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Academic literature on the topic 'Millennium Problems (Clay Mathematics Institute)'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Millennium Problems (Clay Mathematics Institute)"

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Maguru, Patrick. "A Case Study on Determining the Sequence of Prime Numbers in Fulfillment of Millennium Prize Problems from Clay Mathematics Institute." Journal of Statistics and Actuarial Research 8, no. 3 (2024): 1–8. http://dx.doi.org/10.47604/jsar.2776.

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Purpose: I have been serving as a civil servant in the Ministry of Environment and Natural Resources, department of Kenya Forestry Research Institute (KEFRI). Over the years, I developed a flare for research as a result of liaising at work for many years with various research programs that have been complementarily successful. After leaving KEFRI, I became instigated to come up with an idea that could bring a solution to one of the unsolved millennium prize problems hence, the research on the sequence of prime numbers. The seven millennium problems were selected by the Clay Mathematics Institu

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Temur, Z. Kalanov. "BRAIN Journal - Man versus Computer: Difference of the Essences. The Problem of the Scientific Creation." BRAIN: Broad Research in Artificial Intelligence and Neuroscience 8, no. 2 (2017): 151–78. https://doi.org/10.5281/zenodo.1045075.

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ABSTRACT In this study it is proposed the critical analysis of the creation of Artificial Intelligence (AI) and of Artificial General Intelligence (AGI). The unity of formal logic and rational dialectics is the methodological basis of the analysis. The main results of the analysis are as follows: (1) the model of man represents the unity of the two material aspects: “physiological body” (controllable aspect) and “psychical body” (controlling aspect); (2) the “psychical body” is the subsystem “subconsciousness + consciousness”; (3) in the comprehensive sense of the word, the thinking is an attr

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Talios, Vaggelis. "Quantum Theory, Standard Model, Yang-Mills (Mass Gap), and the New Model." Journal of Electrical Electronics Engineering 4, no. 2 (2025): 01–09. https://doi.org/10.33140/jeee.04.02.02.

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With the discovery of the atom by Einstein (1905) and the proof that atoms have subdivisions, Rutherford (1911), that they are composed of other smaller particles, the formation of the theory of Quantum, the theory of the particles that are inside the atom, began. It was first discovered that each atom consists of a nucleus which is also the solid part of the atom, which consists of protons (particles with a positive electromagnetic charge) and electrons (particles with a negative electromagnetic charge) around which other electrons revolve. Then it was discovered that the assumption that atom

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Roberts, Craig D. "Resonance Electroproduction and the Origin of Mass." EPJ Web of Conferences 241 (2020): 02008. http://dx.doi.org/10.1051/epjconf/202024102008.

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One of the greatest challenges within the Standard Model is to discover the source of visible mass. Indeed, this is the focus of a “Millennium Problem”, posed by the Clay Mathematics Institute. The answer is hidden within quantum chromodynamics (QCD); and it is probable that revealing the origin of mass will also explain the nature of confinement. In connection with these issues, this perspective will describe insights that have recently been drawn using contemporary methods for solving the continuum bound-state problem in relativistic quantum field theory and how they have been informed and e

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XU, RENXIN. "PULSARS: GIGANTIC NUCLEI." International Journal of Modern Physics E 20, supp01 (2011): 149–57. http://dx.doi.org/10.1142/s0218301311040190.

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What is the real nature of pulsars? This is essentially a question of the fundamental strong interaction between quarks at low-energy scale and hence of the non-perturbative quantum chromo-dynamics, the solution of which would certainly be meaningful for us to understand one of the seven millennium prize problems (i.e., "Yang-Mills Theory") named by the Clay Mathematical Institute. After a historical note, it is argued here that a pulsar is very similar to an extremely big nucleus, but is a little bit different from the gigantic nucleus speculated 80 years ago by L. Landau. The paper demonstra

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Louiz, Akram. "A Proof That the Set of NP-problems is Bigger Than the Set of P-problems by Using a Logical Consideration." WSEAS TRANSACTIONS ON COMPUTERS 22 (October 3, 2023): 159–70. http://dx.doi.org/10.37394/23205.2023.22.19.

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The field of informatics is the domain that emerged by applying the mathematical logic on electronic devices called computers in order to simplify many tasks for humans. The application of informatics in all economic and scientific areas is the most important factor that made our civilization reach our current phase of development. Nowadays, the experts and even the beginners of informatics are eager to use quantum computers. However, there is still an unsolved problem of classical theoretical informatics in ordinary electronic computers. It is the famous philosophical problem of the “Milleniu

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Neuberger, John, John Neuberger, and James Swift. "A linear condition determining local or global existence for nonlinear problems." Open Mathematics 11, no. 8 (2013). http://dx.doi.org/10.2478/s11533-013-0249-1.

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AbstractGiven a nonlinear autonomous system of ordinary or partial differential equations that has at least local existence and uniqueness, we offer a linear condition which is necessary and sufficient for existence to be global. This paper is largely concerned with numerically testing this condition. For larger systems, principals of computations are clear but actual implementation poses considerable challenges. We give examples for smaller systems and discuss challenges related to larger systems. This work is the second part of a program, the first part being [Neuberger J.W., How to distingu

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Frank, Vega. "Short Note about the Riemann Hypothesis." October 27, 2020. https://doi.org/10.5281/zenodo.4142165.

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In mathematics, the Riemann Hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $\frac{1}{2}$. Many consider it to be the most important unsolved problem in pure mathematics. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US 1,000,000 prize for the first correct solution. The Robin's inequality consists in $\sigma(n) < e^{\gamma } \times n \times \ln \ln n$ where $\sigma(n)$ is the sum-of-divisors function and $\gamma \approx 0.57721$ is the E

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Frank, Vega. "Properties of the First Possible Counterexample in the Robin's Inequality." October 29, 2020. https://doi.org/10.5281/zenodo.4150954.

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In mathematics, the Riemann Hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $\frac{1}{2}$. Many consider it to be the most important unsolved problem in pure mathematics. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US 1,000,000 prize for the first correct solution. In 1915, Ramanujan proved that under the assumption of the Riemann Hypothesis, the inequality $\sigma(n) < e^{\gamma } \times n \times \ln \ln n$ holds for all sufficiently large

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Frank, Vega. "On Solé and Planat criterion for the Riemann hypothesis." October 17, 2022. https://doi.org/10.5281/zenodo.7215522.

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The Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $\frac{1}{2}$. This is one of the Clay Mathematics Institute's Millennium Prize Problems. There are several statements equivalent to the famous Riemann hypothesis. In 2011, Sol{\'e} and Planat stated that the Riemann hypothesis is true if and only if the inequality $\zeta(2) \cdot \prod_{p\leq p_{k}} (1+\frac{1}{p}) > e^{\gamma} \cdot \log \theta(p_{k})$ holds for all prime numbers $p_{k}> 3$, where $\theta(x)$ is the Chebyshev

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Books on the topic "Millennium Problems (Clay Mathematics Institute)"

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Ellwood, D. (David), 1966- editor of compilation, Rodnianski, Igor, 1972- editor of compilation, Staffilani, Gigliola, 1966- editor of compilation, and Wunsch, Jared, editor of compilation, eds. Evolution equations: Clay Mathematics Institute Summer School, evolution equations, Eidgenössische Technische Hochschule, Zürich, Switzerland, June 23-July 18, 2008. American Mathematical Society, 2013.

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Clay Mathematics Institute Workshop on Moduli Spaces of Vector Bundles, with a View toward Coherent Sheaves (2006 Cambridge, Mass.). Grassmannians, moduli spaces, and vector bundles: Clay Mathematics Institute Workshop on Moduli Spaces of Vector Bundles, with a View towards Coherent Sheaves, October 6-11, 2006, Cambridge, Massachusetts. Edited by Ellwood D. (David) 1966- and Previato Emma. American Mathematical Society, 2011.

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3

Devlin, Keith. The Millennium Problems. Granta Books, 2005.

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Book chapters on the topic "Millennium Problems (Clay Mathematics Institute)"

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Wilson, Robin. "8. How to win a million dollars." In Number Theory: A Very Short Introduction. Oxford University Press, 2020. http://dx.doi.org/10.1093/actrade/9780198798095.003.0008.

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What is the Riemann hypothesis, and why does it matter? ‘How to win a million dollars’ looks in detail at Riemann’s conjecture. While Gauss attempted to explain why primes thin out, Bernhard Riemann in 1859 proposed an exact formula for the distribution of primes, employing Euler’s ‘zeta function’ and the idea of complex numbers. In 2000, the Clay Mathematics Institute offered a million dollars for the solutions of each of seven famous problems, of which the Riemann hypothesis was one. The Riemann hypothesis implies strong bounds on the growth of other arithmetic functions, in addition to the

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Conference papers on the topic "Millennium Problems (Clay Mathematics Institute)"

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RAHIMOV, Svetlana. "Istoria Didacticii Matematicii în contextul civilizației Mesopotamiene." In Inter/transdisciplinary approaches in the teaching of the real sciences, (STEAM concept) = Abordări inter/transdisciplinare în predarea ştiinţelor reale, (concept STEAM). Ion Creangă Pedagogical State University, 2023. http://dx.doi.org/10.46727/c.steam-2023.p128-132.

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What circumstances were the basis for the emergence of mathematics didactics? Initially, rudimentarily, some sporadic ideas attributable to this field resulted from the use of mathematics in everyday practice in the form of certain prescriptions or guidelines without clarification. Solving mathematical problems began to be a significant concern in educating the young generation as early as the second millennium BC. Over one million clay tablets contain various pieces of information, including accounting calculations and arithmetic operations based on the hexadecimal numeracy system.

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Venkataraman, P. "Approximate Analytical Solution for Laminar Flow Over a Backward Step." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46177.

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Analytical solution of Navier-Stokes equations are extremely difficult and rare. It is one of the unsolved Clay Millennium problems in mathematics. Many solutions that exist are examples of degenerate cases where the nonlinearity is controlled. In this paper we explore the application of Bézier functions to solve the two-dimensional laminar fluid flow over a backward step. The Bézier functions provide a mesh free alternative to domain discretization methods that are currently used to solve such problems. The Navier-Stokes equation are handled directly without transformation and the setup is di

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