Thoughts on the riemann hypothesis
@article{Chaitin2003ThoughtsOT,
title={Thoughts on the riemann hypothesis},
author={Gregory J. Chaitin},
journal={The Mathematical Intelligencer},
year={2003},
volume={26},
pages={4-7}
}The Opinion column offers mathematicians the opportunity to write about any issue of interest to the international mathematical community. Disagreement and controversy are welcome. The views and opinions expressed here, however, are exclusively those of the author, and neither the publisher nor the editor-in-chief endorses or accepts responsibility for them. An Opinion should be submitted to the editor-in-chief, Chandler Davis.
20 Citations
A Probabilistic Approach to the Generalized Riemann Hypothesis
- Mathematics
- 2003
In this brief note, which is a follow-up to the recently archived note “A Probabilistic Approach to the Riemann Hypothesis” (2003), we attempt to use the same approach discussed in that paper to…
A Probabilistic Approach to the Riemann Hypothesis
- Mathematics
- 2003
In this brief note, inspired by the recent article by Gregory Chaitin “Thoughts on the Riemann Hypothesis” (2003), we explore a probabilistic approach to proving the Riemann Hypothesis which attempts…
Implications of Experimental Mathematics for the Philosophy of Mathematics
- Philosophy
- 2008
Somewhat unusually, I can exactly place the day at registration that I became a mathematician and I recall the reason why. I was about to deposit my punch cards in the ‘honours history bin’. I…
A New Measure of the Difficulty of Problems
- MathematicsJ. Multiple Valued Log. Soft Comput.
- 2006
According to a measure proposed, Riemann Hypothesis is more complex than Goldbach’s Conjecture and the Collatz 3x+1 Problem is finitely refutable; consequently, the method cannot be applied, hence stronger versions of this problem are studied.
2 1 Ju l 2 00 5 Complexity Theory for Simpletons
- Mathematics
- 2005
In this article, we shall describe some of the most interesting topics in the subject of Complexity Theory for a general audience. Anyone with a solid foundation in high school mathematics (with some…
Experimental Mathematics in Action
- Computer Science
- 2007
The goal in this book is to present a coherent variety of accessible examples of modern mathematics where intelligent computing plays a significant role and in so doing to highlight some of the key algorithms and to teach some the key experimental approaches.
Complexity Science for Simpletons
- EducationArXiv
- 2005
Two other famous mathematics problems, the Collatz 3n + 1 Conjecture and the Riemann Hypothesis are described, and both Chaitin’s incompleteness theorem and Wolfram's notion of “computational irreducibility” are important for understanding why no one has, as of yet, solved these two problems.
The Riemann Zeros as Spectrum and the Riemann Hypothesis
- MathematicsSymmetry
- 2019
A spectral realization of the Riemann zeros based on the propagation of a massless Dirac fermion in a region of Rindler spacetime and under the action of delta function potentials localized on the square free integers suggests a proof of theRiemann hypothesis in the limit where the potentials vanish.
Fractal Supersymmetric Qm, Geometric Probability and the Riemann Hypothesis
- Mathematics
- 2004
The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form sn=1/2+iλn. Earlier work on the RH based on supersymmetric QM, whose potential was related…
Möbius convolutions and the Riemann hypothesis
- MathematicsInt. J. Math. Math. Sci.
- 2005
The well-known necessary and sufficient criteria for the Riemann hypothesis of M. Riesz and of Hardy and Littlewood are embedded in a general theorem for a class of entire functions, which in turn is seen to be a consequence of a rather transparent convolution criterion.
References
SHOWING 1-9 OF 9 REFERENCES
New Directions in the Philosophy of Mathematics
- PhilosophyPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
- 1984
Mathematical axioms have traditionally been thought of as obvious or self-evident truths, but current set theoretic work in the search for new axioms belies this conception. This raises…
Information-Theoretic Limitations of Formal Systems
- Computer ScienceJACM
- 1974
An attempt is made to apply information-theoretic computational complexity to meta-mathematics by measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the theoremic proofs.
From Philosophy to Program Size
- Philosophy
- 2003
Most work on computational complexity is concerned with time. However this course will try to show that program-size complexity, which measures algorithmic information, is of much greater…
Two Philosophical Applications of Algorithmic Information Theory
- PhilosophyDMTCS
- 2003
Two philosophical applications of the concept of program-size complexity are discussed and it is proposed that the notion of algorithmic independence sheds light on the question of being and how the world of the authors' experience can be partitioned into separate entities.
Apostolos Doxiadis home page
- Apostolos Doxiadis home page
Experimental mathematics website
- Experimental mathematics website
Mertens function
- Mertens function