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The OP wrote: Are there any good sources (references, books, videos (most preferable) etc.) that provide a walkthrough to help "discover/create" the findings of Fourier by yourself? I think chapters 8 and 9 of 17 Equations That Changed the World by Ian Stewart provide such a walkthrough.


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Cardano's formula is useless if you want to really solve the cubic equation. In our culture we say that "solving an equation" means writing its solution in some closed form using a certain set of mathematical symbols. But this is just an agreement, and it was not always the case. If you need to solve an equation not to pass an exam, but for some ...


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The motivation for the theory of quadratic forms was representation of integers by sums of squares. This business was started by Fermat and continued by Euler, Lagrange and Legendre, then Gauss. Generalization from sums of squares to arbitrary quadratic forms is natural. Two forms represent the same integers when they are equivalent. Discriminant is the ...


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The Greek word "theorem" has a precise meaning "a statement for which a mathematical proof exists". As far as we know these notions were invented only once: in ancient Greece in 6 century BC. More precisely in the Greek city of Miletus on the territory of modern Turkey. This is what the Greek tradition says. From what we know, this ...


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Complex numbers were used long before Gauss. They appeared for the first time in 16th century when people found a formula for solving cubic equations. One problem with this formula is that even for simplest equations like $x^3-x=0$ which have 3 real solutions, square roots of negative numbers occur in the formula (they cancel in the end, when you do ...


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IMO, the notation $P(x,y)$ is "more correct". See e.g. Felix Klein, Elementary Mathematics from an Advanced Standpoint: Geometry (1908), page 10. As you have already noted, the usual representation of the coordinate plane is quite late: I suppose that we cannot find it in any 19th Century treatise regarding Analytic Geometry.


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The book came out in 1977, not 1995; look at the year at the end of the Foreword that Marcus wrote. My copy has a copyright from 1977 too. LaTex or even TeX was not an option in 1977 since that was the year before the original version of TeX was released. The typesetting in the original version of Marcus was clearly done on a typewriter. I agree it is ...


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Actually Legendre proved, starting from a false theorem, that between $L$ and $L+2\sqrt{L}$ there is always a prime number, see the second edition of Essai sur la Théorie des Nombres at page 406 (paragraph 409). From the same theorem Desboves proved in 1855 as a corollary (p. 290, Corollary II) that there is always a prime number between two consecutive ...


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Merton and Scholes received the 1997 Nobel prize in Economics for the famous Black–Scholes–Merton model, which is a mathematical model for the dynamics of a financial market containing derivative investment instruments and the foundation of the mathematical finance.


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Yes, the reference is to Euler's Introductio in Analysin Infinitorum (Introduction to Analysis of the Infinite) in which Euler investigates infinite series. The reference seems to point to Volume 1, Chapter XV, which is titled "Concerning Series Arising From the Expansion of Factors." The English translation by Ian Bruce of the Introductio is in the public ...


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Here is a list of "Mathematicians who were awarded Nobel prize" taken from this paper 1902 Lorentz (Physics) 1904 Rayleigh (Physics) 1911 Wien (Physics) 1918 Planck (Physics) 1921 Einstein (Physics) 1922 Bohr (Physics) 1929 de Broglie (Physics) 1932 Heisenberg (Physics) 1933 Schroedinger (Physics) 1933 Dirac (Physics) 1945 Pauli (Physics) 1950 ...


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Not quite. There was some vagueness in Dedekind's early formulations, but the tendency was to use "Körper" or "field" when the multiplication is commutative from the start. As a curiosity, in Russian general division algebra is called тело, literally "body", which is apparently the translation of German Körper, as opposed to commutative поле, the translation ...


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With all due credit to Gauß, see the other answer, it seems to have been Adrien-Marie Legendre who first published this conjecturally. More precisely, on the last page of the introduction (p. 19) of the first edition of his Essai sur la théorie des nombres (1798), he says in a footnote: Au reste, il est vraisemblable que la formule rigoureouse qui donne ...


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Gauss also came up with the more discrete $n/\ln (n)$- in volume 10 of his collected works appears a short (5-6 pages) fragment entitled "asymptotic laws of arithmetics", which is dated to the year 1791. In [1] of this fragment Gauss states this approximation of the primes counting function, as well as additional conjecture on the asymptotics of k-prime ...


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Are you asking about the history of conjectures or the history of results? All conjectures were made on the basis of study of the tables of primes. The first proved result about this is due to Chebyshev. He proved that there exist constants $a$ and $A$ such that $$ax/\ln x<\pi(x)<Ax/\ln x.$$ Then Hadamard and Valle-Poussin independently proved that $$\...


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