80 votes
Accepted

What's the famous story about a mathematician who gave a talk without saying a word?

You are most likely referring to the 1903 presentation by American mathematician Frank Cole. The original false conjecture was that the 67-th Mersenne number $M_{67}:=2^{67}-1$ is prime, and it goes ...
  • 69.5k
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 ...
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 ...
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26 votes
Accepted

Who introduced the Principle of Mathematical Induction for the first time?

The issue is thorny ... According to Morris Kline, Mathematical Thought from Ancient to Modern Time. Volume I (1972), page 272 [only entry of the Subject Index regarding : mathematical Induction] : ...
26 votes
Accepted

What new mathematics was inspired by biology and chemistry?

In 1959, Eugene Wigner presented a talk on The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Many papers on the unreasonable effectiveness of mathematics in this field, that field,...
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24 votes

Who first realized that $\int \frac 1x dx =\ln(x)+c$?

By about 1640, the solution to the "area problem" for curves with equation $Y^n = aX^m$ was known by Fermat for all integer cases except when $n = 1, m = -1$. I.e., the only unsolved area ...
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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 ...
20 votes
Accepted

What cipher(s) did Isaac Newton use?

Newton used anagrams which are not the usual ciphers. It is not designed for a secret communication, but only for proving at a later time that you knew something. So nobody is supposed to be able to ...
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 ...
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18 votes
Accepted

What attracted Einstein to the anomalous precession of Mercury?

Who or what attracted Einstein's attention to Mercury, and when? What alerted him to the idea that Mercury's case was different from all those other cases, when a mundane explanation was involved? I ...
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17 votes
Accepted

Who was the first to calculate $\pi$?

It depends on the meaning of "calculate", since $\pi$ is a transcendental number it can not be "calculated" in the usual meaning of the word. The first analytic formula (in the form of an infinite ...
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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 ...
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16 votes
Accepted

What is the origin of polynomials and notation for them?

Although many problems that we now reduce to polynomial equations were solved since time immemorial early occurences are coached in verbal and/or geometric terms, and polynomials are not treated as ...
  • 69.5k
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 ...
15 votes
Accepted

Apparently different objects discovered to be the same

Such "bidentifications" of concepts in math with major impact are what some important mathematical ideas are all about. Here are some examples, and the list could very easily be extended. 1) ...
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15 votes
Accepted

Is it true that Euler did not prove the sum of the Basel series $\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$?

The question can be answered "yes" or "no" depending on how the word "prove" is interpreted. Euler was working in the context of "algebraic analysis" of 18th ...
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14 votes

Apparently different objects discovered to be the same

I would say that the most famous discovery of this sort was the explanation, why "gravitational mass" and "inertial mass" are the same. (The fact was so well known since Galileo that nobody really ...
14 votes
Accepted

When did humans realize that sex leads to pregnancy?

The question asked in the title is not at all the same as the fist question in the body of the text. Because any meaningful answer to the latter seemingly presupposes (wrongly in my opinion) the ...
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14 votes
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Who invented short and long division?

The history of the idea underlying the short/long/synthetic division turned out to be far more complicated than I expected, somewhat reminiscent of the history of $0$, with no single inventor. ...
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14 votes
Accepted

Why don't we learn Buridan's laws of motion?

The next to last sentence has all the reasons in a nutshell:"Buridan used the theory of impetus to give an accurate qualitative account of the motion of projectiles but he ultimately saw his theory as ...
  • 69.5k
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 ...
  • 69.5k
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 ...
  • 69.5k
14 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 ...
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13 votes
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Was Galileo a plagiarizer?

See Heytesbury and the Physical Sciences and Nicole Oresme for detailed information about the so-called Oxford Calculators and their contribution (mainly) to mathematics. The issue is not so clearly ...
13 votes

Was Galileo a plagiarizer?

By this standard why single out Galileo? Euclid "plagiarized" Elements, there isn't a single theorem in it that can be reliably attributed to him, and there are entire books that can be attributed to ...
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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. ...
  • 69.5k
12 votes

Who introduced the Principle of Mathematical Induction for the first time?

Well, you could go with Plato. From this (Wayback Machine), For a start, although the principle itself is not explicitly stated in any ancient Greek text, there are several places that contain ...
  • 8,213
12 votes

Why were hot-air balloons invented so late?

Hot air balloons that can carry people require very large amounts of fabric. They were first created a few decades after the "flying shuttle" made it possible for a single weaver to weave cloth wider ...
12 votes
Accepted

Why didn't Aristarchus' theory of Heliocentrism stick?

I agree with the answer of David, but I would like to add few points to it: It is a common misconception that Aristarchus found (or attempted to find) the sizes of Sun and Moon or distances to them. ...
12 votes

What new mathematics was inspired by biology and chemistry?

This is a correct observation. Chemistry and biology indeed contributed very little to mathematics itself. One of the examples of chemistry contribution is the "Belousov-Zhabotinsky reaction". This ...

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