joseph mazur - Academia.edu (original) (raw)
Papers by joseph mazur
Transactions of the American Mathematical Society, 1975
Artin's conditions for the existence of a new contraction of an algebraic subspace are changed. T... more Artin's conditions for the existence of a new contraction of an algebraic subspace are changed. The new conditions are more applicable in special cases, especially when the subspace has a conormal bundle.
The Mathematical Intelligencer
The Mathematical Intelligencer, 2016
Enlightening Symbols, 2014
Nature, 2007
Had Keats lived long enough to read Ian Stewart's latest book, Why Beauty is Truth, he might have... more Had Keats lived long enough to read Ian Stewart's latest book, Why Beauty is Truth, he might have been inspired to write a sixth great ode, soft-piping sweet melodies in praise of symmetry. But what did Keats mean in Ode on a Grecian Urn when he wrote some of the most famous lines in English poetry: "Beauty is truth, truth beauty-that is all/ Ye know on earth, and all ye need to know"? Stewart is onto something deep, something mathematicians must have been keenly aware of since Greeks began turning urns. What is the underlying beauty of mathematics? Is it the artful way a proof is expressed? Or is it something deeper-something guiding pythagorean and platonist mathematicians to see better, something at the molecular structure of mathematics, some "unravish'd bride of quietness", some "Attic shape"-that enlightens and delights us. Stewart, a professor of mathematics at the University of Warwick, is renowned for his popular science books, but Why Beauty is Truth is without a doubt his finest. If it were just an authentic history of mathematics, it would be creditable. If it were only for its lively informal style, its historical characters, its intrigue ("The Galois group has a terrible secret"), its beautiful prose, it would be praiseworthy. Yet, its real uniqueness-its power-is in what it uncovers. It brings us the heart of why mathematicians pursue mathematics. Beauty is not always as visible as the iridescent butterfly on the cover of Stewart's book. We are aware that it is not the dazzling colour that makes such an insect beautiful, but rather its shape, in particular its symmetry. It is this kind of beauty that Stewart's book reveals. We encounter it most obviously when we perceive it in geometry, in the wings of a butterfly, the sections of a cone, or the appearance of regular solids. But Stewart wants us to 'see' the invisible symmetries of algebra. He starts with Évariste Galois, a young nineteenth-century French revolutionary who saw
Philosophical Investigations, 1989
Transactions of the American Mathematical Society, 1975
Artin's conditions for the existence of a new contraction of an algebraic subspace are changed. T... more Artin's conditions for the existence of a new contraction of an algebraic subspace are changed. The new conditions are more applicable in special cases, especially when the subspace has a conormal bundle.
The Mathematical Intelligencer
The Mathematical Intelligencer, 2016
Enlightening Symbols, 2014
Nature, 2007
Had Keats lived long enough to read Ian Stewart's latest book, Why Beauty is Truth, he might have... more Had Keats lived long enough to read Ian Stewart's latest book, Why Beauty is Truth, he might have been inspired to write a sixth great ode, soft-piping sweet melodies in praise of symmetry. But what did Keats mean in Ode on a Grecian Urn when he wrote some of the most famous lines in English poetry: "Beauty is truth, truth beauty-that is all/ Ye know on earth, and all ye need to know"? Stewart is onto something deep, something mathematicians must have been keenly aware of since Greeks began turning urns. What is the underlying beauty of mathematics? Is it the artful way a proof is expressed? Or is it something deeper-something guiding pythagorean and platonist mathematicians to see better, something at the molecular structure of mathematics, some "unravish'd bride of quietness", some "Attic shape"-that enlightens and delights us. Stewart, a professor of mathematics at the University of Warwick, is renowned for his popular science books, but Why Beauty is Truth is without a doubt his finest. If it were just an authentic history of mathematics, it would be creditable. If it were only for its lively informal style, its historical characters, its intrigue ("The Galois group has a terrible secret"), its beautiful prose, it would be praiseworthy. Yet, its real uniqueness-its power-is in what it uncovers. It brings us the heart of why mathematicians pursue mathematics. Beauty is not always as visible as the iridescent butterfly on the cover of Stewart's book. We are aware that it is not the dazzling colour that makes such an insect beautiful, but rather its shape, in particular its symmetry. It is this kind of beauty that Stewart's book reveals. We encounter it most obviously when we perceive it in geometry, in the wings of a butterfly, the sections of a cone, or the appearance of regular solids. But Stewart wants us to 'see' the invisible symmetries of algebra. He starts with Évariste Galois, a young nineteenth-century French revolutionary who saw
Philosophical Investigations, 1989