30 votes

What are the earliest inventions to store and release energy (e.g. fly wheels)?

One early invention for storing energy was a basin above the level of the river. It was filled with water when the water in the river was high, and then, when the water in the river was low, it was ...
Alexandre Eremenko's user avatar
29 votes

What was the motivation for Minkowski spacetime before special relativity?

Not quite. Minkowski had the idea of representing special ralativity as geometry in 1907 under the direct influence of Einstein's 1905 paper, and he developed it in Raum und Zeit (1907) and Zwei ...
Conifold's user avatar
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21 votes

What are the earliest inventions to store and release energy (e.g. fly wheels)?

This is probably not what you were thinking of but "the earliest invention that allowed energy to be stored and released after a delay even it's just a short time" was a stone. I can store ...
candied_orange's user avatar
19 votes
Accepted

How did Planck derive the black body radiation formula without using the Bose statistics?

Bose derived the black body radiation formula in early 1924 by considering the ideal gas of light quanta. Nothing could be further from Planck's mind in 1900. The idea of light quanta did not appear ...
Conifold's user avatar
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17 votes
Accepted

How much did John Nash contribute to proving the Riemann hypothesis?

Nash was known to have been captivated by RH at an early age after reading E.T. Bell's Men of Mathematics. He had confided in some friends and colleagues that he had an idea that might work involving ...
nwr's user avatar
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16 votes

Did amateurs ever produce important proofs or similar?

A case from this year is that of Aubrey de Grey. Aubrey de Grey, a biologist known for his claims that people alive today will live to the age of 1,000, posted a paper to the scientific preprint site ...
Bence Mélykúti's user avatar
15 votes
Accepted

Who first solved the classical harmonic oscillator?

It was "solved" by Huygens in Horologium Oscillatorum (1673). The scare quotes are there because he never wrote down the equation, and even Newton's laws were not yet explicitly formulated. Huygens ...
Conifold's user avatar
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14 votes
Accepted

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

The short answer is Euler. Some details are given in the following long quote from Hald's History of Probability and Statistics and Their Applications before 1750 (p.438): In 1743 Euler solved the ...
Conifold's user avatar
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14 votes

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

The idea that matter was made up of "primordial" particles, and currents in metals consisted of them was well established by then. Stoney suggested the name "electron" in 1891, and Lorentz's theory of ...
Conifold's user avatar
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13 votes
Accepted

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

The two most famous paradigmatic examples of de-unification are phlogiston and ether. The Kaluza-Klein theory of gravity and electromagnetism did not get to spread as far and wide before faltering. ...
Conifold's user avatar
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12 votes
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Did du Bois-Reymond invent the diagonal argument before Cantor?

This paper is one in a series of papers in which du Bois Reymond studied functions on the positive real line ordered by the "order of infinity" (order of growth at infinity), what he later ...
Conifold's user avatar
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12 votes
Accepted

Does Blum's speedup theorem have any conceptual predecessors?

The resemblance is not superficial. There is a precise relation between computer programs and formal proofs known as the Curry–Howard correspondence that took shape in 1960s. And Gödel's results on ...
Conifold's user avatar
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10 votes

Why is it called the butterfly effect?

SEE for more Ed Lorenz in 1963 wrote One meteorologist remarked that if the theory were correct, one flap of a sea gull's wings would be enough to alter the course of the weather forever. The ...
Gerald Edgar's user avatar
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10 votes
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What actually led Feynman to the path integral formulation of quantum mechanics?

It was Dirac's paper The Lagrangian in Quantum Mechanics. He gave more than just a remark about $\exp{iS/\hbar}$, he described the general structure of the path integral expression for the transition ...
Conifold's user avatar
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10 votes

What are the earliest inventions to store and release energy (e.g. fly wheels)?

Agriculture The purpose of farming is to harness the freely available energy from the sun, and convert it into a form that can fuel the human body. Agriculture enabled significant food surpluses, ...
Nuclear Hoagie's user avatar
10 votes

Why did Columbus think the Earth was much smaller than it is?

Answering the earlier version of the question first (on Columbus mistakes). There were two main sources of mistakes: exaggerating the size of Asia and underestimating the size of the Earth. Columbus ...
Alexandre Eremenko's user avatar
9 votes
Accepted

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

MAA has a very nice presentation of the problem's history and solution authored by Paoletti. For what happened after Euler see Was there a continuation to Euler's work on the Seven Bridges of ...
Conifold's user avatar
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9 votes
Accepted

Why was China slow to recognise the sphericity of Earth?

It is hard to say why history happened one way rather than another. But we can point at some differences between ancient Greece, Hellenistic Mediterranean or Renaissance Europe and ancient and ...
Conifold's user avatar
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9 votes

Did amateurs ever produce important proofs or similar?

A well-known example is the work of Marjorie Rice on pentagonal tilings of the plane. Wikipeidia: In December 1975, Rice came across a Scientific American article on tessellations. Despite having ...
Gerald Edgar's user avatar
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9 votes
Accepted

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

Thomson drew his conclusion based on his calculation of the charge to mass ratio of the "corpuscular carriers of negative charge in cathode rays". Quoting Thomson's Nobel Lecture of 1906: ...
nwr's user avatar
  • 6,849
8 votes

What was the motivation for Minkowski spacetime before special relativity?

Minkowski space time was considered by mathematicians before Einstein and before Minkowski. Of course the name "space-time" was not used. The reasons were purely mathematical, not physical. The most ...
Alexandre Eremenko's user avatar
8 votes
Accepted

Who introduced random variables into probability?

Concerning the notation $\text{Pr}(|\xi|>\varepsilon)$ here's what I've found so far: Cajori's 1929 A History of Mathematical Notations says nothing on probability theory, which suggest that the ...
Michael Bächtold's user avatar
8 votes
Accepted

Madhava and $\pi$

According to this page: Although almost all of Madhava's original work is lost, he is referred to in the work of later Kerala mathematicians as the source for several infinite series expansions (...
nwr's user avatar
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8 votes
Accepted

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

Here is a partial translation of a Russian article about the history of semiconductors (part that addresses Soviet contributions): 1948-1950. Not only in the United States, but also in other ...
Moishe Kohan's user avatar
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8 votes

Foundational crises in non-Western historical mathematical communities

Let me point out that the Fraenkel-Bar-Hillel "march to rigorization" quote reflects the early 20-th century "rational reconstructions" of history that were worked out by mathematician-historians like ...
Conifold's user avatar
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8 votes
Accepted

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

It is true. Wikipedia links to the website of Ollivier, which hosts both the original posthumous publication in Latin, De investigando ordine systematis aequationum differentialum vulgarium ...
Conifold's user avatar
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8 votes
Accepted

What motivated the idea of the Tschirnhaus transformation of polynomial equations?

Attempting to find substitutions that would generalize Cardano's and Ferrari's solutions to the cubic and quartic was a popular enterprise in the 17-18th centuries. Gregory, Leibniz, Euler, Bezout and ...
Conifold's user avatar
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7 votes
Accepted

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

While Nick R assumes in his answer that from Boyer's writing the formula is due to De Moivre, I think that is misleading and the first derivation of the formula you ask about really should be credited ...
KCd's user avatar
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7 votes
Accepted

Who invented or discovered the hyperbolic numbers?

According to the text Bicomplex Holomorphic Funtions by Luna-Elizarraras, et al, as far as we know Cockle was the first to introduce and study these objects, and their introduction was almost ...
nwr's user avatar
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