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70

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 back to the preface to Mersenne's own Cogitata Physica-Mathematica (1644). However, Cole was already confirming rather than disproving, that $M_{67}$ is ...

30

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 allowed to flow to the fields from the basin. Such a basin could also be filled manually. Such devices were used in ancient Egypt, as a part of their irrigation ...

27

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 Abhand lungen über die Grundgleichungen der Elektrodynamik (1909). See Minkowski on MacTutor. Before that only classical "spacetime" appeared, and only superficially....

24

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 problem was for $Y = \frac 1X$ - the standard equation for the graph of a hyperbola. In 1647, Gregoire de St. Vincent showed the following special property ...

22

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] : The method was recognized explicitly by Maurolycus in his Arithmetica of 1575 and was used by him to prove, for example, that $1+3+5+ \ldots + (2n+1)=n^2$. ...

22

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, and some other field quickly followed suit. As an opposing point of view, the unreasonably effective (800+ papers, 30+ books) mathematician I.M.Gelfand noted ...

20

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 energy in it briefly by flinging it at your head (kinetic). I can store energy in it even longer by putting it on a cliff above your head (potential). Stone ...

18

History of the metric system - Wikipedia says: In 1861, Charles Bright and Latimer Clark proposed the names of ohm, volt, and farad in honour of Georg Ohm, Alessandro Volta and Michael Faraday respectively for the practical units based on the centimetre-gramme-second absolute system. This was supported by Thomson (Lord Kelvin). These names were later scaled ...

17

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 decode the message until you tell what the message was. To do this, he used a simple procedure: he wrote a sentence (in Latin) and then just counted letters in ...

17

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 series) that in principle can calculate $\pi$ to any required accuracy is probably due to medieval Indian mathematician Madhava, who was first to conceive of ...

16

As quoted from this article: Many people's work was needed to prove that the Sun is a star. The first person we know of to suggest that the Sun is a star up close (or, conversely, that stars are Suns far away) was Anaxagoras, around 450 BC. It was again suggested by Aristarchus of Samos, but this idea did not catch on. About 1800 years later, around AD ...

16

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 pseudoprimes, so there was a great deal of anticipation surrounding the announcement of his 1959 lecture at Columbia University sponsored by the American ...

15

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) Logarithms show multiplication on $\mathbf R_{+}$ is a disguised form of addition on $\mathbf R$, and this is why logarithms were such an important computational aide ...

14

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 noticed that it is some strange coincidence. This remarkable coincidence is explained in General relativity). The only competing example is that light and ...

14

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 separate items. For early occurences of geometric problems that lead (today) to quadratic equations see The origin of quadratic equation in actual practice. The ...

14

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 arxiv.org with the title “The Chromatic Number of the Plane Is at Least 5.” In it, he describes the construction of a unit-distance graph that can’t be colored ...

13

The French mathematician André Weil was imprisoned for failure to report for duty for a spell in 1940. It is said that "While in jail for six months at Rouen, he proved the Riemann hypothesis for curves over finite fields." Nowlan. He is said to have sent a 14 page letter to his sister from prison with some groundbreaking ideas on "Analogy in Mathematics". ...

13

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 existence of a mechanism to ascertain if a non-human animal has made an abstract connection in the scientific consensus, I will simply note that paternal care is ...

13

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 know for sure that Henri Poincaré was aware of the problem and of its singularity - had he been in Kelvin's place, he would have added it to the list, and ...

13

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 assessed by modern historiography: There has been some discussion of the meaning of the work of Heytesbury and the other Calculators for the development of the ...

13

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 until Einstein's 1905 photoeffect paper, in 1908 he thought of them as vortices in EM field rather than localized energy packets, and in 1911 remarked that the ...

13

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 homogeneous linear differential equation of the m-th order with constant coefficients (using the same idea as de Moivre) by guessing at a particular ...

13

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. The splitting of jade into two distinct minerals, nephrite and jadeite, is a small scale example. The phlogiston/caloric theory was able to unify chemical and ...

13

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 considered the motion of pendula, and for simple cases knew the "law of the conservation of living force" (mechanical energy), as Bernoullis later called it, see ...

12

Andre Weil's work on zeta functions of algebraic curves over finite fileds. Andre Weil was one of the most famous mathematicians of the last century. He also was a pacifist, and when WWII approached, he left France to visit....Soviet Union:-) After Soviet Union, he visited Finland... just few days before Soviet Union attacked it. He was arrested by the ...

12

Another outstanding example is Jean Leray (who was mentioned in an answer to the question on jail prisoners). He was an outstanding French mathematician with main interests in fluid dynamics. When confined to a German POW camp, where he stayed until the liberation he was afraid that Germans will force him to work in his area (which has important military ...

12

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 than the weaver's arms -- and then made mechanized looms possible. On the shuttle and the looms see https://en.wikipedia.org/wiki/Loom The hugely increased ...

12

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 was an experimental discovery whose explanation stimulated to some extent the development of the theory of dynamical systems (known as "chaos theory" in the ...

12

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. According to the Angelfire timeline the modern long division symbol of English-speaking countries is first used in the 1888 teacher's edition of The Elements of ...

12

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 a correction to Aristotle". Buridan's account, as Aristotle's or Avicenna's before him, was qualitative, he never put it into equations, which would allow for ...

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