Related papers: The Work of John Tate
This paper looks at Turing's postulations about Artificial Intelligence in his paper 'Computing Machinery and Intelligence', published in 1950. It notes how accurate they were and how relevant they still are today. This paper notes the…
This paper has two goals. The first goal is to show how an extension of second-order logic is a natural framework to formalize portions of Aristotle's \emph{Topics} and to bring to the foreground the logical, linguistic and philosophical…
We give a type system in which the universe of types is closed by reflection into it of the logical relation defined externally by induction on the structure of types. This contribution is placed in the context of the search for a natural,…
This is a philosophy paper rather than mathematical physics work. I will publish it in some other place.
The main aim of the paper is to formulate and prove a result about the structure of double affine Hecke algebras which allows its two commutative subalgebras to play a symmetric role. This result is essential for the theory of intertwiners…
Index of notation added. Shortening of some section, simplification of some of the arguments, some small added results and strengthening of thm 3.10. Also a significant re-writing of the last section.
This essay examines how automation has reconfigured mathematical proof and labor, and what might happen in the future. It discusses practical standards of proof, distinguishes between prominent forms of automation in research, provides…
As recommendation is essentially a comparative (or ranking) process, a good explanation should illustrate to users why an item is believed to be better than another, i.e., comparative explanations about the recommended items. Ideally, after…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
Comment: Elaboration on Two Points Raised in ``Classifier Technology and the Illusion of Progress'' [math.ST/0606441]
We develop a descriptive account of scientific reward in physics based on the concept of the time-dependent Polydoxon, defined as the structured set of empirically viable theories at a given time. We argue that highly rewarded…
This is a re-editing, which takes quantum mechanics into account, of Wittgenstein's famous Tractatus. The operation has a playful side in the form, but is a serious attempt to capture possible philosophical implications of the Relational…
A review of Jaynes' posthumous book "Probability Theory--The Logic of Science." I use scientific and personality elements gathered from other papers by Jaynes to help throw light on the origins of Jaynes' life quest.
The article aims at identifying what, from a structural point of view, AI based automatic translators cannot fully capture. It focuses on the machine's mistakes, in order to try to explain its causes. The biblical story of Ca\"in and Abel…
A recent article in which John Searle claims to refute dualism is examined from a scientific perspective.
This article was originally published in Topology 22 (1983). The present hyperTeXed redaction includes references to post-1983 results as Addenda, and corrects a few typographical errors. (See math.GT/0411115 for a more comprehensive…
The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.
The goal of this expository article is to present a proof that is as direct and elementary as possible of the fundamental theorem of complex multiplication (Shimura, Taniyama, Langlands, Tate, Deligne et al.). The article is a revision of…
This book deals with the theory of generalized algebraic transformations, which is elaborated with the aim to provide a relatively simple theoretical tool that enables an exact treatment of diverse more complex lattice-statistical models.…
This paper has been withdrawn by the author due to an error in the sufficient condition given for the proof of the Tate conjecture for Catanese surfaces.