (narrated in the present tense): Dirac makes use of an elegant mathematical tool developed by the Irish mathematician William ...
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1 vote
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### How did someone discover LCM?

How did someone came up with an idea that if we do prime factorization of two numbers and then multiply all the prime factors but including common ones only once, we will get a number that is the ...
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651 views

### Origin of exact and closed differential expressions

In differential geometry and other fields, an expression involving differentials can be closed or exact. In $\mathbb R^2\setminus\{0\}$ for example, $dr$ is exact whereas $d\theta$ is closed but not ...
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### Need a reference for Euler's velocity initial condition for the wave equation

In DOI: 10.4236/ahs.2020.94019 235 Advances in Historical Studies, p.234 D’Alembert and the Wave Equation: Its Disputes and Controversies, or https://www.scirp.org/pdf/ahs_2020112716312281.pdf p.6 of ...
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1 vote
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### In JJ Thomson's cathode ray experiment I need values for the electric field and magnetic field when net force on the cathode beam = 0

I asked here as well https://chemistry.stackexchange.com/questions/177889/in-jj-thomsons-cathode-ray-experiment-why-is-effects-of-gravity-on-electron-not https://physics.stackexchange.com/questions/...
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164 views

### Seeking Comprehensive References on the History of Scientific Notation

I am on a quest to uncover the rich tapestry of history surrounding scientific notation as a way of expressing numbers. Specifically, I'm interested in scholarly books, peer-reviewed articles, and ...
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### How did Schrödinger do quantum mechanics with wave functions?

On my way to learn about the very beginning of quantum mechanics and its different formulations, starting with Heisenberg infinite matrices and Schrödinger's wave functions, I can really not find till ...
102 views

### Euclid's use of antenaresis and Heath's commentary

In Book 7, Prop. 1. Euclid uses repeated subtraction to prove that two numbers are relatively prime. As explained here the Greek word for repeated subtraction is "antenaresis". There isn't ...
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### How did Emmy Noether become interested in abstract algebra?

Emmy Noether was initially interested in invariant theory. But how did she become interested in abstract algebra? And why did she become particularly interested in ring and ideal theory?
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### First recorded use of oxymel to treat wounds

What is the first recorded use of a mixure of honey and vinegar to treat wounds? Cato the Elder indicates it was used during Roman times, but it's unclear if this was as a tonic or if it was used to ...
114 views

### Is there existing footage of Stanislaw Mazur giving Per Enflo a live goose for solving the approximation problem?

There is a famous incident in the history of mathematics involving the mathematician Per Enflo being awarded a live goose by Stanislaw Mazur for solving problem 153 in the Scottish Book by ...
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### Whence Whitehead's essence?

In the article Quine’s New Foundations of The Stanford Encyclopedia of Philosophy (Summer 2019 Edition), Thomas Forster writes: In [1944] Hailperin gave the first of a number of finite ...
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### Who postulated the first Lagrangian for electrodynamics?

I am trying to find who first translated Maxwell's equations and Lorentz's force into the Lagrangian formalism. It seems a very straightforward thing to do if you know enough of electromagnetism and ...
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### What was the motivation for the choice of the subset symbol?

I gather that the symbols $\subset$ and $\supset$ were introduced by Ernst Schröder in his 1890 Vorlesungen über die Algebra der Logik. This account also appears—attributed to good old Cajori—in an ...
1 vote
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### Was "potency set" used for power set?

Cross posted at Math Overflow For historical reasons, the English term "power set" in set theory is a translation of the German "Potenzmenge", which is still in use in German ...
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### The Langevin twins

When did exactly the Langevin twins occur in relativity? My first idea was to simply look up Langevin's original paper (in 1911), but he never mentions them to be twins : our traveller would need ...
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### What scientists and mathematicians were afraid to publish their findings?

Background I am interested in scientists and mathematicians that were afraid to publish their findings during their lifetime, and to what degree such fears hinder scientific progress. So far, I've ...
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### Did Newton know about non-inertial frames?

When answering a Physics.SE question, I made a claim that Newton realized that $F=ma$ worked in some frames, which are called "inertial frames." Nowadays, we know that there are non-...
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### Did Newton say: "If I have ever made any valuable discoveries, it has been due more to patient attention, than to any other talent"?

I came across the above quote, and found it quite interesting. However, I struggled to find an actual source. Did Newton truly say this?
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### Book on the evolution of Quantum Theory

Can anyone recommend some good book(s) on the Evolution of Quantum Theory, focusing on history, not necessarily on explaining the technical/math part? The books I have read so far, "Quantum: ...
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### Did Einstein really explain Relativity using the hot stove/pretty girl analogy and if so why?

I am pretty sure that Albert Einstein explained special relativity by saying in effect, sitting on a hot stove for a minute can seem like an hour; sit with a pretty girl for an hour and it might seem ...
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### Reference request: What were the problems of accepting zero, negative numbers, and complex numbers? And how were they solved?

I asked this question on MSE and comments suggested I should ask it here I am currently reading Baby Rudin as my second analysis book (after Introduction to Real Analysis by Robert G. Bartle and ...
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### How did Hindu-Arabic Numerals get their shapes?

I’ve noticed a recurring post on social media that presents an image suggesting the shapes of Hindu-Arabic numerals are connected to the angles within their design: This claim seems dubious to me. I ...
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### Reference request: What were the problems of accepting zero, negative numbers, and complex numbers? And how were they solved? [duplicate]

I didn't know that can happen and since I already asked the question here I don't know what to do with this question should I delete it ? I am currently reading Baby Rudin as my second analysis book (...
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### Seeking Source of this Pythagorean Quote "Number is the ruler of forms and ideas, and the cause of gods and demons."

I've encountered the quote "Number is the ruler of forms and ideas, and the cause of gods and demons," which is frequently attributed to Pythagoras. My objective is to ascertain the ...
1 vote
55 views

### What was the last "hole" in the electromagnetic spectrum where amplified, tunable, narrow-band power couldn't be produced artificially?

We had radio amplifiers that could transmit powerful signals and those were pushed to microwaves. We had lasers that were originally natural transitions in solids and gasses but now tunable lasers go ...
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### How did the earliest measurements of lasers bounced off of Apollo 11 retroreflectors deal with the light from the Moon and pick out single photons?

Wikipedia's Lunar Laser Ranging Experiments; History mentions the first lasers ever bounced off the whole Moon were in 1962, and probably both the US and Soviet groups used Q-switched ruby lasers. In ...
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### What laser technology/ies were first used to bounce off of the Apollo 11 retroreflectors to accurately measure distance to the Moon?

Wikipedia's Lunar Laser Ranging Experiments; History mentions the first lasers ever bounced off the whole Moon were in 1962, and probably both the US and Soviet groups used Q-switched ruby lasers. In ...
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### A summary of Major events in Pre-Modern Atomist Philosophy of Chemistry [closed]

When I started learning about Laws related to "constant proportions" and other hypothesis like "all matter is composed of smallest indivisible particles", I didn't notice it was ...
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### Who evaluated the surface of the Torricelli solid/Gabriel's horn

The Torricelli solid/Gabriel's Horn is defined as the rotation-invariant solid delimited by a hyperbola. It appears in De solido hyperbolico acuto where Torricelli proves that it has a finite volume, ...
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### What substances from the body did Boyle try when attempting to produce phosphorus?

According to Wikipedia, Hennig Brand discovered phosphorous. Later, Robert Boyle desired to replicate Brand's discovery, but didn't know that urine was used - only that it involved something that &...
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