Questions tagged [discoveries]

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

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7
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1answer
243 views

Does Blum's speedup theorem have any conceptual predecessors?

Blum's speedup theorem seems to me that bears at least some superficial resemblance to Godels research on the length of proofs under certain axiomatic systems. Does Blum's speedup theorem has any ...
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63 views

Are there any mathematicians who expressed non-trivial sequences of rules on how to do research?

I recently saw a paper where there are presented some rules on how to learn mathematics (and do research) which were firstly articulated by Lagrange. Are there any similar rules that were expressed ...
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547 views

How did J.J. Thomson learn that what he discovered was different than an atom or a molecule?

Wikipedia says he discovered that the electron was different than an atom or molecule. His line of reasoning is not shown. I additionally searched stack exchange and unless I missed it..... I am lost ...
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1answer
50 views

Are there any photographs of the original apparatus used by Hertz to demonstrate the photoelectric effect?

There are many schematics and many photographs of tubes used later but I cannot find a single photograph of the original apparatus. Even the sketches that were made in the late 19th century are ...
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68 views

Who was the first to state that scientific theories could be used to make predictions?

It seems to me that very few if any scientists/philosophers stated that science could be used for predictions before the early 1900s. In the scientific context I have only encountered the use of the ...
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26 views

Timeline for the earliest work on Frobenius problems

If $a, b$ are positive and coprime integers, then the set of linear combinations of $a$ and $b$ with nonnegative coefficients is all integers past $(a - 1)(b - 1)$; i.e. $\{ \lambda_1 a + \lambda_2 b :...
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80 views

What was the first “scientific”, non-photographic depiction of Earth as seen from outside of Earth?

For a long time now, I've been thinking about this: when was the first painting, illustration or depiction of any kind where our planet Earth is seen as a sphere in space? Possibly even from the Moon? ...
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84 views

How did Kolmogorov came up with his formalization of intuitionistic logic?

According to this article Kolmogorov published a paper in 1925 in which he attempted to formalize Brouwer’s intuitionistic mathematics. In that paper there are the following logical formulas: \begin{...
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Why do Thai numerals look so different than Arabic numerals?

The Arabic numerals I am referring to are “1234567890”. I have read that Thai numerals, “๑๒๓๔๕๖๗๘๙๐”, are actually distantly related. Both descend from the numeral system invented by the Phoenicians, ...
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162 views

Was Tesla the only scientist whose possessions were confiscated by secret services?

Tesla, especially later in his life was constantly monitored by the FBI. When he died all his notes and other belongings were taken and for a very long time nothing was returned to his family. Has ...
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1answer
153 views

When is the first use of Newton's method for root finding?

I saw this from Wikipedia. The name "Newton's method" is derived from Isaac Newton's description of a special case of the method in De analysi per aequationes numero terminorum infinitas (written in ...
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57 views

When was the Laguerre's method first used to approximate roots?

Is there a specific date when Laguerre published his root finding method? I found his 1880 note Résolution des équations numériques, but I am not sure if this is the source because I can not read ...
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881 views

Who first solved the classical harmonic oscillator?

There is a question Who solved the quantum harmonic oscillator?, but not one for the classical oscillator. Wikipedia's article Harmonic Oscillator does not have historical information either. So who ...
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70 views

When and how was the water cycle discovered?

When and how was the water cycle discovered? Did people like ancient Greek philosophers have any correct ideas on the water cycle or was it's discovery more of a recent thing?
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113 views

Are there any important scientific discoveries, or inventions, that could have been made much earlier in history? [closed]

I can imagine that some discoveries are not made for a long time despite availability of all the information and tools that one would in principle need. Are there clear examples of that?
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117 views

Who first reported the Crab pulsar's pulsing but was dismissed by an astronomer?

This answer to Has great eyesight been necessary for astronomers? mentions Astronomer Jocelyn Bell Burnell's recounting of a likely first visual observation of a pulsar. This can be found for example ...
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73 views

When was the inverse quadratic interpolation method first used?

Do you know anything about it? I couldn't really find something useful on web.
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170 views

Did Jacobi invent the Hungarian algorithm for the assignment problem over a century before Kőnig and Egerváry?

Wikipedia says: In 2006, it was discovered that Carl Gustav Jacobi had solved the assignment problem in the 19th century, and the solution had been published posthumously in 1890 in Latin. The ...
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102 views

When was the ratio between electric and magnetic forces in an electromagnetic field established?

We know that the magnetic force on a particle moving in a magnetic field was found by J.J. Thomson in 1881, with a slight mistake, and then corrected by Heaviside in 1885 to $F_M = q\,v\times B$. Can ...
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1answer
95 views

Who discovered anisotropic materials, and what were they studying?

Thinking of properties of materials, who discovered anisotropy and what materials were they studying? I had read a claim that the first recorded experiments to study anisotropy are those by Duhamel ...
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121 views

Why isn't François Proth's name used for Gilbreath's conjecture as he discovered & published a proof 80 years earlier?

According to Wikipedia's Gilbreath's conjecture page, The statement is named after mathematician Norman L. Gilbreath who, in 1958, presented it to the mathematical community after observing the ...
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1answer
140 views

When was it found that a function could be decomposed as a sum of even and odd functions?

I'm not sure if it's a good question but I was reading about the decomposition of any function, f(x), as a sum of even and odd functions; f(x) is not an even or odd function. Is it possible to know ...
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1answer
149 views

Origin of the “law of quadratic reciprocity”

Today, "reciprocity" is the standard mathematical word used for quadratic reciprocity and its generalizations. I found that the name dates back to no later than 1832, when a paper of Dirichlet (...
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37 views

Difference between Perrin's and J. J. Thomson's experiment

In J. J. Thomson's paper (Phil. Mag. S. 5. Vol. 44. No. 269. Oct. 1897) concerned with cathode rays, Thomson writes, that the experiment by Perrin that supposedly proves that cathode rays are made of ...
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1answer
82 views

Was there a more intuitive early proof of the generalized mean value theorem?

I am interested in the early proofs of the theorem. It is often called Cauchy mean value theorem, so perhaps Cauchy proved it first. In all the proofs that I have seen we construct a contrived ...
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649 views

How did J. J. Thomson establish the particle nature of the electron?

In its article about how the electron was discovered, Wikipedia says that Thomson and his students performed experiments which suggested that cathode rays were negatively charged "particles". But even ...
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90 views

Invention of the SI unit of plane angle:Radian

As I was reading on the topic plane angle then I came across a term radian.Hence I want to know how radians were discovered as well ?
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270 views

Source of claim that Leibniz discovered separation of variables for ODEs in 1691?

Claims I'm evaluating I've read in multiple sources that Leibniz formulated separation of variables for ODEs in 1691. A couple example sources are below. Mathematical Thought from Ancient to Modern ...
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144 views

What are the great works of Richard Phillips Feynman? [closed]

What are the prerequisites to read his book? Why Richard Phillips Feynman is so famous? What are great works of Richard Phillips Feynman?
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1answer
103 views

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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418 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 $\exp{iS/\hbar}$. It was Feynman, however, who had the idea of expressing the ...
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1answer
118 views

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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42 views

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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96 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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1answer
77 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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1answer
606 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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1answer
132 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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1answer
198 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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3answers
634 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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2answers
77 views

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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275 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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1answer
217 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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3answers
518 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
254 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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1answer
138 views

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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34 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
324 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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514 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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2answers
130 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
483 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 ...