Questions tagged [discoveries]
For questions about the location (in space and time) of scientific discoveries and their historical context.
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What motivated the idea of the Tschirnhaus transformation of polynomial equations?
As I studied Cardano's formula for the cubic, Tschirnhaus transformation came up as a very important step. The more I studied it the more attractive and interesting it seemed. So I am curious about ...
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In Geiger-Marsden experiments how was charge of alpha particle and charge of gold atom found?
Here: https://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiments
Some calculations were done to show how JJ Thomson's model predicts alpha particles will be mostly undeflected by the gold foil. ...
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Did the Maclaurin series for sine and cosine unsettle Indian mathematicians?
As many of you may know, sometime around the 14/15th centuries an Indian mathematician by the name of Madhava of Sangamagrama derived the Maclaurin series for sine and cosine for the first time in ...
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When did derivative mean not only "slope of tangent" but also "instantaneous rate of change"?
When did derivative mean not only "slope of tangent" but also "instantaneous rate of change"?
Fermat was interested in minima and maxima, and realized these occur when the tangent ...
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How was the Fundamental Theorem of Calculus discovered?
How was the Fundamental Theorem of Calculus discovered?
The FTC is at once simple enough that Math.SE is full of questions asking "why is it such a big deal" and yet avoided discovery for ...
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How did Newton, Lagrange, Hamilton and others ideate their mechanical formulations?
What exactly did Lagrange do, historically? This is very relevant but the accepted answer just does similar speculations based on contextual details that I have done. It was mentioned that part of ...
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When did people first know that the sky was illuminated by the Sun?
During the day, the sky is bright blue and, along with the yellow light from the Sun, it illuminates the surface of the Earth.
What is the earliest recorded knowledge that the sky wasn't self-...
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What factors influence whether an invention is not patented?
Various inventions that have become well-known were never patented, including matches, emoticons, and the magnetic strip. Other noteworthy examples include the polio vaccine (Jonas Salk), monoclonal ...
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History of triangulation
Snell tends to be quoted as the person to develop triangulation in geodesy. I don't believe, however, that triangulation was invented only then. For example, here Al-Biruni is mentioned to have "...
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Why and when was the kinetic theory of gases generalized to fluids?
I've been reading about kinetic theory of gases, which only deals with gases. I know that the lattice Boltzmann method, which is commonly used to simulate fluid flows, finds its origin in the kinetic ...
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When was it first discovered that face masks protect against disease?
The practice of wearing face masks to protect against disease is actually nothing new. Mask wearing for the specific purpose of warding off disease was common (and even sometimes mandated by public ...
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Was Nikola Tesla aware of Maxwell's equations?
Was Nikola Tesla aware of Maxwell's equations or Heinrich Hertz's experimental proof of the former when he worked on his radio device invention?
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What is the historical significance of Riemann’s discovery of non-flat metrics?
From a perspective of math history, what discoveries resulted directly from Riemann’s discovery and codification of non-flat metrics on Riemannian manifolds? After Albert Einstein modeled the Universe ...
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First example of regularization
Background:
I like to think of L'Hospital as one of the earliest authors of least-squares regression.
L'Hospital, G. (1696). L'analyse des infiniment petits pour l'intelligence des lignes
courbes.
I'm ...
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Context of the discovery of ultraproducts
Łoś's theorem is a fundamental theorem in model theory (a branch of mathematical logic).
Historical question: What was Łoś's original motivation to define ultraproducts and prove Łoś's theorem? Which ...
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$\pi(x)$ and $\operatorname{li}(x)$ cross infinitely many times -- due to Littlewood 1914 or Schmidt 1903?
In Montgomery-Vaughan's Multiplicative Number Theory I: Classical Theory, they prove in Theorem 15.3 that $\pi(x)-\operatorname{li}(x) = \Omega_{\pm}(x^{\Theta-\epsilon})$ for every $\epsilon>0$ ...
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Who proved Rank Nullity Theorem?
I have been learning about the Rank Nullity theorem and was trying to understand Who came up with the rank nullity theorem? While i did look up on the internet i came up with almost no answers. Some ...
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Why did Columbus think the Earth was much smaller than it is?
Columbus set off on his westward journey to Asia, believing the Earth was much smaller than it is.
There was some apparent disagreement about the size, and Columbus was staking his life on it. Why ...
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History of circulant matrices for convolution
Discrete linear convolution $$
y[k]=h[n] * x[n]=\sum_{i=-\infty}^{\infty} x[i] h[k-i]
$$
can be done with circulant matrices with appropriate zero padding. Is anyone aware of the name of the ...
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Why was the cubic specifically so hard to solve?
I'm a huge fan of the history of Algebra and, recently, I've noticed a bit of an oddity. Degree one equations have been known (and solved) for as long as human history. For degree two equations, we ...
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Was Becquerel's discovery of radioactivity inspired by his father?
Becquerel was awarded the Nobel prize for his discovery of radioactivity. He was researching phosphoresence and decided one day to place the stuff he used in a drawer to keep it out of the sun. He put ...
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Singularities on null capacity sets are removable — Wiener or Bouligand?
A classical theorem on harmonic functions states that singularities of bounded harmonic functions are removable if the singular set is of null capacity. This theorem is sometimes attributed to ...
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What are the earliest inventions to store and release energy (e.g. fly wheels)?
I am interested in very early inventions that allowed energy to be stored and released after a delay even it's just a short time. With "invention" I mean a novelty that is the result of ...
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Did Ibn al-Haytham write anything about his experiments that is general enough to be seen as prefiguring the scientific method?
Ibn al-Haytham is considered one of the first experimenters. Since he was also a kind of philosopher did he write anything close in meaning and generality to the scientific method?
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Why couldn't Robert Peary use his theodolite at the North pole
Robert Peary writes in his book The North Pole:
The instruments used in taking
observations for latitude may be either a sextant and an artificial
horizon, or a small theodolite. Both these ...
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Was C.S Peirce the first philosopher to posit that value belief serves as some sort of guide for scientific belief?
I remember reading something to the effect that the moral and aesthetic preferences influence scientific belief in his collected works.
Was C.S Peirce the first philosopher to posit that value belief ...
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Who first defined pressure?
Before learning any topic, I always find the reason of "Why definitions are created for that particular topic?"
In fluid statistics, I encountered a term called "pressure".
But I ...
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Does Blum's speedup theorem have any conceptual predecessors?
Blum's speedup theorem seems to me that bears at least some superficial resemblance to Gödel's research on the length of proofs under certain axiomatic systems.
Does Blum's speedup theorem have any ...
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Are there any mathematicians who expressed non-obvious sets 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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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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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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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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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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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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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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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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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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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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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? Was its discovery more of a recent thing?
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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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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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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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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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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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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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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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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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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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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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