14 votes
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Is there any evidence De Morgan abandoned probability theory due to it being "too tricky/non-intuitive/difficult"?

It depends on what "abandoned" means. De Morgan did write his main works on probability in 1837-38 and then turned his primary attention to logic. In his lengthy 1837 review of Laplace's ...
Conifold's user avatar
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13 votes
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Why wasn't probability developed in ancient Greece?

This is a good point, I mused about it too. First, Pythagoreans and Plato had a very high minded idea of mathematics, gambling would have been seen as a lowly pursuit. This in itself does not explain ...
Conifold's user avatar
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12 votes
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Why did Borel reject countable additivity of probability?

Even Kolmogorov himself "rejected" countable additivity, in the sense of not making it a universal property of probability. His first chapter axiomatizes and studies finitely additive ...
Conifold's user avatar
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11 votes
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What is the history of moment generating functions, and the more general characteristic functions?

The general idea of generating function has much wider scope than its applications to probability. The proper setting is ``harmonic analysis'' which is one of the central and most developed parts of ...
Alexandre Eremenko's user avatar
9 votes
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Who said that theory of probability was not mathematics?

It was Hardy and Littlewood. They said in a footnote to an article in the early 1920s (this was notably before Kolmogorov's measure-theoretic foundations were developed) that "Probability is not a ...
KCd's user avatar
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8 votes

Poincaré and the baker: was the anecdote true?

I first ran across this story at an exhibit in Los Angeles' Museum of Science and Industry some time before 1970, maybe as early as 1964. In the version I read there, a magistrate was involved, and ...
Ernie Gilman's user avatar
8 votes
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Poincaré and the baker: was the anecdote true?

It is interesting that even many of those who retell the anecdote immediately disown it "The following anecdote about him is probably fabricated, but it makes an interesting probability problem", says ...
Conifold's user avatar
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8 votes
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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
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When did the concept of probability density explicitly appear in mathematics?

The answer depends somewhat on what "explicitly" means. The appearance of continuous distributions, and their densities, is generally attributed to Simpson. Namely, his 1757 response to Bayes's ...
Conifold's user avatar
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7 votes

Who is John B. Walsh?

Yes, that is the one. More information HERE (If your library subscribes to MathSciNet, and you go to that page from your library, then you will be able to get links to Walsh's 70 or so publications, ...
Gerald Edgar's user avatar
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6 votes
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Were $\sigma$-algebras defined for probability?

No and no, I am afraid. Those things are not specific to probability, we do them with logical connectives, which parallel set operations, and with areas and volumes, just as well as with probabilities....
Conifold's user avatar
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6 votes
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Was Poisson and other distributions found by solving applied problems or by playing around theoretically?

As a surmise, the boundary between "noodling" and "solving real problems" is rather vague. One needs at least some vague external idea to guide the "noodling", otherwise ...
Conifold's user avatar
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5 votes

Did Karl Popper argue against Bayesian inference?

Bayesian inference seeks to believe in that which has a high conditional probability as computed with Bayes's theorem. The problem with using $P\left( A|B\right)=P\left( B|A\right)\frac{P\left( A\...
J.G.'s user avatar
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5 votes

If Math is Based on Unprovable Axioms and these Axioms can't be Proven - Why Does Math "Work" so Well?

Axioms in mathematics are not arbitrary statements; they are abstractions of everyday experience or physical laws (or other laws of nature). Consider two examples. Axioms and postulates of Euclid ...
Alexandre Eremenko's user avatar
4 votes
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Who introduced moments of a random variable first?

Long before Pearson, Chebyshev and his student A. A. Markov used moments to prove the Central Limit Theorem. The earliest paper of Chebyshev on this topic is dated 1887. But I do not claim that ...
Alexandre Eremenko's user avatar
4 votes

Who introduced moments of a random variable first?

My answer taken from the closed version of this question here From MathWords Moment was taken into Statistics from Mechanics by Karl Pearson when he treated the frequency-curve (or observation ...
Gerald Edgar's user avatar
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4 votes
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First use of litte $o_p$ (little $o$ in probability) notation?

From Earliest use of mathematical symbols: The convergence in probability symbol plim was introduced by H. B. Mann and A. Wald "On Stochastic Limit and Order Relationships," Annals of Mathematical ...
nwr's user avatar
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4 votes
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What is the original source for Gelfand's problem on leading digits of the powers of 2?

I assume that one of the sources is MathWorld. But the question they claim Avez attributes to Gelfand is not the distribution of the leading digits generally, but specifically "will the digit 9 ever ...
Conifold's user avatar
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4 votes

Why wasn't probability developed in ancient Greece?

Imho the Greeks would have considered probabilities as a sophism - the attempt to produce knowledge out of ignorance. And even today they are still not far from truth: except for the frequentist ...
sand1's user avatar
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4 votes

Who is Donald Fisk?

He was a PhD student of Herman Rubin at the Michigan State University in the early 1960-s. Some of the history is reconstructed by Jarrow and Protter in A short history of stochastic integration and ...
Conifold's user avatar
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4 votes
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How were the works of axiomatization of probability progressed prior Kolmogorov?

Kolmogorov's axiomatization achieved greater simplicity, clarity, rigor and unification of applications by grounding probability in measure theory. There were prior axiomatizations that went in a ...
Conifold's user avatar
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4 votes
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Who was the first English author that incorporated Markov's Law of Large Numbers and its derivation?

In 1937, Markov's student J. Uspensky published his English-language Introduction to Mathematical Probability, which has the result in question on p.191. It seems hard to believe this is the first ...
kimchi lover's user avatar
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3 votes

Why wasn't probability developed in ancient Greece?

I hope another answer is okay. Absolutely nothing of what follows is mine. The source[1] is given at the end. That main concern of that article, however, is de Finetti's theory of subjective ...
shvjds's user avatar
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3 votes

What is the original source for Gelfand's problem on leading digits of the powers of 2?

The book of Avez you refer to is indeed rare: it is not listed in the common databases Mathscinet and Zentralblatt (which is very strange). So I cannot say anything about the relation of Gelfand to ...
Alexandre Eremenko's user avatar
3 votes
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Which version of the St Petersburg paradox is the original one?

See : Pierre Remond de Montmort (1713), Essay d'analyse sur les jeux de hazard, Extrait d'une Lettre de M.N.Bernoulli à M.de M... du 9 Septembre 1713 : Cinquiéme Problème. On demande la meme chose ...
Mauro ALLEGRANZA's user avatar
3 votes

Who developed Gaussian Mixture Model (GMM) and applied it to machine learning?

The idea of using Gaussian mixtures was popularized by Duda and Hart in their seminal 1973 text, Pattern Classification and Scene Analysis.
Tyler Durden's user avatar
3 votes

Did Karl Popper argue against Bayesian inference?

The answer is not so straightforward. Of course, the thrust of Popper's position was against probabilistic induction in general, and Bayesianism is often put forth as the leading alternative to ...
Conifold's user avatar
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3 votes

Poincaré and the baker: was the anecdote true?

I think I recall reading this story as a little girl in the Time Life series of science books, in the volume on “Mathematics.” If that is the case (it’s a fifty-plus year old recollection), those ...
ReneeJoan's user avatar
3 votes
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Who coined the term "uniform" as in "uniform distribution"?

The first uses of what we call "uniform distribution" occur very early, discrete arguably already in Cardano, and continuous in Simpson and Bayes. According to Handbook of Beta Distributions: "One ...
Conifold's user avatar
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3 votes
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Was Cramér the first to interpret the PNT's $1/\log(x)$ as probability of primes?

A good place to look is Granville’s paper “Harald Cramér and the distribution of primes numbers.” It is on Granville’s website here. He brings in Cramér’s work starting on the bottom of page 19. The ...
KCd's user avatar
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