Bonnie Mcclellan-Broussard

Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story.In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. The minute mathematicians open their mouths to explain something—the meaning of x, how to find y—they are framing a narrative. 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. 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. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Euclid’s proofs have roots in poetry and rhetoric. Mathematics, Lolli asserts, is not the mere manipulation of formulas.

From the very first moments of the universe to the birth of the first star, our solar system, and our planet: a physicist traces the known and the unknown. Since the beginning of the twentieth century, the horizon of our knowledge about the universe has expanded to encompass the infinitesimally small--and the infinitely vast. In First Dawn, physicist Roberto Battiston takes readers on a journey through space and time, to the boundaries of our knowledge and beyond. From the violence of the Big Bang and the birth of the first star, hundreds of millions of years later, to the emergence of our solar system, the dawn of life on Earth, and the possibility of life on other planets, Battiston maps what we know about the universe and how we came to know it--cautioning us, however, that what we know is a minuscule fraction of what there is to know. Battiston outlines discoveries by some of the greatest theoretical physicists of the twentieth century, including Einstein, Bohr, Schr dinger, Heisenberg, Fermi, and Hubble; discusses the mysteries of dark energy and dark matter; and considers what it means for the universe to have emerged out of nothing. The ignition of the first star illuminated a universe that had been expanding, unobserved and unobservable, in the dark. Drawing on his own research, Battiston discusses the birth of the Sun, the formation of planets, the origins of life, interstellar migrations, extrasolar planets, black holes, gravitational waves, and much more. But, he warns, for some questions--the dimensions of the universe, for example, or the existence of other universes--we are destined to remain in the realm of speculation.