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Questions tagged [discoveries]

For questions about the location (in space and time) of scientific discoveries and their historical context.

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Hydrogen electrode and its electrode potential

In electrochemistry, all electrode potentials are quoted with reference to the standard hydrogen electrode. Its value is assigned to be 0 volts. I have been searching for the origin of this convention ...
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119 views

What actually led Feynman to the path integral formulation of quantum mechanics?

It is commonly known that Feynman's path integral was inspired by Dirac's observation that the kernel is proportional to $\exp{i\hbar S}$. It was Feynman, however, who had the idea of expressing the ...
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The minimax theorem from 1928 to 1956

Minimax theorems are beautiful saddle-point results regarding conditions on a function $f$ under which $\max_x \min_y f(x,y) = \min_y \max_x f(x,y)$. In the common "normal form" game case, $x$ and $y$ ...
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Does anyone know articles or books about what the notion of difficulty in science, especially physics?

In physics, many problems were known at their time to be very challenging, for example the notion of heat, or how to understand the ideal gaz law, or the phase transition criticial behaviors, etc. And ...
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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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54 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 (...
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199 views

How did Ruffini discover his method of polynomial division?

How did Ruffini discover his method of polynomial division? At that time was it known that polynomial division works similar to integer division?
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61 views

How did Quetelet discover that the body mass is proportional to the squared height?

The Body Mass Index (BMI) compares body masses on the assumption they scale with height squared, not cubed, an example of allometry. BMI is due to Lambert Quetelet. Why did he settle on this power law?...
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108 views

When were polynomial equations first factored?

The question pretty much says it all, though I have a specific example in mind. In the mid-1500s while working on his Ars Magna Cardano asked Tartaglia to solve the cubic $x^3=9x+10$. Using ...
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554 views

What are natural science concepts that were once thought the same, but grew to be distinguished?

The history of physics is full of examples of phenomena that used to be described independently, until additional insight proved they were the same thing. Some famous instances are motion of bullets ...
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What are some good books that interweave the history of math and art from renaissance onward?

Ever since learning about projective geometry and its birth in the world of art, I’ve been intrigued to learn more about their union and how they influenced each other. I’m specifically looking for ...
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156 views

Who discovered Bremsstrahlung?

I found a web page that says that it was discovered by Tesla in 1890, is that true or generally acknowledged? Isn't 1890 too early a date?
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When and why was inversive geometry created/studied?

I have been revisiting math from my highschool through undergrad. I picked Courant’s excellent What is Mathematics? The flow is well so far. However, in one of the chapters he introduces inversion - ...
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371 views

Did amateurs ever produce important proofs or similar?

Background Mathematics and some areas of physics and computer science have the peculiar appeal that some problems and results are easy to understand and it is conceivable that somebody armed with ...
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1answer
192 views

When was Euler's log-sine integral first computed by real methods?

In Sec. 2.4 of Inside Interesting Integrals (2015), Paul J Nahin says of $$I:=\int_0^{\pi/2}\ln (a\sin x)dx=\int_0^{\pi/2}\ln (a\cos x)dx$$that: For many years it was commonly claimed in textbooks ...
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Who discovered the expansion for factorial as a successive difference of integers?

Who discovered the following theorem $$\sum_{r=0}^{n}\binom{n}{r}(-1)^r(n-r)^n=n!$$
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What are some good metrics for intellectual progress (of all sorts)?

My thinking about this topic is vague, and I'm looking to clarify it. I'm not sure what "intellectual progress" is or if that's even a useful abstraction, but it seems like it should include things ...
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213 views

Foundational crises in non-Western historical mathematical communities

In Foundations of Set Theory by Fraenkel, Bar-Hillel, and Levy (1973), the authors argue that there have been three distinct periods of crisis in the foundations of mathematics. The first was ...
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278 views

When did architects first become aware of the usefulness of the catenary arch?

The Wikipedia-entry for catenaries lists Robert Hooke as the first to study catenaries mathematically, in the 1670s. However, the dome of the Florence Cathedral, completed structurally in 1436, ...
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97 views

What was the significance of Eisenstein's discovery of invariants?

I am trying to decipher a portion of James Joseph Sylvester's 1869 address entitled "The Study That Knows Nothing of Observation", which, among other things, surveys the landscape of 19th century ...
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1answer
198 views

Why is the Brayton cycle also known as the Joule cycle? What was Joule's contribution?

Did James Prescott Joule also design this thermodynamic workcycle, separate from George Brayton? I've not found any reference to Joule's involvement besides that from George Brayton. Could someone ...
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152 views

How come so many laws were not discovered by people they are named after?

Background Stigler's Law of Eponymy states that: Mathematical and Scientific laws/discoveries/inventions/&c. are simply not named after their original discoverer. Stigler's "Law" is a perfect ...
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Why was China slow to recognise the sphericity of Earth?

Wikipedia notes that, while knowledge Earth is approximately spherical was obtained in ancient Greece, and became standard among educated people in Europe and the Middle East long before 1300 AD, ...
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How did Euler stumble on this proof?

Euler proved $n=641$ divides $2^{32}+1$ by noting $n=5^4+2^4=5\times 2^7+1$ so $$2^{32}\equiv-5^4\times 2^{28}=-(5\times 2^7)^4\equiv-1\,(\text{mod}\, n).$$How did he happen upon this realisation? One ...
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Why was F. W. Lanchester's first aeronautical paper rejected by the Physical Society?

Lanchester was arguably the first to somewhat accurately describe the physical mechanism for the generation of lift. In 1894, the Birmingham Natural History and Philosophical Society read his paper, ...
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158 views

What were the precursor works to Copernicus Heliocentrism?

Was Heliocentrism something that exploded with Copernicus seemingly out of nowhere, or were there predecessors, and what were those predecessors? I read somewhere that their might of been versions ...
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294 views

Was it a major cultural event when Van Leeuwenhoek discovered unseen animals under the microscope?

In the 17e century van Leeuwenhoek discovered with his microscope new kind of animals and cells. How was this discovery of van Leeuwenhoek received by the ordinary people when there seemed to be more ...
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104 views

Discovery of kinetic gas theory

I assume that there was a single person who at a specific day in time was the very first to see and understand perfectly clearly that temperature is somehow identical with the mean kinetic energy of a ...
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240 views

Why is it called the butterfly effect?

The pop-sci answer is that Lorenz characterised chaotic atmospheric dynamics with the hypothetical example of a butterfly's flapping wings changing whether a tornado results. However, since butterfly-...
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131 views

How does human design the first ruler?

How and when did we build the first ruler ? I have an hard time figuring how to build something "straight" without having first a "straight" tool. Sure you could just stretch a thread/wire and then ...
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123 views

Does the word 'science' mean what's been found so far, or the way that human discovers unknown?

I'm writing a piece of paper and trying to understand, the meaning of word 'science' in the context of history. I'm not a native English speaker and I know I could look up in the dictionary, but my ...
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1answer
492 views

Did Russia have their own discoveries in the development of semiconductors and the semiconductor industry?

After the Second World War Russia had a vastly larger number of students being trained in their universities compared to the United States around the time of the International Geophysical Year in 1957....
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151 views

Did Aristotle suggest that different kinds of sound might travel at different speeds?

In this answer there is an interesting passage: Also, Aristotle posited that the speed of sound was dependent on frequency. Gassendi had religious/philosophical issues with Aristotle's views, and ...
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How has it been discovered that water consists of acid and base?

The chemical composition of water was discovered about 1784, but when has it been discovered that it is also composed of acid and base?
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History of molecular constituency and structure

During times when there was no spectroscopy of any kind, people did make guesses on the molecular constituency and structure. For example, John Dalton's original atomic hypothesis was that all ...
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411 views

What was the origin of the Seven Bridges of Königsberg problem before Euler?

I was researching the mathematics of this puzzle and wondered where it is be thought to originate. Any information, including context and precedents, would be greatly appreciated. (I'm particularly ...
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624 views

How important was the prediction of Neptune in 1846 for the Oxford evolution debate?

The short story is that based on Kepler's and Newton's physics, in 1846 Le Verrier mathematically predicted the existence and current location of Neptune within a single angular degree, and it was ...
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When was it first discovered (or comprehended) that air has weight?

When was it first discovered (or comprehended) that air has weight? Did the ancients know of this, or did they think that air is weightless?
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How much contribution did John Nash make to proving Riemann Hypothesis?

At quite the end of the movie "A Beautiful Mind", John Nash tells a student- "I am making progress" (to Riemann hypothesis) Actually, how much contribution he made to the proof of Riemann Hypothesis?
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392 views

First appearance of the sine function [duplicate]

I was wondering when was the sine function (I suppose cosine too) first introduced or defined and what was the need for?
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158 views

Essential basic geometrical discoveries still possible in our era?

Can we imagine that scientific can still discover some basic simple but essential geometric rules such as the Pythagorean theorem in a near of far future: $a^2 + b^2 = c^2$ Or do we consider that ...
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How important were serendipitous scientific discoveries (objectively)?

I'm interested in examining the efficiency of the scientific process. Part of this involves examining what actually goes into making a discovery. One common objection is: Half of all important ...
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1answer
470 views

Who discovered the fixed point iteration method?

I was working on the area of fixed point iteration. I couldn't find any historical account regarding the subject. Who was the first to use the this method?
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250 views

Who first introduced the longhand square-rooting method into European mathematics?

A previous question credits François Viète with introducing the well-known longhand method for the computation of square roots in digit-by-digit manner. This method is related to the binomial theorem. ...
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477 views

Who invented or discovered the hyperbolic numbers?

Hyperbolic numbers have the form $a+bj$ where $a,b \in \mathbb{R}$ and $j^2=1$. These are also known as a the Lorentz numbers or double numbers by some authors. I suppose these are a particular type ...
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What enabled the spread of virtual reality systems?

What new technology enabled us to construct VR recently? Was it just the resolution which makes believable image?
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255 views

How did USA became world leader in STEM?

Looking in the past we can easily see that it was Europe who made most of the discoveries in STEM but today USA triumphs in this area. So, how did this shift took place and what were the reasons for ...
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76 views

Lise Meitner's contribution to this experimental apparatus and research effort?

I am reading a NYTimes obituary of Otto Hahn and the discovery of fission, and I've asked in physics SE about the function of the apparatus shown in that article. The system shown demonstrated the ...
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838 views

Madhava and $\pi$

I recently learned that Madhava of Kerala (c.1340–c.1425) was the first to discover the following formula for $\pi$: $$\frac{\pi}4\ =\ 1 - \frac13+\frac15 - \frac17 + \frac19 - \frac1{11} + \cdots$$ ...
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First evaluation of $\sum_{n \geq 1} 1/n^2$ by Fourier series

There are many ways to evaluate $\sum_{n \geq 1} 1/n^2$ as $\pi^2/6$, including multiple solutions using Fourier series. A colleague asked me who was the first person to use Fourier series (or Fourier ...