# All Questions

2,261 questions
72 views

### Examples of papers co-authored by parent/child, or siblings

I hope this question is not inappropriate for this site; I found hsm.stackexchange better suited for it than MathOverflow or math.stackexchange. The motivation for it is just curiosity. Question: ...
85 views

### Why are there 24 hours in a day?

The question could be answered in a number of ways: Historically (e.g. Egyptians did for <...> reasons) Mathematically (It is a highly composite number) I'm looking for a mathematical answer. I'...
382 views

### Why didn't Lorentz conclude that no object can go faster than light?

Based on Lorentz factor $\gamma = \frac{1}{\sqrt {1-\frac{v^2}{c^2}}}$ it is easy to see $v < c$ since otherwise $\gamma$ would be either undefined or a complex number, which is non-physical. Also, ...
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### Origin of “bootstrapping” in mathematical logic

"Bootstrapping" is a term which in general refers to a self-starting process. It is very heavily used in the field of computer science, but it also has uses elsewhere. For example, in mathematical ...
161 views

### Did the Idea of Universal Gravitation predate Newton?

"Baba wrote over 60 books, almost everyone on a different topic, writing on issues from astronomy, identified stars that European scientists technology could not discover until the late 1800s, ...
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### When did the research field of Astrophysics begin?

I have this vague idea that Astrophysics morphed out of Astronomy as a field of study and research. I am curious if this is true and when did Astrophysics become separate from Astronomy as a field of ...
71 views

### Which book covers topology historically?

Is there a book, which expresses all the questions, or searches for attainment of certain utility/need, or thing, which gave the discovery or invention of all the components of Topology? I need book ...
100 views

### Who developed The Fundamental Theorem of Curves

In any modern differential geometry textbook (Do Carmo, for example), the fundamental theorem of curves can be found. It states that: every regular curve in three-dimensional space, with non-zero ...
87 views

### What experiments led to the sign of the electron's charge?

The famous Millikan's oil drop experiment in 1908 determined the magnitude of charge of the electron to be 1.59*10^(-19) C. However, it was well known that electron has a negative charge. Although ...
69 views

### The “Universal Information Society” of the XIX century?

From the inaugural lecture of J.J. Sylvester at Oxford, December 12, 1885, "On the method of reciprocants as containing an exhaustive theory of the singularities of curves", Collected Mathematical ...
103 views

### Origin of the Heaviside function?

I have tried to find the actual origin of the Heaviside unit step function and could not. I've searched and searched, read one complete biography of Oliver Heaviside, skimmed another, but nowhere can ...
40 views

### Overflow behavior in turn counters of Odhner-style arithmometers

I have a Felix M Arithmometer (shown below) that appears to follow the same design as an Odhner arithmometer. One thing I noticed about the device is that the turn counter (on the left) does not ...
23 views

### How long will it take for humans to find the cure for mortality considering the historical progress of Science? [closed]

The question may be too far fetched but can we draw extrapolations from the supposed conversion of apparent scientific impossibilities such as going to the moon to a reality?
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### What did scientists think was the function of breathing before the discovery of atmospheric gases?

Before we knew about gases in the atmosphere, what did scientists think was the function of breathing?
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### Who first proved that only primes of the form $4k+1$ divide odd integers of the form $n^2+1$?

I am writing a paper and I would like to cite the person(s) who proved that only primes of the form $4k+1$ can evenly divide odd integers of the form $n^2+1$? For example, if $n=8$, $n^2 + 1 = 65$ ...
137 views

### Why didn't John von Neumann win the Turing Award, Fields Medal or Nobel Prize?

From what I've read in Wikipedia, John von Neumann made a stupendous number of contributions to economics, computer science and mathematics. Why, then, didn't he receive a top award in any of these ...
33 views

### Duality while studying properties of an ensemble

Was Einstein the first to propose that observing an ensemble of N particles for time interval of dt is same as observing a single particle of ensemble for time interval of Ndt?
175 views

### How did Maxwell fall short of Einstein?

This source (I believe it's in Ukrainian) claims that Maxwell came very close to creating the relativity theory, however, it was the fact that he was adhering to the traditional scientific frame of ...
126 views

### Where does the word sine'' (as in $\sin x$) come from?

According to wikipedia (https://en.wikipedia.org/wiki/History_of_trigonometry) : the modern word "sine" is derived from the Latin word sinus, which means "bay", "bosom" or "fold" is indirectly, via ...
117 views

### Communication using mathematical notation among people of different languages

Can it be (are there real examples/anecdotes of) that, say during international séminaires or conferences in mathematics, people of different linguistical origins could understand each other with the ...
129 views

### Earliest Known reference to a female scientist?

According to an uncited Wikipedia paragraph, Merit-Ptah is the earliest known female scientist. An ancient Egyptian, Merit-Ptah (c. 2700 BC), described in an inscription as "chief physician", is ...
73 views

### Courant (1943) and History of Finite Element Method

I am interested in the history of Finite Element Methods and Methods of Weighted Residuals (MWR), especially reduced quadrature and collocation methods. I have a paper coming out called “Orthogonal ...
54 views

### Does the story about Thales and the heights of pyramids illustrate that Thales did not know of AAA triangle similarity?

Thales understood similar triangles and right triangles, and what is more, used that knowledge in practical ways. The story is told in DL (loc. cit.) that he measured the height of the pyramids by ...
86 views

### Is it a historical coincidence that relative atomic weights by chemical methods and mass spectrometry are very close?

The concept of relative atomic weight originated from measuring the combining weight of hydrogen with a certain element. In the simplification process H was taken as unity (18th, 19th and 20th century)...
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### Why is electric dipole moment represented by “p”?

"I recently came across a text where the electric dipole moment was represented as "d" instead of the more commonly used "p". The reason behind using "d" here is probably that "dipole moment" begins ...
115 views

### When and how did usage of the term Centigrade give way to Celsius? Are/were they in fact numerically identical?

Discussion below the question Does the US National Weather Service use Celsius or Fahrenheit? and correction of my original use of "Centigrade" to the modern Celsius lead me here. For example, in the ...
115 views

### How did Eratosthenes determine that Alexandria and Syene were on the same meridian?

As discussed over here, Eratosthenes measured the earth’s circumference by comparing shadows cast at apparent noon at two locations separated by a known distance. Although accounts of the event (like ...
45 views

### In the world before thermometers did people use freezing points as a sort of proto-thermometer?

Last night I left a bottle of cleanser in my car, and during the 5-degree night the cleanser turned to a sludge. This started me thinking. Lots of people living before the development of the ...
55 views

### Mathematical analysis vs. Practical genius

Concerning the role of mathematics in technological inventions: which books would you suggest that examine the historical relation between mathematical analysis & practical wisdom? For example, ...
219 views

### What are some of the earliest mentions of scientific “cranks”?

Often professors in math and physics academia have inboxes full of people claiming to have solved deep problems such as dark matter, black holes, prime number conjectures and claim that many big names ...
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### What's the relationship between Aristotle's theory of elements and motion and geometry?

I'm having a hard time gathering my thoughts about this. I'm trying to find a connection or some sort of relation between the first 3 axioms (postulates) of Euclidean geometry (though around Aristotle'...
75 views

### Could someone explain Vives logical notation?

I'm doing a project on the history of George Boole and wanted some background on how notation has changed through the ages, however do not understand Vives logical notation. Wondering if someone could ...
90 views

### Why does the US keep survey miles and feet?

The United States adopted the international mile and foot in 1959, but for some reason they decided to keep alongside the older units as survey mile and survey foot. These units are almost equal to ...
120 views

### What were the smallest numbers encountered in history?

In reference [1], Gelman et al. give an account of one of the first occurrence of Bayesian inference. Laplace used the number of births by gender in Paris from 1745 to 1770 to conclude that the ...
86 views

### Earliest Instances of a Slope/Direction Field for a First-Order ODE

Background When first encountering slope fields in calculus or elementary differential equations, students often ask "What is the purpose?" A concise answer is that slope fields provide a way to ...
67 views

### How on Earth did Ampere come up with Ampere's circuital law?

When I asked for proof of Ampere's circuital law I learned that this law itself is taken as an axiom. Okay I just need to know how did he come up with such a law? how to confirm that result ...
47 views

### Resources for handwritten scientific notes?

I am interested in looking at the notebooks, manuscripts, and letters of scientists and mathematicians from history. It is usually possible to search for a particular person, but tracking images and ...
80 views

### What was the scientific explanation of earthquakes in the 18th century?

I'd like to know what western scientists thought about the causes of earthquakes in the mid to late 18th century (especially pertaining to the one in Lisbon in 1755). I've read that the ancient greeks ...
46 views

### Who discovered fluid visocity?

Who discovered fluid viscosity and what is the history behind the concept of fluid viscosity? Further, who first defined or parametrized viscosity as shown in Equation 1.1-2 below? Equation 1.1-2 (...
74 views

### High voltage / current sources in 19th century cathode ray experiments

In modern chemistry textbooks, a DC source (battery symbol) is usually shown for cathode ray tube experiments by Thomson and others. Certainly, no battery can provide very high voltages needed for gas ...
77 views

### Cauchy's Integral Theorem Motivation

How did Cauchy go about Cauchy's integral theorem? What was his motivation?
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### Where is the first reference to the “Z combinator”, a call-by-value fix-point combinator?

I'd like to know the earliest reference to the Z-combinator. This could be either where the name was first coined, or even the first discussion of a need for an applicative-order Y combinator. I didn'...
86 views

### Is there any relation of the word “normal” with a subgroup being normal?

From Gallian, Contemporary Abstract Algebra: ...if G is a group and H is a subgroup of G, it is not always true that aH = Ha for all a in G. There are certain situations where this does hold, ...
66 views

### Who associated the sharp, principal, diffuse, fundamental spectral terms with electron's momentum?

It is well documented that the notation for the electronic configuration (s,p,d,f) of atoms as used today originates from the words sharp, principal, diffuse, fundamental from alkali metal spectra (...
167 views

### What are some references that Lev Landau was atheist?

In Wikipedia and many other sources copying it, it is claimed that Lev Landau was an atheist (I have no problem to believe the claim), however the (two) sources are not satisfying at all, to me. I ...
88 views

### How did Peano prove his existence theorem without Ascoli's theorem?

In modern proofs of the Peano Existence Theorem for ordinary differential equations, Ascoli's theorem is used. Ascoli's theorem came after Peano's proof. Did Peano prove a form of Ascoli's theorem in ...
79 views

### Did the French ever use the decimal time in science?

Have you ever seen a scientific paper/document that uses the decimal time introduced during the French Revolution? I'm not looking for any paper that uses decimal time like in astronomy, but instead ...
190 views

### Did the author of Alice in Wonderland make any substantial original discoveries in mathematics?

Charles Lutwidge Dodgson, better known by his pen name of Lewis Carroll, was a mathematics lecturer at Oxford University and today is primarily famous for his fanciful stories laced with mathematical ...