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The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field.His seminal work had a profound impact in numerous areas of mathematics and he is widely credited for introducing and popularizing modern notation and terminology.
Examples of unexpected applications of mathematical theories can be found in many areas of mathematics. A notable example is the prime factorization of natural numbers that was discovered more than 2,000 years before its common use for secure internet communications through the RSA cryptosystem. [127]
In these papers, Poincaré introduced the notions of homology and the fundamental group, provided an early formulation of Poincaré duality, gave the Euler–Poincaré characteristic for chain complexes, and mentioned several important conjectures including the Poincaré conjecture, demonstrated by Grigori Perelman in 2003.
A Mathematician's Apology 1st edition Author G. H. Hardy Subjects Philosophy of mathematics, mathematical beauty Publisher Cambridge University Press Publication date 1940 OCLC 488849413 A Mathematician's Apology is a 1940 essay by British mathematician G. H. Hardy which defends the pursuit of mathematics for its own sake. Central to Hardy's "apology" – in the sense of a formal justification ...
Euler's identity is a special case of Euler's formula, which the physicist Richard Feynman called "our jewel" and "the most remarkable formula in mathematics". [7] Modern examples include the modularity theorem, which establishes an important connection between elliptic curves and modular forms (work on which led to the awarding of the Wolf ...
It is in this essay that the term 'potential function' first occurs. Herein also his remarkable theorem in pure mathematics, since universally known as Green's theorem, and probably the most important instrument of investigation in the whole range of mathematical physics, made its appearance. We are all now able to understand, in a general way ...
The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics, and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.
Elementary mathematics, also known as primary or secondary school mathematics, is the study of mathematics topics that are commonly taught at the primary or secondary school levels around the world. It includes a wide range of mathematical concepts and skills, including number sense , algebra , geometry , measurement , and data analysis .