The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory.
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The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. It also presents a model of elementary particle physics based on noncommutative geometry. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. roblem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the p. The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. Noncommutative Geometry, Quantum Fields and Motives (Paperback) Mathematics, Lolli asserts, is not the mere manipulation of formulas. Euclid's proofs have roots in poetry and rhetoric. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Just as fairy tales offer a narrative structure in which new characters can be inserted into recurring forms of the genre in original ways, in mathematics, each new abstract concept is the protagonist of a different theory supported by the general techniques of mathematical reasoning. Every proof is the story of an adventure, writes Lolli, a journey into an unknown land to open a new, connected route once the road is open, we correct it, expand it.
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The minute mathematicians open their mouths to explain something-the meaning of x, how to find y-they are framing a narrative.
Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. ctions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Why mathematics is not merely formulaic- an argument that to write a mathematical proof is tantamount to inventing a story. The Meaning of Proofs: Mathematics as Storytelling (Trade Paperback / Paperback)īy Lolli, Gabriele Mcclellan-Broussard, Bonnie Foreword by Marcolli, Matilde
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