24

Karatsuba's own report can be found in his 1995 paper Сложность вычислений (Complexity of computations). The phrasing he uses is "сильно взволновалo", which Google does translate as "very excited" or "greatly agitated". But we can see the usual dynamic of an anecdote in the making on the Reddit thread, where Kolmogorov is "...


11

Fortunately, Buchberger himself described the context of his discovery, see Historical background to Gröbner's paper by Abramson. The method, in general outline, was known to Gröbner long before the Buchberger's thesis (1965). In the 1950 paper Über die Eliminationstheorie (Abramson's English translation) it is applied to finding bases of integrals of ...


8

It is true. Wikipedia links to the website of Ollivier, which hosts both the original posthumous publication in Latin, De investigando ordine systematis aequationum differentialum vulgarium cujuscunque, and its English translation, About the Research of the Order of a System of Arbitrary Ordinary Differential Equations, by Ollivier himself. Unfortunately, ...


6

According to Maley's Higher Order Approximations to Solutions of Transcendental Systems (1960), the earliest occurrence of the inverse quadratic interpolation for finding roots is in Dandelin's Recherches sur la resolution des equations numeriques (1826) published in Nouveaux mémoires de l'Académie royale des sciences et belles-lettres de Bruxelles. Dandelin ...


4

Wegner writes of "pivot element" that partitions the array in Sorting a linked list with equal keys (1982), while none of his references (Sedgewick, Rivest, Loeser, Motzkin) does, as far as I can tell. But it does not pick up until 1986, when multiple authors start using it, including Bing-Chao and Knuth in A one-way, stackless quicksort algorithm. ...


3

Surely the Rhind Papyrus (around 1500 BC) contains many algorithms. At that time, such things were presented this way: State a specific problem, then show how to solve it. After several such problems/solutions, the algorithm is supposed to be clear, and the student can solve similar problems in the same way.


3

Trial division was used even before Pythagoreans, Euclid's number theory allowed restricting trials to primes, with the sieve of Eratosthenes identifying the primes. Al-Banna explicitly limited the size of tried factors by the square root, as did Fibonacci later. More sophisticated methods before Gauss were given by Fermat and Euler. There is no cutoff date, ...


3

TL; DR. This is one of those cases where "first use" very much depends on what is meant. Depending on that, it can be ascribed to Babylonians (c. 1600 BC), al-Tusi (c. 1250), Briggs (1633), Newton (1669), Raphson (1690) or Simpson (1740). The Babylonian rule (1800–1600 BC) for approximating square roots converted into modern notation gives the same ...


1

The scanned pages might be more readily available here. Indeed the method is presented as a novel; it is only compared to Newton's method. It is first introduced as a method for finding root enclosures and approximations of the largest and smallest roots of polynomials under the condition that all roots are real. Under this condition the usual "trick" ...


1

No, Romans were not at all bad at computations before Arab numerals were introduced to them. In fact, Romans had a perfectly fine way of doing computations that was every bit as good as Arabic numerals. They used a table and stones to do computations, similar to an abacus. Roman numerals were just used to record numbers, not to do long computations. Though ...


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