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1500 questions
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How did Newton prove the generalised binomial theorem?

Do we have any idea of how Newton proved the generalised binomial theorem?
copper
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What are some of the most complete genealogies of scientific and mathematical subject areas?

I am interested in the way scientific and mathematical subject areas developed (and are still developing). One of the great visual tools that can help us gain insight in how these areas developed is by creating a "genealogy". For the case of…
Max Muller
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When were the modern notions of work and energy created

Reading through Wikipedia says that Coriolis was the first to introduce the notion of work, described as "weight lifted through a height". Our modern conception of work is of a force that realizes a displacement. This is general and valid for most…
Mark Fantini
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How did journal subscriptions evolve over time, and what factors account for it?

Nowadays, many academic journals have some impressively high subscription costs. E.g. Harvard's expenditures for library resources in 2012 was $16,391,638. How did journal subscriptions evolve over time, and what factors accounted for it?
Franck Dernoncourt
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8
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Was $1+2+3+\cdots=-\frac{1}{12}$ in Ramanujan's letter?

In the letter Ramanujan wrote to Hardy did he say that $1+2+3+\cdots=-\frac{1}{12}$. I have been hearing this ridiculous statement for some time now. And now people say that Ramanujan wrote it. Is it true?
user4237
8
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What was the reaction to Kepler's *Somnium* when it was published?

Kepler's Somnium ("The Dream") is a work of fiction that is sometimes regarded as the first example of science fiction (e.g. by Carl Sagan). In it, Kepler describes a journey to the Moon and various scientific observations, along with a number of…
winwaed
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How did Staudinger demonstrate that polymers are high molecular weight covalently bonded molecules?

Hermann Staudinger was awarded the 1953 Nobel Prize in Chemistry for his work demonstrating that polymers are high molecular weight covalently bonded molecules. Prior to his work, the consensus among chemists was that polymers were loosely…
Colin McFaul
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8
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What was the first programming language that implemented hash maps / dictionaries as a base type?

I'm having a discussion elsewhere about this. I suspect that it was Perl, with the hash maps, but that is because I don't know much about older languages rather than any exhaustive research on the matter. The wikipedia article says that the data…
Kevin
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What Is the Origin of the Twin Primes Conjecture?

Is there any written work by Euclid about consecutive primes differing by two? What work was done on the problem from the time of Euclid about 2,300 years ago to the time of Polignac in 1849?
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Which book gives a thorough understanding on the scientific environment of antiquity?

I have started reading Rene Dugas' History of Mechanics book. I want to understand physics from the spectacle of seeing its intellectual evolution instead of directly jumping into its general theories/paradigms, for I don't want leaps in the…
Sensebe
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How did Newton and Kepler (actually) do it?

Today if I want to calculate an elliptical orbit of some object due to the gravity of another, I use Runge-Kutta integration, and I can see the individual steps I use shown in that article. Back "in the day..." Kepler, Newton, and others might have…
uhoh
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Did Feynman develop QED based on Stueckelberg's manuscript?

I found some rumors on the internet regarding Stückelbergs manuscript and it's role for the development of QED. In a comment on here somebody writes: Crease and Mann say in their book The Second Creation (revised edition, Rutgers 1996) (page 143)…
asmaier
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Did Einstein really say: "If I were wrong, it would only take one."

The story is that Einstein was shown a German newspaper that claimed "One hundred German physicists claim Einsteins theory of relativity is wrong." Einsteins reply was supposedly, "If I were wrong, it would only take one." I have looked and looked…
lvoyster
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What is the original source for Gelfand's problem on leading digits of the powers of 2?

The question of the distribution of the leading digits of the sequence $2^n$ is called Gelfand's problem or Gelfand's question. Is there any source that indicates Gelfand's own work on this, or the exact context where it arose with him? References…
KCd
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History of $0 \in \mathbb N$.

There are different conventions around whether $0 \in \mathbb N$. I know that $\mathbb N = \{0,1,2,3, \cdots\}$ is called the Bourbakian definition of $\mathbb N$. But did this convention really come form Bourbaki? In the axioms of Peano, which…
wythagoras
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