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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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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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134 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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68 views

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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2answers
192 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
188 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 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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30 views

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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3answers
173 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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187 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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83 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
130 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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141 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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472 views

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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101 views

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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1answer
113 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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1answer
193 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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94 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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1answer
183 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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1answer
113 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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119 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
287 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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1answer
131 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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71 views

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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1answer
300 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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2answers
308 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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3answers
1k views

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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1answer
7k views

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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2answers
325 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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2answers
157 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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70 views

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
373 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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1answer
214 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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1answer
411 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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30 views

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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3answers
237 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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1answer
69 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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695 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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1answer
129 views

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 ...
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81 views

What are some greatest blunders from the great minds from science?

Einstein said that incorporating the cosmological constant to his equations of general relativity was the greatest blunder of his life. But as it turns out, cosmological constant does indeed have ...
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2answers
311 views

Who derived $\int_{0}^{\infty} \mathrm{e}^{-x^2}\, dx = \frac{\sqrt \pi}{2}$?

I want to know who derived $$\int_{0}^{\infty} \mathrm{e}^{-x^2}\, dx = \frac{\sqrt \pi}{2}$$ In school, our book mentioned that Euler proved this result. But on Math Stack Exchange, some people say ...
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1answer
418 views

Serendipitous discoveries in Mathematics and Computer Science

I have recently been reading about serendipitous discoveries in science and I found them quite inspiring. Most of those discoveries are in Chemistry. I'm looking for examples of these kinds of ...
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1answer
525 views

Who invented the exponential ansatz for linear differential equations with constant coefficients?

Who invented using $e^{\lambda t}$ as ansatz for solving linear differential equations with constant coefficients?
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1answer
581 views

History of elementary proof of Fermat's last theorem for $x^3 + y^3 = z^3 $ [closed]

What was the historical back ground that probably Fermat’s could had known about a much simpler proof than the first (Euler’s elementary proof of Fermat’s last theorem for $n = 3$), at least for the ...
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1answer
877 views

Did Maxwell invent the Maxwell's wheel?

Tried to find it online, but nothing. Everyone refers to it and that it's named after the famous James Clerk Maxwell (of the Maxwell electromagnetic laws and some other things), but there is no direct ...
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1answer
221 views

light rays and wave fronts [duplicate]

Who made first the connection between light rays and wave fronts? The fact is stated in many places, e.g., wikipedia, but I couldn't find a history.
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68 views

Have humans gotten better at the methods of science over time? [closed]

Im currently reading the book A Short History of Nearly Everything by Bill Bryson, and as I'm reading about the history of many fields of science (e.g. paleontology, geology, astronomy, etc.) it seems ...
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63 views

Edward Lorenz and sensitivity to initial conditions

Lore says that Edward Lorenz found out that atmosphere fluidodynamics was very sensitive to initial conditions when he stopped a numerical simulation, dutifully copied the partial results, and after ...