Where I Am and Where I Need to Go

Pages 88-10

On the alleged simplicity of impure proof

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim

Theodor and Marcella Boveri : chromosomes and cytoplasm in heredity and development

The chromosome theory of heredity, developed in 1902–1904, became one of the foundation stones of twentieth-century genetics. It is usually referred to as the Sutton-Boveri theory after Walter Sutton and Theodor Boveri. However, the contributions of Theodor Boveri and his co-worker, Marcella O’Grady Boveri (also his wife), to the understanding of heredity and development go beyond the localization of the Mendelian hereditary factors onto the chromosomes. They investigated the interaction of cytoplasm and chromosomes, and demonstrated its relevance in heredity and development

A letter from Julie Pycior to Dr. Hector P. Garcia.

A letter from Julie Pycior to Dr. Hector P. Garcia, thanking him for his help with information on Lyndon John's relationship with Mexican Americans

A letter from Julie Pycior to Dr. Hector P. Garcia.

A letter from Julie Pycior to Dr. Hector P. Garcia, regarding an upcoming oral interview