Thoughts on the Riemann Hypothesis

Chaitin, G. J.
January 2004
Mathematical Intelligencer;Winter2004, Vol. 26 Issue 1, p4
Academic Journal
Focuses on the involvement of Riemann Hypothesis (RH) in the notion of randomness. Addition of RH as an axioms. Sources of the mathematical knowledge; Definition of algorithmic randomness.


Related Articles

  • Foundations for Mathematical Structuralism. NODELMAN, URI; ZALTA, EDWARD N. // Mind;Jan2014, Vol. 123 Issue 489, p39 

    We investigate the form of mathematical structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to criticisms recently, and our view is that the problems raised are resolved by proper, mathematics-free...

  • Informal versus formal mathematics. Francisco Doria // Synthese;Feb2007, Vol. 154 Issue 3, p401 

    Abstract??We discuss Kunen?s algorithmic implementation of a proof for the Paris?Harrington theorem, and the author?s and da Costa?s proposed ?exotic? formulation for theP=?NPhypothesis. Out of those two examples we ponder the relation between mathematics within an axiomatic framework, and...

  • The Influence of Epistemology on the Design of Artificial Agents. Lee, M. H.; Lacey, N. J. // Minds & Machines;Aug2003, Vol. 13 Issue 3, p367 

    Unlike natural agents, artificial agents are, to varying extent, designed according to sets of principles or assumptions. We argue that the designer's philosophical position on truth, belief and knowledge has far reaching implications for the design and performance of the resulting agents. Of...

  • Structuralism's Unpaid Epistemological Debts. HALE, BOB // Philosophia Mathematica;Jan1996, Vol. 4 Issue 2, p124 

    One kind of structuralism holds that mathematics is about structures, conceived as a type of abstract entity. Another denies that it is about any distinctively mathematical entities at all—even abstract structures; rather it gives purely general information about what holds of any...

  • Syntactic foundations for unawareness of theorems. Galanis, Spyros // Theory & Decision;Oct2011, Vol. 71 Issue 4, p593 

    We provide a syntactic model of unawareness. By introducing multiple knowledge modalities, one for each sub-language, we specifically model agents whose only mistake in reasoning (other than their unawareness) is to underestimate the knowledge of more aware agents. We show that the model is a...

  • the·o·rem.  // American Heritage Student Science Dictionary;2009, p341 

    A definition of the term "theorem" is presented. It refers to a mathematical statement whose truth can be proved on the basis of a given set of axioms or assumptions.

  • DEFINING KNOWLEDGE IN TERMS OF BELIEF: THE MODAL LOGIC PERSPECTIVE. Halpern, Joseph Y.; Samet, Dov; Segev, Ella // Review of Symbolic Logic;Sep2009, Vol. 2 Issue 3, p469 

    The question of whether knowledge is definable in terms of belief, which has played an important role in epistemology for the last 50 years, is studied here in the framework of epistemic and doxastic logics. Three notions of definability are considered: explicit definability, implicit...

  • Assessing Parameter Invariance in the BLIM: Bipartition Models. Chiusole, Debora; Stefanutti, Luca; Anselmi, Pasquale; Robusto, Egidio // Psychometrika;Oct2013, Vol. 78 Issue 4, p710 

    In knowledge space theory, the knowledge state of a student is the set of all problems he is capable of solving in a specific knowledge domain and a knowledge structure is the collection of knowledge states. The basic local independence model (BLIM) is a probabilistic model for knowledge...

  • What Harvard statisticians don't tell us. Shvyrkov, Vladislav V. // Quality & Quantity;1987, Vol. 21 Issue 4, p335 

    To make good decision one needs good data and for that statisticians need to develop a new quality philosophy regarding a datum and a data set. Experience is the starting and end point of knowledge. Statistical research also starts from experience or observation, then formulates two types of...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics