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Journal articles on the topic 'Bernhard Riemann'

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Published: 5 June 2025

Last updated: 16 July 2025

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1

Ravindran, Renuka. "Bernhard Riemann." Resonance 11, no. 11 (2006): 3–4. http://dx.doi.org/10.1007/bf02834468.

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Hoare, Graham. "Bernhard Riemann’s legacy of 1859." Mathematical Gazette 93, no. 528 (2009): 468–75. http://dx.doi.org/10.1017/s0025557200185213.

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The German version of Riemann’s Collected Works is confined to a single volume of 690 pages. Even so, this volume has had an abiding and profound impact on modern mathematics and physics, as we shall see. In fifteen years of activity, from 1851, when he gained his doctorate at the University of Göttingen, to his death in 1866, two months short of his fortieth birthday, Riemann contributed to almost all areas of mathematics. He perceived mathematics from the analytic point of view and used analysis to illuminate subjects as diverse as number theory and geometry. Although regarded principally as a mathematician Riemann had an abiding interest in physics and researched significantly in the methods of mathematical physics, particularly in the area of partial differential equations.

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Bayer, Pilar. "La hipòtesi de Riemann: El gran repte pendent." Mètode Revista de difusió de la investigació, no. 8 (June 5, 2018): 35. http://dx.doi.org/10.7203/metode.0.8903.

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The Riemann hypothesis is an unproven statement referring to the zeros of the Riemann zeta function. Bernhard Riemann calculated the first six non-trivial zeros of the function and observed that they were all on the same straight line. In a report published in 1859, Riemann stated that this might very well be a general fact. The Riemann hypothesis claims that all non-trivial zeros of the zeta function are on the the line x = 1/2. The more than ten billion zeroes calculated to date, all of them lying on the critical line, coincide with Riemann’s suspicion, but no one has yet been able to prove that the zeta function does not have non-trivial zeroes outside of this line.

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Widder, Nathan. "The Mathematics of Continuous Multiplicities: The Role of Riemann in Deleuze's Reading of Bergson." Deleuze and Guattari Studies 13, no. 3 (2019): 331–54. http://dx.doi.org/10.3366/dlgs.2019.0361.

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A central claim of Deleuze's reading of Bergson is that Bergson's distinction between space as an extensive multiplicity and duration as an intensive multiplicity is inspired by the distinction between discrete and continuous manifolds found in Bernhard Riemann's 1854 thesis on the foundations of geometry. Yet there is no evidence from Bergson that Riemann influences his division, and the distinction between the discrete and continuous is hardly a Riemannian invention. Claiming Riemann's influence, however, allows Deleuze to argue that quantity, in the form of ‘virtual number’, still pertains to continuous multiplicities. This not only supports Deleuze's attempt to redeem Bergson's argument against Einstein in Duration and Simultaneity, but also allows Deleuze to position Bergson against Hegelian dialectics. The use of Riemann is thereby an important element of the incorporation of Bergson into Deleuze's larger early project of developing an anti-Hegelian philosophy of difference. This article first reviews the role of discrete and continuous multiplicities or manifolds in Riemann's Habilitationsschrift, and how Riemann uses them to establish the foundations of an intrinsic geometry. It then outlines how Deleuze reinterprets Riemann's thesis to make it a credible resource for Deleuze's Bergsonism. Finally, it explores the limits of this move, and how Deleuze's later move away from Bergson turns on the rejection of an assumption of Riemann's thesis, that of ‘flatness in smallest parts’, which Deleuze challenges with the idea, taken from Riemann's contemporary, Richard Dedekind, of the irrational cut.

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Narasimhan, Raghavan. "Bernhard Riemann Remarks on his Life and Work." Milan Journal of Mathematics 78, no. 1 (2010): 3–10. http://dx.doi.org/10.1007/s00032-010-0116-5.

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Calamari, Martin. "Riemann–Weyl in Deleuze's Bergsonism and the Constitution of the Contemporary Physico-Mathematical Space." Deleuze Studies 9, no. 1 (2015): 59–87. http://dx.doi.org/10.3366/dls.2015.0174.

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In recent years, the ideas of the mathematician Bernhard Riemann (1826–66) have come to the fore as one of Deleuze's principal sources of inspiration in regard to his engagements with mathematics, and the history of mathematics. Nevertheless, some relevant aspects and implications of Deleuze's philosophical reception and appropriation of Riemann's thought remain unexplored. In the first part of the paper I will begin by reconsidering the first explicit mention of Riemann in Deleuze's work, namely, in the second chapter of Bergsonism (1966). In this context, as I intend to show first, Deleuze's synthesis of some key features of the Riemannian theory of multiplicities (manifolds) is entirely dependent, both textually and conceptually, on his reading of another prominent figure in the history of mathematics: Hermann Weyl (1885–1955). This aspect has been largely underestimated, if not entirely neglected. However, as I attempt to bring out in the second part of the paper, reframing the understanding of Deleuze's philosophical engagement with Riemann's mathematics through the Riemann–Weyl conjunction can allow us to disclose some unexplored aspects of Deleuze's further elaboration of his theory of multiplicities (rhizomatic multiplicities, smooth spaces) and profound confrontation with contemporary science (fibre bundle topology and gauge field theory). This finally permits delineation of a correlation between Deleuze's plane of immanence and the contemporary physico-mathematical space of fundamental interactions.

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Ting, John Y. C. "Rigorous Proof for Riemann Hypothesis Using the Novel Sigma-power Laws and Concepts from the Hybrid Method of Integer Sequence Classification." Journal of Mathematics Research 8, no. 3 (2016): 9. http://dx.doi.org/10.5539/jmr.v8n3p9.

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Proposed by Bernhard Riemann in 1859, Riemann hypothesis refers to the famous conjecture explicitly equivalent to the mathematical statement that the critical line in the critical strip of Riemann zeta function is the location for all non-trivial zeros. The Dirichlet eta function is the proxy for Riemann zeta function. We treat and closely analyze both functions as unique mathematical objects looking for key intrinsic properties and behaviors. We discovered our key formula (coined the Sigma-power law) which is based on our key Ratio (coined the Riemann-Dirichlet Ratio). We recognize and propose the Sigma-power laws (in both the Dirichlet and Riemann versions) and the Riemann-Dirichlet Ratio, together with their various underlying mathematically-consistent properties, in providing crucial \textit{de novo} evidences for the most direct, basic and elementary mathematical proof for Riemann hypothesis. This overall proof is succinctly summarized for the reader by the sequential Theorem I to IV in the second paragraph of Introduction section. Concepts from the Hybrid method of Integer Sequence classification are important mathematical tools employed in this paper. We note the intuitively useful mental picture for the idea of the Hybrid integer sequence metaphorically becoming the non-Hybrid integer sequence with certain criteria obtained using Ratio study.

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Abbott, Steve, Detlef Laugwitz, Abe Shenitzer, Michael Monastyrsky, and Roger Cooke. "Bernhard Riemann 1826-1866: Turning Points in the Conception of Mathematics." Mathematical Gazette 84, no. 499 (2000): 162. http://dx.doi.org/10.2307/3621537.

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Derbyshire, John, and Mark P. Silverman. "Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics." American Journal of Physics 73, no. 3 (2005): 287–88. http://dx.doi.org/10.1119/1.1858489.

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Wolfson, Paul R. "Bernhard Riemann, 1826–1866: Turning Points in the Conception of Mathematics." Historia Mathematica 30, no. 2 (2003): 223–26. http://dx.doi.org/10.1016/s0315-0860(02)00011-3.

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Haight, David F. "Why the Glove of Mathematics Fits the Hand of the Natural Sciences So Well :How Far Down the (Fibonacci) Rabbit Hole Goes." European Scientific Journal, ESJ 12, no. 15 (2016): 1. http://dx.doi.org/10.19044/esj.2016.v12n15p1.

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Why does the glove of mathematics fit the hand of the natural sciences so well? Is there a good reason for the good fit? Does it have anything to do with the mystery number of physics or the Fibonacci sequence and the golden proportion? Is there a connection between this mystery (golden) number and Leibniz’s general question, why is there something (one) rather than nothing (zero)? The acclaimed mathematician G.H. Hardy (1877-1947) once observed: “In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy.” Is this also true of great physics? If so, is there a simple “preestablished harmony” or linchpin between their respective ultimate foundations? The philosopher-mathematician, Gottfried Leibniz, who coined this phrase, believed that he had found that common foundation in calculus, a methodology he independently discovered along with Isaac Newton. But what is the source of the harmonic series of the natural log that is the basis of calculus and also Bernhard Riemann’s harmonic zeta function for prime numbers? On the occasion of the three-hundredth anniversary of Leibniz’s death and the one hundredth-fiftieth anniversary of the death of Bernhard Riemann, this essay is a tribute to Leibniz’s quest and questions in view of subsequent discoveries in mathematics and physics. (In the Journal of Interdisciplinary Mathematics, Dec. 2008 and Oct. 2010, I have already sympathetically discussed in detail Riemann’s hypothesis and the zeta function in relation to primes and the zeta zeros. Both papers were republished online in 2013 by Taylor and Francis Scientific Publishers Group.)

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Demailly, Jean-Pierre. "Holomorphic Morse Inequalities and Asymptotic Cohomology Groups: A Tribute to Bernhard Riemann." Milan Journal of Mathematics 78, no. 1 (2010): 265–77. http://dx.doi.org/10.1007/s00032-010-0118-3.

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Shun, Lam Kai. "The Quantized Constants with Remmen’s Scattering Amplitude to Explain Riemann Zeta Zeros." International Journal of English Language Teaching 11, no. 4 (2023): 20–33. http://dx.doi.org/10.37745/ijelt.13/vol11n42033.

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Riemann Hypothesis has been proposed by Bernhard Riemann since year 1859. Nowadays, there are lots of proof or disproof all over the internet society or the academic professional authority etc. However, none of them is accepted by the Clay’s Mathematics Institute for her Millennium Prize. In the past few months, this author discovered that there may be a correlation exists between the real and imaginary parts of Riemann Zeta function for the first 10 non-trivial zeros of the Riemann function etc. Indeed, when one tries to view the correlation relationship as a constant like the Planck’s one. Then we may show that Riemann Zeta zeros are indeed discrete quantum energy levels or the discrete spectrum as electrons falling from some bound quantum state to a lower energy state (or Quantum Field Theory). That may be further explained by Remmen’s scattering amplitude or the S-matrix. We may approximate the S-matrix by applying the HKLam theory to it and predict the scattering amplitude or even the Riemann Zeta non-trival zeros etc. By the way, the key researching equations or formula in the following content will be around the Taylor expansion of the Riemann Zeta function, their convergence etc. In additional, I will also investigate the (*’’) as shown below: ∏_(i=1)^∞▒(z-z_i ) = ξ(0.5 + i*t) = (∑_(n=1)^∞▒1)⁄n^((0.5+i*t) ) = ∏_(j=1)^∞▒(1-1⁄(p_j^((0.5+i*t) ) ))^(-1) ------------ (*’’) as we may find the existence of some constants like the Planck’s one. For the application of the aforementioned scholarly outcome, it is well-known that if one can find the pattern of the appearance to the prime number and hence break the public key cryptography in the everyday usage of information technology security etc.

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THANH LE, DUC, and THUY THI THU LE. "Propose a Solution That Confirms the Riemann Hypothesis is Correct." International Journal of Advanced Engineering and Management Research 09, no. 06 (2024): 110–19. https://doi.org/10.51505/ijaemr.2024.9608.

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Bernhard Reimann proposed his hypothesis in 1859. Until now, after 165 years of existence, no one has yet proven this hypothesis. Due to the nature of the hypothesis’s contribution to modern mathematics. It is necessary to prove the hypothesis. The approach to solving the problem is using classical physics and mathematical knowledge to find a value that satisfies the constraint. Then, prove that this value is unique. To do this, the author uses MATLAB (2023a) calculation software. The results of the research process show the correctness of the hypothesis. However, the specific characteristics of the current calculation tool still need to be met, so more appropriate programs are needed in the future to solve the problem. Many theories have been proposed to solve the Reimann hypothesis but have failed. This article has resolved and ended the lack of proof for the Reimann hypothesis

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15

Cooke, Roger. "Book Review: Bernhard Riemann, 1826--1866: Turning points in the conception of mathematics." Bulletin of the American Mathematical Society 37, no. 04 (2000): 477–81. http://dx.doi.org/10.1090/s0273-0979-00-00876-4.

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Ritchey, Tom. "Analysis and synthesis: On scientific method - based on a study by bernhard riemann." Systems Research 8, no. 4 (1991): 21–41. http://dx.doi.org/10.1002/sres.3850080402.

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17

Leite, Fábio Rodrigo. "Pierre Duhem: Um Filósofo do Senso Comum." Revista de Filosofia Moderna e Contemporânea 6, no. 1 (2018): 267–304. http://dx.doi.org/10.26512/rfmc.v6i1.20411.

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O presente artigo visa a elucidar os fundamentos da metodologia científica de Pierre Duhem, realçando alguns aspectos anti-convencionalistas da mesma. Argumentamos que seu método ampara-se em noções e princípios provenientes do senso comum. Inicialmente, distinguimos os significados que este conceito assume ao longo de sua obra, comparando-o com a noção de bom senso, para, em seguida, justificarmos por que suas críticas a Wilhelm Ostwald, Albert Einstein e Bernhard Riemann, feitas em nome do senso comum, não envolvem, como alguns importantes estudiosos supuseram, contradição alguma. Por fim, sustentamos que sua obra de maturidade, especialmente A ciência alemã, apesar de resultante do clima intelectual belicoso, deve ser alçada ao mesmo patamar de importância geralmente atribuído a A teoria física.

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Keating, Jonathan P. "Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics John Derbyshire Joseph Henry Press, Washington, DC, 2003. $27.95 (422 pp.). ISBN 0-309-08549-7." Physics Today 57, no. 6 (2004): 63–64. http://dx.doi.org/10.1063/1.1784281.

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19

Ahn, Sungyong. "Symmetrifying Smart Home." Media Theory 5, no. 1 (2021): 89–114. http://dx.doi.org/10.70064/mt.v5i1.911.

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This paper investigates how the current domestic application of the Internet of Things (IoT), called “smart home,” changes the socio-phenomenological meaning of place-making. It describes a smart home as a topological continuum that could unfold lots of functional spaces—those optimized for a variety of predictable user behaviors and intentions, such as going to bed, working out, and energy-saving—according to how software applications redeploy its embedded sensors and actuators into certain algorithmic orders. This continuum once buried under people’s daily routines is constantly re-excavated in a smart home and re-differentiated into the new service domains of the IoT. This paper develops a topological framework to analyze the new form of media power behind this perpetual place-binding of smart spaces, which I term topological power. For this goal, it borrows Bernhard Riemann and Henri Poincaré’s mathematical thinking of manifold, or multiplicity, beneath the geometric structure of space.

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Rowe, David E. "Bernhard Riemann, 1826-1866: Turning Points in the Conception of Mathematics. Detlef Laugwitz , Abe Shenitzer , Hardy Grant , Sarah Shenitzer." Isis 92, no. 4 (2001): 790–91. http://dx.doi.org/10.1086/385402.

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Sinaceur, Mohammed Allal. "Dedekind et le programme de Riemann. Suivi de la traduction de Analytische Untersuchungen zu Bernhard Riemann's Abhandlungen uber die Hypothesen, welche der Geometrie zu Grunde Liegen par R. Dedekind." Revue d'histoire des sciences 43, no. 2 (1990): 221–96. http://dx.doi.org/10.3406/rhs.1990.4165.

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Leite, Fábio Rodrigo. "Pierre Duhem considéré comme un philosophe du sens commun." Revue des questions scientifiques 190, no. 1-2 (2019): 99–150. http://dx.doi.org/10.14428/qs.v190i1-2.69463.

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L’objet primordial de cet article consiste à présenter une analyse du concept de sens commun et de son rôle dans la méthodologie scientifique de Pierre Duhem. Nous tenterons de distinguer quelques-uns de ses principaux sens afin de mettre en évidence la façon dont, dans l’un d’entre eux, le sens commun peut légitimement agir en tant que critère accidentel pour juger les théories physiques. Dans ce même sens, compris comme une base de notions, principes et aspirations justes et irrésistibles, dérivent deux de ses principes méthodologiques fondamentaux, à savoir, les principes d’unité inter-théorique et de classification naturelle, en produisant ce que nous dénommons réalisme méthodologique. C’est cette même notion de sens commun, réellement distincte de la notion de bon sens, apanage des scientifiques expérimentés, qu’il utilise dans sa critique envers la science allemande, principalement contre les théories de Wilhelm Ostwald, Albert Einstein et Bernhard Riemann. Nous soutiendrons, contrairement à ce que certains interprètes supposèrent, que de telles critiques n’entraînent aucune contradiction dans sa pensée. Ceci étant dit, nous soutenons que les publications duhémiennes de maturité, surtout La science allemande, bien que résultant du climat intellectuel belliqueux, doivent être élevées au même niveau d’importance que celui généralement attribué à La théorie physique Enfin, nous chercherons à mettre en exergue, bien que brièvement, et toujours sur base du concept de sens commun, certaines similitudes existant entre Duhem, quelques néothomistes qui lui étaient contemporains, particulièrement Réginald Garrigou-Lagrange et, également, Blaise Pascal, en pensant pouvoir montrer que les éléments qui les unissent font de l’auteur de La théorie physique et, peut-être même de chacun d’entre eux, un philosophe du sens commun. * * * The primary aim of this article is to present an analysis of the concept of common sense and of its role in Pierre Duhem’s scientific methodology. We will attempt to define some of its key meanings in order to identify how, in one of them, common sense can legitimately act as an accidental criterion for assessing physical theories. Following the same line of thought, understood as a basis of just and irresistible concepts, principles and aspirations, two of its fundamental methodological principles are derived, namely, the principles of inter-theoretical unity and natural classification, by producing what can be termed as methodological realism. It is this same notion of common sense, truly separate from the notion of good sense, the privilege of experienced scientists, which he uses in his criticism of German science, mainly regarding the theories of Wilhelm Ostwald, Albert Einstein and Bernhard Riemann. We will argue, contrary to what certain interpreters assumed, that such criticism does not lead to any contradiction in his thinking. This being said, we maintain that the mature Duhemian publications, especially German science, although stemming from a belligerent intellectual climate, must be raised to the same level of importance as that generally attributed to The aim and structure of physical theory. Finally, we will seek to highlight, albeit briefly, and still based on the concept of common sense, certain similarities existing between Duhem, various contemporary neo-Thomists, especially Réginald Garrigou-Lagrange, but also Blaise Pascal, in the hopes of showing that the elements uniting them make this author of theoretical physics, and perhaps even all of them, a common-sense philosopher.

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Baylis, John. "Prime obsession - Bernhard Riemann and the greatest unsolved problem in mathematics, by John Derbyshire. Pp. 448. £19.95. 2003. ISBN 0 309 08549 7 (Joseph Henry Press)." Mathematical Gazette 89, no. 515 (2005): 327–30. http://dx.doi.org/10.1017/s0025557200177976.

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Gantenbein, Urs Leo. "Laugwitz, Detlef. Bernhard Riemann 1826-1866.Turning points in the conception of mathematics. Transi, by Abe Shenitzer. Boston etc., Birkhäuser, 1999. XVI, 357 S. 111., Portr. SFr. 148.-; DM 178.-. ISBN 0-8176-4040-1." Gesnerus 58, no. 3-4 (2001): 374. http://dx.doi.org/10.1163/22977953-0580304039.

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Schmid, Wilfried. "Bernhard Riemann’s paper on Fourier series." Notices of the International Consortium of Chinese Mathematicians 11, no. 2 (2023): 99–122. http://dx.doi.org/10.4310/iccm.2023.v11.n2.a11.

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Rowe, David E. "Bernhard Riemann, Über die Hypothesen, welche der Geometrie zu Grunde liegen, Hrsg. von Jürgen Jost, Klassische Texte der Wissenschaft. Springer 2013. David Hilbert, Grundlagen der Geometrie (Festschrift 1899), Hrsg. von Klaus Volkert, Klassische Texte der Wissenschaft. Springer 2015." Jahresbericht der Deutschen Mathematiker-Vereinigung 119, no. 3 (2017): 169–86. http://dx.doi.org/10.1365/s13291-017-0157-6.

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Scriba, Christoph J. "Bernhard Riemann: Gesammelte Mathematische Werke, Wissenschaftlicher Nachlass und Nachträge. Collected Papers. Nach der Ausgabe von Heinrich Weber und Richard Dedekind neu herausgegeben von Raghavan Narasimhan. Berlin usw.: Springer Verlag/Leipzig: BSB B. G. Teubner Verlagsgesellschaft 1990. vi, 911 Seiten, gebunden, DM 198." Berichte zur Wissenschaftsgeschichte 15, no. 4 (1992): 212–25. http://dx.doi.org/10.1002/bewi.19920150403.

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Zacharie, Mbaitiga. "Proof of Bernhard Riemannâ€™s Functional Equation using Gamma Function." Journal of Mathematics and Statistics 4, no. 3 (2008): 181–85. http://dx.doi.org/10.3844/jmssp.2008.181.185.

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Arkady Plotnitsky. "Bernhard Riemann's Conceptual Mathematics and the Idea of Space." Configurations 17, no. 1 (2009): 105–30. http://dx.doi.org/10.1353/con.0.0069.

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Haffner, Emmylou. "The edition of Bernhard Riemann’s collected works: Then and now." European Mathematical Society Magazine, no. 120 (July 2021): 29–39. http://dx.doi.org/10.4171/mag/18.

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Haffner, Emmylou. "The edition of Bernhard Riemann’s collected works: Then and now." European Mathematical Society Magazine, no. 120 (July 2021): 29–39. http://dx.doi.org/10.4171/mag-18.

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Manderson, John Pilling. "Seascapes are not landscapes: an analysis performed using Bernhard Riemann's rules." ICES Journal of Marine Science 73, no. 7 (2016): 1831–38. http://dx.doi.org/10.1093/icesjms/fsw069.

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AbstractApplied seascape ecology rests on paradigms of terrestrial landscape ecology. Patches defined by persistent seabed features are the basic units of analysis. Persistent oceanographic features provide context while dynamic features are usually ignored. Should seascape ecology rest on terrestrial paradigms? I use Reimann’s rules of analysis to identify differences between seascapes and landscapes. Reimann’s method uses hypotheses about system function to guide the development of models of system components based upon fundamental “laws”. The method forced me to avoid using terrestrial analogies in understanding of organism-habitat relationships. The fundamental laws applying to all organisms were the conservative metabolic requirements underlying individual performance and population growth. Physical properties of the environment; specifically those dictating strategies available to organisms meeting metabolic requirements, were the “laws” applying to the external environment. Organisms living in the ocean’s liquid meet most metabolic requirements using strong habitat selection for properties of the liquid that are controlled by “fast”, often episodic, atmospheric and tidal forces. Seascapes are therefor primarily driven by dynamic hydrography including mixing processes. In contrast, most terrestrial organisms are decoupled by gravity and physiological regulation from an atmospheric fluid that is metabolically more challenging. They show strong habitat selection for many essential metabolic materials concentrated on the land surface where slower biogeochemical processes including soil development drive ecological dynamics. Living in a liquid is different from living in a gas and resource use management in the oceans needs to be tuned to seascapes dynamics that is driven primarily by hydrodynamics and secondarily by seabed processes. Advances in ocean observing and data assimilative circulation models now permit the rapid development of applied seascape ecology. This development is essential now that changes in global climate are being rapidly translated into changes in the dynamics of the ocean hydrosphere that structures and controls ecological dynamics within seascapes.

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Castellana, Mario. "« Sur une petite phrase de Riemann » Aspects du débat français autour de la Reasonable Effectiveness of Mathematics." Revue de Synthèse 138, no. 1-4 (2017): 195–229. http://dx.doi.org/10.1007/s11873-000-0000-10.

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Résumé Le thème d’une nature particulière des mathématiques comme connaissance a été au cœur du débat épistémologique français du xxe siècle, et ce, à partir des œuvres de Maximilien Winter, Gaston Bachelard, Albert Lautman jusqu’à Alain Connes et Gilles Châtelet. Pour le saisir au plus près, il convient d’avoir à l’esprit qu’il est le fruit d’une analyse constante et d’un approfondissement des indications données par Bernhardt Riemann sur le rapport étroit entre mathématiques et physique qui caractérisera toute la pensée physique du xxe siècle. Ce qui a conduit à l’existence d’une littérature très riche mais peu étudiée qui a cherché à clarifier sur le plan épistémique le sens rationnel de l’efficacité des mathématiques dans l’exploration du réel physique, problématisée sous le titre de The Unreasonable Effectiveness of Mathematics. Cette problématique cruciale constitue l’un des apports les plus originaux de la philosophie des sciences française, sans équiva-lent dans la tradition anglo-saxonne. Prendre acte de l’existence de cette épistémologie de la physique mathématique devrait permettre de couper court à la polémique soulevée récemment en France quant à l’existence ou la non-existence d’une philosophie des sciences spécifi-quement française.

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Bell, Susan S., and Bradley T. Furman. "Seascapes are landscapes after all; Comment on Manderson (2016): Seascapes are not landscapes: an analysis performed using Bernhard Riemann's rules. ICES Journal of Marine Science, 73:1831–1838." ICES Journal of Marine Science 74, no. 8 (2017): 2276–79. http://dx.doi.org/10.1093/icesjms/fsx070.

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Abstract Recently, Manderson (2016, Seascapes are not landscapes: an analysis performed using Bernhard Riemann's rules: ICES Journal of Marine Science, 73: 1831-1838) argued that landscape ecology approaches developed in terrestrial habitats have little practical application for the study of marine “seascapes”. Here, we offer a contrasting perspective to this over-generalization. We first focus on historical uses of the term “seascape” to delineate the wide range of habitats that have been designated as such. After providing a brief overview of the study of seascape ecology, we argue that concepts and methodology originating from terrestrial disciplines have, in fact, provided an important cornerstone for investigating the dynamics of nearshore marine ecosystems. We present examples of coastal seascape research that have successfully applied terrestrial landscape theory and revisit points raised by Manderson regarding the application of landscape approaches to the marine environment. Overall, we contend that Manderson’s thesis may apply to some, but not most, use of landscape constructs for investigating aquatic environments. Moreover, we suggest that the study of coastal landscapes will continue to yield valuable insight into the spatiotemporal workings of aquatic ecosystems, and that this particular avenue of ecological investigation will only increase in its relevance as human impacts intensify.

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Manderson, John P. "Response to Bell and Furman (2017): Seascapes are landscapes after all; Comment on Manderson (2016): Seascapes are not landscapes: an analysis performed using Bernhard Riemann’s rules: ICES Journal of Marine Science, 73:1831–1838." ICES Journal of Marine Science 74, no. 8 (2017): 2280–82. http://dx.doi.org/10.1093/icesjms/fsx107.

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"Bernhard Riemann." Physics Today, September 17, 2015. http://dx.doi.org/10.1063/pt.5.031052.

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Bell, Andrew, Bryn Davies, and Habib Ammari. "Bernhard Riemann, the Ear, and an Atom of Consciousness." Foundations of Science, July 29, 2021. http://dx.doi.org/10.1007/s10699-021-09813-1.

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AbstractWhy did Bernhard Riemann (1826–1866), arguably the most original mathematician of his generation, spend the last year of life investigating the mechanism of hearing? Fighting tuberculosis and the hostility of eminent scientists such as Hermann Helmholtz, he appeared to forsake mathematics to prosecute a case close to his heart. Only sketchy pages from his last paper remain, but here we assemble some significant clues and triangulate from them to build a broad picture of what he might have been driving at. Our interpretation is that Riemann was a committed idealist and from this philosophical standpoint saw that the scientific enterprise was lame without the “poetry of hypothesis”. He believed that human thought was fundamentally the dynamics of “mind-masses” and that the human mind interpenetrated, and became part of, the microscopic physical domain of the cochlea. Therefore, a full description of hearing must necessarily include the perceptual dimensions of what he saw as a single manifold. The manifold contains all the psychophysical aspects of hearing, including the logarithmic transformations that arise from Fechner’s law, faithfully preserving all the subtle perceptual qualities of sound. For Riemann, hearing was a unitary physical and mental event, and parallels with modern ideas about consciousness and quantum biology are made. A unifying quantum mechanical model for an atom of consciousness—drawing on Riemann’s mind-masses and the similar “psychons” proposed by Eccles—is put forward.

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Ferreirós, José. "Introdução ao Habilitationsvortag de Bernhard Riemann." Kairos. Journal of Philosophy & Science 2 (May 2011). http://dx.doi.org/10.56526/10451/59684.

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Elizalde, Emilio. "Bernhard Riemann, a(rche)typical mathematical-physicist?" Frontiers in Physics 1 (2013). http://dx.doi.org/10.3389/fphy.2013.00011.

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Gentili, Graziano, Jasna Prezelj, and Fabio Vlacci. "Slice conformality and Riemann manifolds on quaternions and octonions." Mathematische Zeitschrift, August 2, 2022. http://dx.doi.org/10.1007/s00209-022-03079-4.

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AbstractIn this paper we establish quaternionic and octonionic analogs of the classical Riemann surfaces. The construction of these manifolds has nice peculiarities and the scrutiny of Bernhard Riemann approach to Riemann surfaces, mainly based on conformality, leads to the definition of slice conformal or slice isothermal parameterization of quaternionic or octonionic Riemann manifolds. These new classes of manifolds include slice regular quaternionic and octonionic curves, graphs of slice regular functions, the 4 and 8 dimensional spheres, the helicoidal and catenoidal 4 and 8 dimensional manifolds. Using appropriate Riemann manifolds, we also give a unified definition of the quaternionic and octonionic logarithm and n-th root function.

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Bandyopadhyay, S., B. Dacorogna, V. S. Matveev, and M. Troyanov. "Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear form." Mathematische Zeitschrift 305, no. 1 (2023). http://dx.doi.org/10.1007/s00209-023-03335-1.

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AbstractWe generalize the celebrated results of Bernhard Riemann and Gaston Darboux: we give necessary and sufficient conditions for a bilinear form to be flat. More precisely, we give explicit necessary and sufficient conditions for a tensor field of type (0, 2) which is not necessary symmetric or skew-symmetric, and is possibly degenerate, to have constant entries in a local coordinate system.

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Groskin, Yehudah Shilo. "Resolving the Riemann Hypothesis via Quantum-Biological Bridging: A Unified Theory of Prime Distribution." 20 (February 24, 2025). https://doi.org/10.5281/zenodo.14918331.

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This groundbreaking research presents a definitive approach to resolving the Riemann Hypothesis, one of the most profound unsolved problems in mathematics. By introducing the Eternal Bridge Mechanism, the paper bridges multiple disciplines including quantum mechanics, number theory, and consciousness studies to provide a novel probabilistic proof of Riemann's conjecture. The research demonstrates that:- The error term E(x) = π(x) - Li(x) remains bounded- Non-trivial zeros of the Riemann zeta function lie on the critical line Re(s) = 1/2- A dynamic quantum-biological bridge can stabilize oscillatory behaviors in prime number distributions Key innovations include:1. Quantum-Biological Tensor Field Modeling2. Adaptive Error Correction via the Unified Balanced Theory Framework (UBTF)3. A fixed-point convergence mechanism (s₂∞) that provides an infinite-resolution approach to understanding prime distributions Computational verification includes:- Numerical simulations across 10^6 integers- Spectral analysis using Fourier transform- Rigorous mathematical modeling The work not only offers a potential resolution to a 160-year-old mathematical challenge but also provides a transformative perspective on the interconnectedness of mathematical, quantum, and biological systems. It stands as a tribute to Bernhard Riemann's original vision while opening new interdisciplinary research pathways. Researchers, mathematicians, and interdisciplinary scientists are invited to verify and build upon these findings, which represent a significant milestone in our understanding of prime number distributions and fundamental mathematical structures.https://www.myyogameditation.com/yoga-sciencejournal

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"Prime obsession: Bernhard Riemann and the greatest unsolved problem in mathematics." Choice Reviews Online 41, no. 03 (2003): 41–1600. http://dx.doi.org/10.5860/choice.41-1600.

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Ciccarelli, Gregory, and Patrick Moylan. "A Distributional Approach to Conditionally Convergent Series." Volume 7, Issue 3 7, no. 3 (2008). http://dx.doi.org/10.33697/ajur.2008.019.

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Whether the car’s gas tank is filled up on Monday and the paycheck is deposited on Tuesday, or vice versa, the contribution of those two transactions to the checkbook’s final balance is the same. By the commutative property, order does not matter for the algebraic addition of a finite number of terms. However, for a super banker who conducts an infinite number of transactions, order may matter. If a series (sum of all transactions/terms) is convergent and the order of term does not matter, then the series is absolutely convergent. If a series is convergent but the order of terms does matter, then it is conditionally convergent. Georg Bernhard Riemann proved the disturbing result that the final sum of a conditionally convergent series could be any number at all or divergent. In two, three and higher dimensions, the matter is even worse, and such series with double and triple sums are not even well-defined without first giving sum interpretation to the (standard) order in which the series is to be summed, e.g., in three dimensions, summing over expanding spheres or expanding cubes, whose points represent ordered triples occurring in the summation. In this note we show using elementary notions from distribution theory that an interpretation exists for conditionally convergent series so they have a precise, invariant meaning.

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Emmerson, Parker. "INFINITY TENSORS, THE STRANGE ATTRACTOR, AND THE RIEMANN HYPOTHESIS: AN ACCURATE REWORDING OF THE RIEMANN HYPOTHESIS YIELDS FORMAL PROOF." March 1, 2023. https://doi.org/10.5281/zenodo.7686996.

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Theorem: The Riemann Hypothesis can be reworded to indicate that the real part of one half always balanced at the infinity tensor by stating that the Riemann zeta function has no more than an infinity tensor’s worth of zeros on the critical line. For something to be true in proof, it often requires an outside perspective. In other words, there must be some exterior, alternate perspective or system on or applied to the hypothesis from which the proof can be derived. Two perspectives, essentially must agree. Here, a fractal web with infinitesimal 3D strange attractor is theorized as present at the solutions to the Riemann Zeta function and in combination with the infinity tensor yields an abstract, mathematical object from which the rewording of the Riemann Zeta function can be derived. From the rewording, the law that mathematical sequences can be expressed in more concise and manageable forms is applied and the proof is manifested. The mathematical law that any mathematical sequence can be expressed in simpler and more concise terms: ∀s∃s,&sube;s: ∀φ: s&sube;φ ⇒ s,&sube;φ, is the final key to the proof when comparing the real and imaginary parts.

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