Related papers: Isaac Newton as a Probabilist
This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern…
The paper presents a general introduction to the astonishing method for deriving probability approximations that was invented by Charles Stein around 50 years ago.
The classical platonist / formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: \emph{Is new mathematics discovered or invented? Using examples from my own mathematical work during the…
Over a century ago, Oliver Wendell Holmes invited scholars to look at the law through the lens of probability theory: "The prophecies of what the courts will do in fact, and nothing more pretentious, are what I mean by the law." Yet few…
In 1905 Einstein presented the Clock Paradox and in 1911 Paul Langevin expanded Einstein's result to human observers, the "Twin Paradox." I will explain the crucial difference between Einstein and Langevin. Einstein did not present the…
If we accept Savage's set of axioms, then all uncertainties must be treated like ordinary probability. Savage espoused subjective probability, allowing, for example, the probability of Donald Trump's re-election. But Savage's probability…
In the 16th century, Simon Stevin initiated a modern approach to decimal representation of measuring numbers, marking a transition from the discrete arithmetic practised by the Greeks to the arithmetic of the continuum taken for granted…
Inductive inference is a recursion-theoretic theory of learning, first developed by E. M. Gold (1967). This paper surveys developments in probabilistic inductive inference. We mainly focus on finite inference of recursive functions, since…
In a prophet inequality problem, $n$ independent random variables are presented to a gambler one by one. The gambler decides when to stop the sequence and obtains the most recent value as reward. We evaluate a stopping rule by the…
In spite of its title, the book mostly treats probability theory: the law of large numbers (regarded as a principle); formal definition of a random variable and law of distribution; the misnamed Cauchy distribution; functions now named…
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
The Bayesian Classification represents a supervised learning method as well as a statistical method for classification. Assumes an underlying probabilistic model and it allows us to capture uncertainty about the model in a principled way by…
Newton in his Principia gives an ingenious generalization of the Hellenistic theory of ratios and inspired experimentally gives a tensor-like definition of multiplication of quantities measured with his ratios. An extraordinary feature of…
The Jacobian conjecture is thought to have been proposed by O. H. Keller in 1939. However, we have found that the statement of the conjecture is precisely the main result of a paper published by L. Kraus in 1884. Although the final step of…
A new method is presented for finding the derivative of the sine and cosine using the discoveries of Leibniz in calculus between the years 1675 and 1677, namely the derivative of the product and the quotient of two functions as well as the…
Randomness is an unavoidable notion in discussing quantum physics, and this may trigger the curiosity to know more of its cultural history. This text is an invitation to explore the position on the matter of Thomas Aquinas, one of the most…
The manuscripts that presumably contained Newton's early development of the fundamental concepts that led to his Principia have been lost. A plausible reconstruction of this development is presened based on Newton's exchange of letters with…
We mathematically model the supertask, introduced by Hansen, in which an infinity of gods together select a random natural number by each randomly removing a finite number of balls from an urn, leaving one final ball. We show that this…
A paradox associated with the astrophysical Poynting-Robertson effect is presented. The paradox arises when relativity theory and Mie's solution of Maxwell's equations are confronted with the statements on the Poynting-Robertson effect.…
After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…