Recent zbMATH articles in MSC 01https://zbmath.org/atom/cc/012024-03-13T18:33:02.981707ZUnknown authorWerkzeugEditorial for the special issue in memory of Emmanuele DiBenedetto (1947--2021)https://zbmath.org/1528.000142024-03-13T18:33:02.981707Z(no abstract)Preface: Special issue dedicated to Professor Boris Mordukhovich on the occasion of his 70th birthdayhttps://zbmath.org/1528.000202024-03-13T18:33:02.981707ZThe Special Issue consists of seventeen research articles devoted to many areas of variational analysis and applications to optimization.Henri Poincaré. A biography through the daily papers. With prefaces by Nicolas Poincaré and Cédric Villanihttps://zbmath.org/1528.010012024-03-13T18:33:02.981707Z"Ginoux, Jean-Marc"https://zbmath.org/authors/?q=ai:ginoux.jean-marc"Gerini, Christian"https://zbmath.org/authors/?q=ai:gerini.christianPublisher's description: Ce livre présente un portrait inédit du mathématicien français Henri Poincaré à partir de ce qu'en disaient les journaux de son temps.
Un choix abondant de coupures de presse permet en effet une approche originale du personnage : on y découvre les faits les plus marquants de sa carrière mais aussi son rôle dans l'espace public, tant pour ses multiples compétences scientifiques et techniques que pour ses éclairages philosophiques.
Doublement académicien, auteur d'ouvrages largement diffusés, son aura dépassa le seul cercle des érudits pour toucher le grand public dans les domaines les plus variés, société savante et presse généraliste ayant fait de lui une sorte de référent dans la plupart des champs de la connaissance et au-delà.
Des anecdotes les plus insolites aux publications méconnues, en passant par les diverses polémiques dans lesquelles on l'entraîna souvent malgré lui, les journaux nous dévoilent un Poincaré inattendu, qui se prêta au jeu de cette dialectique entre espace savant et espace public, assumant ainsi de façon originale une forme de \guillemotleft vulgarisation scientifique \guillemotright comme un rôle d'éclaireur.
See the review of the first English edition in [Zbl 1329.01004].Underground mathematics. Craft culture and knowledge production in early modern Europehttps://zbmath.org/1528.010022024-03-13T18:33:02.981707Z"Morel, Thomas"https://zbmath.org/authors/?q=ai:morel.thomasIn the book under review, the author, professor in the history of mathematics and its teaching at the Bergische Universität Wuppertal, focuses on the origins and evolution of \textit{Markscheidekunst} from its origins up to the beginning of the nineteenth century. Mathematics, technology, politics, economics and history are combined to the pleasure of the readers in order to lift the veil on a neglected domain of practical mathematics, so fundamental to the economy of the Holy Roman Empire: \textit{Markscheidekunst}. This is the German term for `` `the art of setting limits'. Concretely, it encompassed all measuring operations used in the delimitation of concessions and in the daily running of metal mines'' (p.~5). Thus, the \textit{Markscheider} is the surveyor, who has to determine boundaries between mining concessions. Differences between \textit{Markscheidekunst} and classical surveying exist because of boundaries underground: it is precisely the main objective of the subterranean geometry, born in the mining pits of the Holy Roman Empire. This ``discipline fell outside of the academic geometry of its time, and vastly differed from the deductive implementation of theories that early modern scholars labeled `applied' or `mixed' mathematics'' (p.~5). The author points out that ``the history of subterranean geometry illustrates the growing reliance on numbers and geometric figures in civil society at large'' (p.~6), and he tries to clarify the tortuous relationships between scholars and practitioners. Hence, the book under review provides a very interesting insight into the general history of mathematics, and into the history of the mathematization of nature.
The book is scholarly, really well-edited and well-illustrated, which doesn't spoil anything. The reading is very comfortable. In addition, numerous footnotes and an impressive 28-page bibliography (pp.~253--280, with three sections: primary sources, printed primary sources and secondary sources) make for in-depth reading. The unique index (pp. 281--292) -- bringing together the index \textit{nominum}, \textit{locorum}, \textit{rerum} and \textit{verborum} -- is very useful.
The author divides his book into seven chapters. In the first chapter ``Of scholars and miners'' (pp.~20--49), focusing on treatises from two humanist Renaissance scholars: the \textit{De re metallica} written by Agricola (1494--1555) and the \textit{Vom Marscheden kurtzer und gründlicher Unterricht} by Reinhold the younger (1538--1592), the author shows that their scholarly underground geometry, established in academic circles, is largely different from the actual surveying of a \textit{Markscheider}. ``\dots\ there was an important gap between the crafts and the books that were written about it'' (p.~49).
In the second chapter ``A mathematical culture. The art of setting limits'' (pp.~50--82), the author examines in detail the art of setting limits used in metallic mines developed within a specific technical, administrative, and economic context. He ``dissect[s] the actual procedures of underground geometry in order to understand the encroachment of mathematics into human affairs'' (p.~51). His knowledge of various sources (not necessarily mathematical, as mining laws, customs and rulings, sermons or town chronicles) is extensive. He shows, among others, how surveying tasks become more and more complex, how the surveyors made their mark with their knowledge and practices required for successful mining, how \textit{Markscheider} turns into a specialized profession established on a specific mathematical culture, or how religion is so important in the daily life of miners. Finally, ``the omnipresence of measurements, combined with their legal and religious recognition, ultimately conferred a higher status to the discipline'' (p.~16).
In the third chapter ``The mines and the court'' (pp.~83--117), the author explores ``two dynasties for Saxon practitioners [the Öders and the Rieses] whose careers illustrate the interplay between the mines and the court'' (p.~84). He considers those two dynasties, subterranean surveyors for the first family and reckoning masters for the second, as paradigmatic in the context of the mining towns of the Empire.
The fourth chapter ``Writing it down'' (pp.~118--148) is an opportunity to reappraise the general conception about the seventeenth-century mining literature, by studying unpublished manuscripts included in a new original scribal tradition \textit{Geometria subterranea} or \textit{New subterranean geometry}. This tradition, largely detailed is this chapter, was allegedly created by the mining official Balthasar Rösler (1605--1673). The author shows how those manuscripts were used to train the apprentice surveyors, as ``the subterranean geometry was not an art taught in schools'' (p.~129).
In the fifth chapter `` `So fair a subterraneous city' '' (pp.~149--182), the main subject is Abraham von Schönberg (1640--1711), Captain-general of the Saxon mining administration, and his effort to develop the mining map. A large part of this chapter is devoted to the \textit{Freiberga subterranea}, ``a gigantic cartography of the Ore Mountains running continuously over several hundred sheets'' (p.~151). Thus, the author reveals with strong arguments that ``drawing mining maps and working on them became widespread in the second half of the seventeenth century, gradually replacing alternative tools such as written reports of visitations, wood models, or annotated sketches'' (p.~17).
In the very valuable sixth chapter ``How to teach it?'' (pp.~183--212), the author describes (in his own words, p.~183) ``the challenges met by the mining culture of mathematics during the eighteenth century, its evolution, and how it finally came to be taught around a new kind of institution, the mining academies''. He sheds light on a very slow maturation in the whole century ``trying to standardize and improve existing practices without getting lost in abstract or unpractical solutions'' (p.~14), with a special emphasize on the biography of a mining master and autodidact mathematician: Johann Andreas Scheidhauer (1718--1784).
Finally, in the seventh chapter `` `One of geometry's nicest applications' '' (pp.~213--242), the author focuses on the very interesting history of the Deep-George Tunnel (1771--1799), a 10\,km long drainage tunnel at a depth of 284\,m, following testimonies and scientific writings of Jean-André Deluc (1727--1817), Swiss scholar, fellow of the Royal Society and foreign associate to the Académie des Sciences.
As one may have guessed from my review, the book is an enjoyable read, thanks to the quality of the writing (particularly the clarity of the plan) and the quantity and nature of the sources used. Historians of mathematics will discover a vast, hitherto unexplored field.
Reviewer: Marc Moyon (Limoges)Johannes Kepler. From Tübingen to Żagań. Proceedings of the conference, Zielona Góra, Poland, 2008https://zbmath.org/1528.010032024-03-13T18:33:02.981707ZFrom the Editors' preface: The papers printed in this volume of Studia Copernicana were first presented orally at the conference Kepler 2008: From Tübingen to Żagań, held June 22--26, 2008, at the University of Zielona Góra. Under the auspices of the Institute of Astronomy of the University of Zielona Góra and the Institute for the History of Science, Warsaw, a distinguished group of historians of science met to mark the 380th anniversary of the arrival of Johannes Kepler in Żagań (Sagan).
Contents:
J. V. Field, Kepler's harmony of the world (11--28),
Volker Bialas, Kepler's philosophy of nature (29--40),
Nick Jardine, God's ``Ideal reader'': Kepler and his serious jokes (41--52),
William H. Donahue, Kepler as a reader of Aristotle (53--66),
Eberhard Knobloch, Kepler's \textit{De stella nova} (67--76),
Richard L. Kremer, Kepler and the Graz Calendar Makers: computational foundations for astrological prognostication (77--100),
A. E. L. Davis, \textit{Astronomia nova}: classification of the planetary eggs (101--112),
Owen Gingerich, Kepler versus Lansbergen: on computing Ephemerides, 1632--1662 (113--118),
Jarosław Włodarczyk, Kepler's Moon (119--130),
Granada, Miguel A., Kepler and Bruno on the Infinity of the universe and of solar systems (131--158),
Patrick J. Boner, Finding favour in the heavens and Earth: stadius, Kepler and astrological calendars in early modern Graz (159--178),
Sheila Rabin, Kepler's astrology and the physical universe (179--186),
Bruce Stephenson, Kepler and astrological world history (187--196),
Alena Hadravová and Petr Hadrava, Johannes Kepler and Czech history (197--204),
Giora Hon, Kepler's conception of error in optics and astronomy: a comparison with Galileo (205--222),
Rhonda Martens, Kepler: models and representations (239--252),
Andrzej K. Wróblewski, Venus in Sole Visa in Żagań (253--255).
The articles of this volume will not be indexed individually.Astronomical tables in the ``Lü-li zhi'': on the characteristics and adoption of ``\textit{licheng}'' pick-up tableshttps://zbmath.org/1528.010042024-03-13T18:33:02.981707Z"Li, Liang"https://zbmath.org/authors/?q=ai:li.liang.1|li.liang.2|li.liang.4|li.liang.3|li.liangSummary: This article discusses the development of astronomical tables in ancient China based on the calendrical chapter titled ``Lü-li zhi'' (Monograph on harmonics and calendrical astronomy) in official histories. After surveying various types of astral scientific tables in ancient China and their layouts, this paper discusses the characteristics and adoption of ``\textit{licheng}'' tables, a specific kind of pick-up table that seems to have come into use in the Sui period (581--618) and to have been widespread from the Tang period (618--907) onward. The emergence of \textit{licheng} tables relates largely to the internal development of ancient Chinese astronomy, but they were also probably inspired by auspicial tables and foreign astronomical tables. By comparing tables recorded in the ``Lü-li zhi'' and the existing \textit{licheng} tables, we find that most \textit{licheng} were deleted during the compilation of ``Lü-li zhi'' to reduce the number of volumes. Moreover, this paper discusses several common solutions used to compress the size of tables in ``Lü-li zhi.'' The adoption of \textit{licheng} tables into the ancient Chinese astral sciences and the reformatting of them in ``Lü-li zhi'' give us a different perspective for understanding the development of ancient Chinese astronomical tables and the compilation of the calendrical portion of official histories.A study of planetary theory in the \textit{Great expansion system} (\textit{Dayan Li}, 727 CE): the case of Marshttps://zbmath.org/1528.010052024-03-13T18:33:02.981707Z"Tang, Quan"https://zbmath.org/authors/?q=ai:tang.quanSummary: The planetary theory in the \textit{Great Expansion System} (\textit{Dayan li}, 727 CE) is investigated, with a detailed example of Mars. In ancient Chinese astrology, the position of one planet and the relative positions of different planets had important astrological significance. Thus, planetary theory is an important part of Chinese mathematical astronomy. The \textit{Great Expansion System}, which was compiled by Yixing of the Tang dynasty (618--907 CE), provided many innovations in planetary theory. Based on the extant \textit{Treatises on Mathematical Harmonics and Astronomy} (\textit{Lü li zhi}) in Chinese official histories, the \textit{Great Expansion System} was the first Chinese astronomical system to include tables of the planetary equation of center and procedures for correcting the influence of the planetary equation of center on the position of a planet. It was also the first Chinese system to design a table of the planetary phases of motion for calculating the mean position of a planet, which was the basis for calculating the true position of the planet. In addition, Yixing proposed the concept of the precession of planetary perihelion and gave the values of the precession of planetary perihelion for the first time in ancient China. The innovations of the \textit{Great Expansion System} regarding planetary theory established its important position in the history of Chinese astronomical systems. Mars is taken as a case study to investigate the planetary theory in the \textit{Great Expansion System}, including the astronomical constants related to Mars, two important astronomical tables, namely the table of the equation of center and the table of the phase motion of Mars in one synodic period, and the procedures for calculating the position of Mars on any given day using the planetary and solar equations of center. Two questions are addressed. First, how did Yixing correct the influence of the equation of center of Mars on the time of mean conjunction and the mean position of Mars? Second, how did Yixing calculate the true position of Mars on any given day? The original text of the \textit{Great Expansion System} is analyzed to show how Yixing developed the planetary theory in the Sui and early Tang periods and constructed a complete method for predicting the true positions of planets using the planetary and solar equations of center.Preliminary research on the mathematical methods and order of problems in the ``\textit{Fangcheng}'' chapter of Yang Hui's \textit{Mathematical methods} (1261 CE)https://zbmath.org/1528.010062024-03-13T18:33:02.981707Z"Xiaohan, Zhou"https://zbmath.org/authors/?q=ai:xiaohan.zhouSummary: Yang Hui was one of the most important authors of mathematical works during the thirteenth century. \textit{Mathematical Methods Explaining in Detail The Nine Chapters} (\textit{Xiangjie jiuzhang suanfa}, 1261 CE) is the earliest extant work attributed to Yang Hui. From the thirteenth to the fifteenth century, this work played a crucial role in the circulation and popularization of \textit{The Nine Chapters on Mathematical Procedures} (\textit{Jiuzhang suanshu}). However, the only surviving printed edition of \textit{Mathematical Methods} is incomplete and contains many mistakes obstructing contemporary researchers' understanding of this work. The ``\textit{Fangcheng}'' chapter of \textit{The Nine Chapters} deals with problems related to solving what today are known as simultaneous sets of linear equations. However, interpreting the text in this chapter of \textit{Mathematical Methods} and recovering the mathematical practices relating to \textit{fangcheng} are difficult. Through detailed textual and mathematical analyses, the author of this paper explains Yang Hui's understanding and practice relating to ``the \textit{fangcheng} method'' and ``the method of the positive and the negative.'' This paper includes an appendix that provides a detailed translation of the ambiguous text relating to ``the method of the positive and the negative'' and gives reasons supporting the interpretation provided here. Yang Hui's understanding of the concepts of ``positive'' and ``negative'' and his practice relating to these two concepts may easily be confused with their apparent counterparts in modern mathematics. Also, careful analysis of the mathematical methods in this work reveal that the order of problems in Yang Hui's \textit{Reclassifications of Mathematical Methods Explaining in Detail The Nine Chapters} ([\textit{Xiangjie jiuzhang suanfa zuanlei}], namely, the last section of \textit{Mathematical Methods}) were rearranged according to commentaries to specific methods that appear in \textit{Mathematical Methods}. Some textual clues referring to the ``previous question'' (\textit{qianwen}) in certain commentaries of \textit{Mathematical Methods} indeed reflect the order of problems in \textit{Reclassifications}. Yang Hui made especially detailed commentaries on the problems that he arranged in a sequence that differs with respect to the original order of problems as they appear in the ancient classic work, \textit{The Nine Chapters}. All these discoveries reveal and serve to prove a close relationship between Yang Hui's \textit{Mathematical Methods and his Reclassifications}.Decimal numerals and zero in ancient Jaina literaturehttps://zbmath.org/1528.010072024-03-13T18:33:02.981707Z"Gupta, R. C."https://zbmath.org/authors/?q=ai:gupta.radha-charan|gupta.ramesh-c.1|gupta.ramesh-cThe most ancient Jaina literature consists of \textit{Āgamas} of various categories such as \textit{Aṅgas}, \textit{Upāṅgas}, etc. In ancient times, numbers were in words and counting was in decimal scale. A special period of 8400,000 years gave rise to a new scale for reckoning time upto \textit{Śirṣaprahelikā}. The decimal place-value method was clearly known to the author. The famous Prakrit work \textit{Tiloya-paṇṇattī} uses the modern place-value system with zero with ease.
\textit{Śūnya} or \textit{suṇṇa} is the most common word for zero. Cāṇakya uses it in the sense of \textit{abhāva} or absence \textit{avidyaṃ jīvanaṃ śūnyam}. Panini had used the word \textit{lopa} for his linguistic zero \textit{adarśanaṃ lopaḥ}. \textit{Nabha} and \textit{gagana} means sky and denote zero as a \textit{Bhūta-saṃkhyā}. \textit{Ananta} meaning endless also meant zero due to the vastness of the sky.
An important early Jaina text is the comprehensive work \textit{Tiloya-paṇṇattī} portions of which are devoted to mathematics. It gives the traditional Jaina rules for finding the circumference and area of a circle. Interestingly \(\sqrt{10}\) is the measure given for \(\pi\).
Two names stand out in Jaina mathematics, Śrīdhara and Mahāvīrā. \textit{Pāṭīgaṇita} and \textit{Triśatikā} are the well-known works of Śrīdhara. In his \textit{Pāṭīgaṇita}, Śrīdhara has given rules regarding the operations of \textit{Śūnya} or zero. He rightly avoids talking about \(x/0\). Mahāvīrā in his \textit{Gaṇita-sārasaṅgraha} has also given rules for zero. In addition to Śrīdhara's rules, he adds \(x/0 = x\) which is not correct. According to the author, in spite of the above lapse, \textit{Gaṇita-sārasaṅgraha} will remain a great work of Jaina mathematics. This is an interesting article on Jaina mathematics. The long list of references and notes will be very useful for research students.
For the entire collection see [Zbl 1507.01004].
Reviewer: Sita Sundar Ram (Chennai)Procedures of Leibnizian infinitesimal calculus: an account in three modern frameworkshttps://zbmath.org/1528.010082024-03-13T18:33:02.981707Z"Bair, Jacques"https://zbmath.org/authors/?q=ai:bair.jacques"Błaszczyk, Piotr"https://zbmath.org/authors/?q=ai:blaszczyk.piotr"Ely, Robert"https://zbmath.org/authors/?q=ai:ely.robert"Katz, Mikhail G."https://zbmath.org/authors/?q=ai:katz.mikhail-g"Kuhlemann, Karl"https://zbmath.org/authors/?q=ai:kuhlemann.karlSummary: Recent Leibniz scholarship has sought to gauge which foundational framework provides the most successful account of the procedures of the Leibnizian calculus (LC). While many scholars (e.g. Ishiguro, Levey) opt for a default Weierstrassian framework, Arthur compares LC to a non-Archimedean framework SIA (Smooth Infinitesimal Analysis) of Lawvere-Kock-Bell. We analyze Arthur's comparison and find it rife with equivocations and misunderstandings on issues including the non-punctiform nature of the continuum, infinite-sided polygons, and the fictionality of infinitesimals. Rabouin and Arthur claim that Leibniz considers infinities as contradictory, and that Leibniz' definition of incomparables should be understood as nominal rather than as semantic. However, such claims hinge upon a conflation of Leibnizian notions of bounded infinity and unbounded infinity, a distinction emphasized by early Knobloch. The most faithful account of LC is arguably provided by Robinson's framework for infinitesimal analysis. We exploit an axiomatic framework for infinitesimal analysis SPOT to formalize LC.Helmholtz, the conservation of force and the conservation of \textit{vis viva}https://zbmath.org/1528.010092024-03-13T18:33:02.981707Z"Caneva, Kenneth L."https://zbmath.org/authors/?q=ai:caneva.kenneth-lHelmholtz famously announced a ``principle of the conservation of force,'' where Helmholtz's ``force'' corresponds to the modern ``energy.'' This article traces the history of mechanical conservation principles before Helmholtz, with (largely inconclusive) attention to what sources Helmholtz might have been most familiar with.
Conservation principles were commonplace already in the 17th century. The idea that some kind of total ``quantity of motion'' or ``force'' would remain unchanged during mechanical interactions of bodies was regarded as a virtually truistic reflection of the metaphysical equality of cause and effect. But precise quantitative articulations of this principle differed. Leibniz argued for the fundamental role of vis viva (kinetic energy) \(mv^2\) as the correct measure of the ``motive force'' contained in a moving body, as opposed to the Cartesian conception of ``quantity of motion'' (momentum) \(mv\). Hence, according to Leibniz, vis viva was conserved in purely kinetic scenarios such as collisions, but not generally since the ``living'' force that a body possesses by virtue of its motion is interchangeable with ``dead'' forces such as potential energy \(mgh\) or the capacity for action stored in a compressed spring. Johann Bernoulli followed this perspective but shifted the terminology so that ``living force'' meant any ``faculty of acting,'' including that stored in a compressed spring for example. This terminological drift enabled him to postulate ``the conservation of vis viva'' as a general principle.
The conservation of vis viva was not mentioned at all in Euler's mechanics book, and only passingly in the second addition of d'Alembert's. But other mechanicians, such as Carnot, took up the principle in various forms. It was often applied to a system of bodies subject to internal actions and central forces such as gravity. It was commonly stated in terms of path independence for a cyclic process. For example, if a mass particle goes around a roller coaster while subject to gravity it will have the same vis viva (kinetic energy) when it gets back to its starting point, regardless of the shape of the roller coaster. It was also well understood that, if one wanted to compare the vis viva for two distinct endpoints, then the difference could be obtained by integrating the relevant forces along the path in question, or by evaluating a suitable (potential) function at the endpoints. Lagrange treated such things with mathematical depth, but he left many things merely as analytic expressions without attempting a conceptual synthesis in terms of concepts such as work. The same goes for Poisson, who furthermore found the statement of the principle for different endpoints more important than the statement in terms of a system returning to its initial position. For this reason, Poisson rebranded this the ``principle of living forces,'' dropping the ``conservation'' part of the name. This terminology was subsequently followed by others, such as Coriolis, Poncelet, and Ohm.
From the outset, conservation laws were linked to the impossibility of perpetual motion, or in other words machines from which an indefinite amount of work could be extracted. Leibniz made use of this link, and regarded it as commonly accepted that ``it is just the same in physics and in mechanics to reduce to a mechanical perpetual motion and to reduce to an absurdity.'' But in 18th-century rational mechanics the connection between conservation of vis viva and the impossibility of perpetual motion did not play a direct role. For example, Carnot discussed both the conservation of vis viva and the impossibility of perpetual motion, but in two different works, and he did not make any direct deductive connection between these two principles.
In the early 19th century, these threads were being brought together in a form more familiar today. Thus Coriolis introduced the concept of work to clarify both the theoretical principle of vis viva as well as its connections to actual machines. However, Helmholtz seems not to have been very well read in French authors such as Coriolis and Poisson, or in any case did not follow their terminological innovations, instead introducing his own work-like concept defined as the integral of ``tensional forces.'' Furthermore, Helmholtz seems to have been original in incorporating the impossibility of perpetual motion as a fundamental principle on which physical theory should be built.
Reviewer: Viktor Blåsjö (Utrecht)Ladislaus von Bortkiewicz -- statistician, economist and a European intellectualhttps://zbmath.org/1528.010102024-03-13T18:33:02.981707Z"Härdle, Wolfgang Karl"https://zbmath.org/authors/?q=ai:hardle.wolfgang-karl"Vogt, Annette B."https://zbmath.org/authors/?q=ai:vogt.annette-bThe paper is devoted to a presentation of the life and work of Ladislaus von Bortkiewicz (1868--1931). He was a European statistician and worked scientifically in theoretical economics, stochastics, mathematical statistics and radiology. It is stressed that his clear views on mathematical principles with their applications in these fields were in conflict with the mainstream economic schools in Germany at the dawn of the 20th century. His prominent role in today's statistical thinking is pointed out.
Reviewer: Roman Murawski (Poznań)Space as a concept of series -- Ernst Cassirer's interpretation of the development of geometry in the 19th centuryhttps://zbmath.org/1528.010112024-03-13T18:33:02.981707Z"Koenig, Daniel"https://zbmath.org/authors/?q=ai:konig.danielThe paper deals with Ernst Cassirer's work on the history of mathematics and its connection to his philosophy of mathematics, with a specific focus on the rise of non-Euclidean geometry in the 19th century. The author explains how Cassirer tried to explain the problem of non-Euclidean geometry by taking recourse to Kantian philosophy. Geometry is not to be understood as ontological statements about space as a substantive entity in itself; but rather serves a structuring function in human cognition. The author shows that Cassirer therefore also did not believe that empirical investigations would be able to single out Euclidean geometry, but that Euclidean geometry could be singled out on the basis of functional aspects, e.g., its homogeneity. The role assigned to the space of geometry is thereby similar to the role assigned to number systems, and the author shows that Cassirer saw both numbers and geometric spaces as types of sequences, that is structures that are iteratively constructed from one (numbers) or a few (geometric spaces in projective geometry) unit objects.
For the entire collection see [Zbl 1522.01002].
Reviewer: Alexander Blum (Berlin)The artistic, algebraic, and severe ``Russian'' genius Arthur Cayleyhttps://zbmath.org/1528.010122024-03-13T18:33:02.981707Z"Lorenat, Jemma"https://zbmath.org/authors/?q=ai:lorenat.jemmaThis article discusses the challenge of classifying Arthur Cayley (1821--1895), whose diverse contributions led to differing opinions among scholars. Debates centered on his expertise in algebra, geometry, and formalism, as well as his writing style, which was praised for clarity but criticized for its synthetic approach. The obituaries also speculated about his supposed Russian heritage and its influence on his genius. Despite these debates, Cayley's legacy remains a testament to his multifaceted contributions to mathematics.
Reviewer: Ren Guo (Corvallis)Academician Volodymyr Oleksandrovych Marchenko (on the centenary of his birthday)https://zbmath.org/1528.010132024-03-13T18:33:02.981707Z(no abstract)Nikolai Neumaierhttps://zbmath.org/1528.010142024-03-13T18:33:02.981707Z"Bordemann, Martin"https://zbmath.org/authors/?q=ai:bordemann.martin"Ebrahimi-Fard, Kurusch"https://zbmath.org/authors/?q=ai:ebrahimi-fard.kurusch"Makhlouf, Abdenacer"https://zbmath.org/authors/?q=ai:makhlouf.abdenacer"Schlichenmaier, Martin"https://zbmath.org/authors/?q=ai:schlichenmaier.martin"Waldmann, Stefan"https://zbmath.org/authors/?q=ai:waldmann.stefanFor the entire collection see [Zbl 1253.00017].Yulij Sergeevich Ilyashenkohttps://zbmath.org/1528.010152024-03-13T18:33:02.981707Z"Bufetov, Alexander"https://zbmath.org/authors/?q=ai:bufetov.aleksander-igorevich"Filimonov, Dmitry"https://zbmath.org/authors/?q=ai:filimonov.dmitry"Glutsyuk, Alexey"https://zbmath.org/authors/?q=ai:glutsyuk.alexey-a"Gusein-Zade, Sabir"https://zbmath.org/authors/?q=ai:gusein-zade.sabir-m"Kleptsyn, Victor"https://zbmath.org/authors/?q=ai:kleptsyn.victor-a"Lando, Sergei"https://zbmath.org/authors/?q=ai:lando.sergei-k"Novikov, Dmitry"https://zbmath.org/authors/?q=ai:novikov.dmitry"Skripchenko, Alexandra"https://zbmath.org/authors/?q=ai:skripchenko.alexandra"Sossinsky, Alexei"https://zbmath.org/authors/?q=ai:sosinskii.aleksei-b"Tabachnikov, Sergei"https://zbmath.org/authors/?q=ai:tabachnikov.serge-l"Timorin, Vladlen"https://zbmath.org/authors/?q=ai:timorin.vladlen"Tsfasman, Michael"https://zbmath.org/authors/?q=ai:tsfasman.michael-a"Yakovenko, Sergey"https://zbmath.org/authors/?q=ai:yakovenko.sergei(no abstract)Professor G. C. Sharma (Gokul Chandra Sharma): a leading mathematicianhttps://zbmath.org/1528.010162024-03-13T18:33:02.981707Z"Chandel, R. C. Singh"https://zbmath.org/authors/?q=ai:chandel.r-c-singh(no abstract)Professor Vinod Prakash Saxena (V. P. Saxena): a towering and leading mathematicianhttps://zbmath.org/1528.010172024-03-13T18:33:02.981707Z"Chandel, R. C. Singh"https://zbmath.org/authors/?q=ai:chandel.r-c-singh(no abstract)Maciej Sablikhttps://zbmath.org/1528.010182024-03-13T18:33:02.981707Z"Ger, Roman"https://zbmath.org/authors/?q=ai:ger.roman(no abstract)László Székelyhidihttps://zbmath.org/1528.010192024-03-13T18:33:02.981707Z"Gilányi, Attila"https://zbmath.org/authors/?q=ai:gilanyi.attila(no abstract)Steven Weinberg in memoriamhttps://zbmath.org/1528.010202024-03-13T18:33:02.981707Z"Glashow, Sheldon Lee"https://zbmath.org/authors/?q=ai:glashov.sheldon-lee(no abstract)In memoriam: Asen L. Dontchev (1948--2021)https://zbmath.org/1528.010212024-03-13T18:33:02.981707Z"Hager, William W."https://zbmath.org/authors/?q=ai:hager.william-w"Rockafellar, R. Tyrrell"https://zbmath.org/authors/?q=ai:rockafellar.ralph-tyrrell"Veliov, Vladimir M."https://zbmath.org/authors/?q=ai:veliov.vladimir-m(no abstract)A master in harmony and differential equations. A tribute to Carlos E. Kenig on his 70th birthdayhttps://zbmath.org/1528.010222024-03-13T18:33:02.981707Z(no abstract)A biography of Robert M Ziffhttps://zbmath.org/1528.010232024-03-13T18:33:02.981707Z"Jacobsen, Jesper Lykke"https://zbmath.org/authors/?q=ai:jacobsen.jesper-lykke"Mertens, Stephan"https://zbmath.org/authors/?q=ai:mertens.stephan"Scullard, Christian R."https://zbmath.org/authors/?q=ai:scullard.christian-r(no abstract)Victor A. Vedernikov (1940--2022)https://zbmath.org/1528.010242024-03-13T18:33:02.981707Z"Monakhov, V. S."https://zbmath.org/authors/?q=ai:monakhov.victor-stepanovich"Skiba, A. N."https://zbmath.org/authors/?q=ai:skiba.alexander-n"Sorokina, M. M."https://zbmath.org/authors/?q=ai:sorokina.marina-m|sorokina.m-m(no abstract)Obituary for: Prof. Dr. habil. Alfred Göpfert (1934--2023)https://zbmath.org/1528.010252024-03-13T18:33:02.981707Z"Tammer, Christiane"https://zbmath.org/authors/?q=ai:tammer.christiane"Köbis, Elisabeth"https://zbmath.org/authors/?q=ai:kobis.elisabeth"Elster, Rosalind"https://zbmath.org/authors/?q=ai:elster.rosalind"Grecksch, Wilfried"https://zbmath.org/authors/?q=ai:grecksch.wilfried(no abstract)Professor Xihua Cao and his schoolhttps://zbmath.org/1528.010262024-03-13T18:33:02.981707Z"Tan, Lin"https://zbmath.org/authors/?q=ai:tan.linThis are the opening remarks of a conference celebrating the centenary of the birth of Xihua Cao, who -- according to the author -- brought modern algebra to China after the Cultural Revolution. In keeping with the occasion, it provides an interesting biographical sketch of Cao's academic career as well as some telling personal anecdotes but does not provide many references.
For the entire collection see [Zbl 1508.20002].
Reviewer: Alexander Blum (Berlin)Daryl John Daley, 4 April 1939 -- 16 April 2023. An internationally acclaimed researcher in applied probability and a gentleman of great kindnesshttps://zbmath.org/1528.010272024-03-13T18:33:02.981707Z"Taylor, Peter"https://zbmath.org/authors/?q=ai:taylor.peter-j|taylor.peter-g|taylor.peter-neal|taylor.peter-r|taylor.peter-a|taylor.peter-charles|taylor.peter-d|taylor.peter-k(no abstract)In memoriam: Matthieu Ernsthttps://zbmath.org/1528.010282024-03-13T18:33:02.981707Z"van Beijeren, Henk"https://zbmath.org/authors/?q=ai:van-beijeren.henk"Dorfman, Bob"https://zbmath.org/authors/?q=ai:dorfman.bob(no abstract)Subrata Mukherjee (1945--2022)https://zbmath.org/1528.010292024-03-13T18:33:02.981707Z"Ye, Wenjing"https://zbmath.org/authors/?q=ai:ye.wenjing"Liu, Yijun"https://zbmath.org/authors/?q=ai:liu.yijun(no abstract)In memoriam: Steven Weinberg (May 3, 1933 -- July 23, 2021)https://zbmath.org/1528.010302024-03-13T18:33:02.981707Z"Zee, A."https://zbmath.org/authors/?q=ai:zee.anthony(no abstract)The origin and development of the Savilian Libraryhttps://zbmath.org/1528.010312024-03-13T18:33:02.981707Z"Poole, William"https://zbmath.org/authors/?q=ai:poole.william-g-junIn this impeccably researched article, the author gives a study of one of the earliest academic libraries in Europe -- the Savilian library -- from its origin in 1619 to 1884 when it was surrendered to the more famous Bodleian library. The library bears the name of Henry Savile (1549--1622) who founded the two professorships of astronomy and geometry at Oxford in 1619. He provided the professors with astronomical and mathematical books, manuscripts and instruments, who in turn augmented the library with their own books. Savile's life is well studied in [\textit{R. Goulding}, Defending Hypatia. Ramus, Savile, and the Renaissance rediscovery of mathematical history. Dordrecht: Springer (2010; Zbl 1279.01002)]. The great mathematician John Wallis who considerably contributed to the augmentation of the library was the third Savilian professor in geometry (or reader as they were called at the time), from 1649 to 1703. He was followed by the famous astronomer Edmond Halley, 1704--1742, who lost the astronomy chair to David Gregory in 1691.
This article is of great interest to historians of mathematics, but also to librarians of the considered period.
For the entire collection see [Zbl 1508.01001].
Reviewer: Martin Lukarevski (Štip)Transnational mathematics and movements: Shiing-Shen Chern, Hua Luogeng, and the Princeton Institute for Advanced Study from World War II to the Cold Warhttps://zbmath.org/1528.010322024-03-13T18:33:02.981707Z"Wang, Zuoyue"https://zbmath.org/authors/?q=ai:wang.zuoyue"Guo, Jinhai"https://zbmath.org/authors/?q=ai:guo.jinhaiSummary: This paper reconstructs, based on American and Chinese primary sources, the visits of Chinese mathematicians Shiing-shen Chern (Chen Xingshen) and Hua Luogeng (Loo-Keng Hua) to the Institute for Advanced Study in Princeton in the United States in the 1940s, especially their interactions with Oswald Veblen and Hermann Weyl, two leading mathematicians at the IAS. It argues that Chern's and Hua's motivations and choices in regard to their transnational movements between China and the US were more nuanced and multifaceted than what is presented in existing accounts, and that socio-political factors combined with professional-personal ones to shape their decisions. The paper further uses their experiences to demonstrate the importance of transnational scientific interactions for the development of science in China, the US, and elsewhere in the twentieth century.The fourteen Victoria Delfino problems and their status in the year 2020https://zbmath.org/1528.030012024-03-13T18:33:02.981707Z"Caicedo, Andrés Eduardo"https://zbmath.org/authors/?q=ai:caicedo.andres-eduardo"Löw, Benedikt"https://zbmath.org/authors/?q=ai:low.benediktFor the entire collection see [Zbl 1465.03026].Historical overview of the Cherlin-Zilber conjecturehttps://zbmath.org/1528.030022024-03-13T18:33:02.981707Z"Frécon, Olivier"https://zbmath.org/authors/?q=ai:frecon.olivierFor the entire collection see [Zbl 1429.00034].From the foundations of mathematics to mathematical pluralismhttps://zbmath.org/1528.030042024-03-13T18:33:02.981707Z"Priest, Graham"https://zbmath.org/authors/?q=ai:priest.grahamSummary: In this paper I will review the developments in the foundations of mathematics in the last 150 years in such a way as to show that they have delivered something of a rather different kind: mathematical pluralism.
For the entire collection see [Zbl 1502.03003].Calculus as method or calculus as rules? Boole and Frege on the aims of a logical calculushttps://zbmath.org/1528.030052024-03-13T18:33:02.981707Z"Waszek, David"https://zbmath.org/authors/?q=ai:waszek.david"Schlimm, Dirk"https://zbmath.org/authors/?q=ai:schlimm.dirkSummary: By way of a close reading of Boole and Frege's solutions to the same logical problem, we highlight an underappreciated aspect of Boole's work -- and of its difference with Frege's better-known approach -- which we believe sheds light on the concepts of `calculus' and `mechanization' and on their history. Boole has a clear notion of a logical \textit{problem}; for him, the whole point of a logical calculus is to enable systematic and goal-directed solution methods for such problems. Frege's \textit{Begriffsschrift}, on the other hand, is a visual tool to scrutinize concepts and inferences, and is a calculus only in the thin sense that every possible transition between sentences is fully and unambiguously specified in advance. While Frege's outlook has dominated much of philosophical thinking about logical symbolism, we believe there is value -- particularly in light of recent interest in the role of notations in mathematics and logic -- in reviving Boole's idea of an intrinsic link between, as he put it, a `calculus' and a `directive method' to solve problems.Peirce and proof: a view from the treeshttps://zbmath.org/1528.030122024-03-13T18:33:02.981707Z"Beisecker, Dave"https://zbmath.org/authors/?q=ai:beisecker.daveSummary: Using the proof of Peirce's Law \([\{(x \rightarrow y) \rightarrow x\} \rightarrow x]\) as an example, I show how bilateral tableau systems (or ``2-sided trees'') are not only more economical than rival systems of logical proof, they also better reflect the reasoning Peirce actually gives for securing the law's acceptance as an axiom. Moreover, bilateral proof trees are readily adapted to Peirce's own graphical notation, producing a proof system in that notation that is even more efficient and easier to learn than Peirce's system of permissions. This is in part due to the fact that Peirce's graphical notation is similarly bilateral. In effect bilateral proof trees in Peirce's notation can be understood as representing the space of outcomes for a game very much like what Peirce envisions as his endopereutic, and they embody insights of certain expressions of the pragmatic maxim that Peirce offers around 1905. Taken together, this suggests to me that Peirce would have embraced such a system of logic, and so I find it especially unfortunate that he was evidently unaware of Lewis Carroll's pioneering efforts to develop tree-like proof systems to solve logical puzzles with multiliteral sorites.
For the entire collection see [Zbl 1387.68019].Generality and objectivity in Frege's foundations of arithmetichttps://zbmath.org/1528.030222024-03-13T18:33:02.981707Z"Demopoulos, William"https://zbmath.org/authors/?q=ai:demopoulos.williamSummary: This chapter argues for two principal contentions, both of which mark points of divergence from the neo-Fregean position first developed in Crispin Wright's monograph \textit{Frege's Conception of Numbers as Objects}, and developed further in an extended series of works by Wright and Bob Hale. First, that Frege can be regarded as addressing the \textit{apriority} of arithmetic in a manner that is independent of the ideas that numbers are logical objects or that arithmetic is analytic or a part of logic. Second, that Frege can secure the \textit{objectivity} of arithmetic in a way that is independent of the idea that numbers are logical objects.
For the entire collection see [Zbl 1437.03010].Iconic logic and ideal diagrams: the Wittgensteinian approachhttps://zbmath.org/1528.030422024-03-13T18:33:02.981707Z"Lampert, Timm"https://zbmath.org/authors/?q=ai:lampert.timmSummary: This paper provides a programmatic overview of a conception of iconic logic from a Wittgensteinian point of view (WIL for short). The crucial differences between WIL and a standard version of symbolic logic (SSL) are identified and discussed. WIL differs from other versions of logic in that in WIL, logical forms are identified by means of so-called ideal diagrams. A logical proof consists of an equivalence transformation of formulas into ideal diagrams, from which logical forms can be read off directly. Logical forms specify properties that identify sets of models (conditions of truth) and sets of counter-models (conditions of falsehood). In this way, WIL allows the sets of models and counter-models to be described by finite means. Against this background, the question of the decidability of first-order-logic (FOL) is revisited. In the last section, WIL is contrasted with Peirce's iconic logic (PIL).
For the entire collection see [Zbl 1387.68019].A brief history of determinacyhttps://zbmath.org/1528.032132024-03-13T18:33:02.981707Z"Larson, Paul B."https://zbmath.org/authors/?q=ai:larson.paul-bFor the entire collection see [Zbl 1465.03026].Conceptions of proof from aristotle to Gentzen's calculihttps://zbmath.org/1528.032222024-03-13T18:33:02.981707Z"Centrone, Stefania"https://zbmath.org/authors/?q=ai:centrone.stefaniaSummary: The present paper aims to show how some key ideas at the basis of the normalization results in proof theory have their deep grounds in a number of fundamental questions that are posed always anew within the philosophical reflection on mathematics. Two different paradigms of proofs, \textit{synthetic and analytic}, are contrasted and their origin is traced back to Aristotle as well as to Bernard Bolzano's idea of a \textit{better grounded presentation of mathematics} at the beginnings of the 19th century. Two different proofs of the \textit{cut-elimination theorem} are then sketched with the aim of showing, on the one hand, what happens when one tries to implement formally the traditional idea of \textit{rigorous scientific proof} and, on the other hand, how high are ``the costs'' in terms of complexity of the proofs when one avoids the use of transitivity, that is, in traditional terms, the use of \textit{fortuitous alien intermediate concepts} in the proofs.
For the entire collection see [Zbl 1486.03009].Three stages in the development of approximation theoryhttps://zbmath.org/1528.410012024-03-13T18:33:02.981707Z"Tikhomirov, V. M."https://zbmath.org/authors/?q=ai:tikhomirov.vladimir-mSummary: Some fundamental ideas and the results of approximation theory based on them are reviewed. The review covers the development of this branch of mathematics from its origins to the end of the 20th century.A conversation with Paul Embrechtshttps://zbmath.org/1528.600032024-03-13T18:33:02.981707Z"Genest, Christian"https://zbmath.org/authors/?q=ai:genest.christian"Nešlehová, Johanna G."https://zbmath.org/authors/?q=ai:neslehova.johanna-gSummary: Paul Embrechts was born in Schoten, Belgium, on 3 February 1953. He holds a Licentiaat in Mathematics from Universiteit Antwerpen (1975) and a DSc from Katholieke Universiteit Leuven (1979), where he was also a Research Assistant from 1975 to 1983. He then held a lectureship in Statistics at Imperial College, London (1983-1985) and was a Docent at Limburgs Universitair Centrum, Belgium (1985-1989) before joining ETH Zürich as a Full Professor of Mathematics in 1989, where he remained until his retirement as an Emeritus in 2018. A renowned specialist of extreme-value theory and quantitative risk management, he authored or coauthored nearly 200 scientific papers and five books, including the highly influential `Modelling of Extremal Events for Insurance and Finance' (Springer, 1997) and `Quantitative Risk Management: Concepts, Techniques and Tools' (Princeton University Press, 2005, 2015). He served in numerous editorial capacities, notably as Editor-in-Chief of the (1996-2005). Praised for his natural leadership and exceptional communication skills, he helped to bridge the gap between academia and industry through the foundation of RiskLab Switzerland and his sustained leadership for nearly 20 years. He gave numerous prestigious invited and keynote lectures worldwide and served as a member of the board of, or consultant for, various banks, insurance companies and international regulatory authorities. His work was recognised through several visiting positions, including at the Oxford-Man Institute, and many awards. He is, inter alia, an Elected Fellow of the Institute of Mathematical Statistics (1995) and the American Statistical Association (2014), an Honorary Fellow of the Institute and the Faculty of Actuaries (2000), Honorary Member of the Belgian (2010) and French (2015) Institute of Actuaries and was granted four honorary degrees (University of Waterloo, 2007; Heriot-Watt University, 2011; Université catholique de Louvain, 2012; City, University of London, 2017). The following conversation took place in Paul's office at ETH Zürich, 17-18 December 2018.
{{\copyright} 2020 The Authors. International Statistical Review published by John Wiley \& Sons Ltd on behalf of International Statistical Institute.}The future of probabilityhttps://zbmath.org/1528.600042024-03-13T18:33:02.981707Z"Protter, Philip"https://zbmath.org/authors/?q=ai:protter.philip-eSummary: Probability as a subject in and of itself has rarely been truly appreciated by mathematicians in other disciplines. This has gradually changed over the last 50 years, as occasionally brilliant mathematicians show how it can be used to solve, or to explain, and/or to give intuitive content to thorny mathematical issues. We provide some examples and then give a wild speculation as to where the field, at least in Mathematical Finance, might go in the future.
For the entire collection see [Zbl 1515.01005].A proposed automatic calculating machine (1937)https://zbmath.org/1528.680022024-03-13T18:33:02.981707Z"Aiken, Howard Hathaway"https://zbmath.org/authors/?q=ai:aiken.howard-hathawayReprint of [\textit{H. H. Aiken} et al., IEEE Spectrum 1, No. 8, 62--69 (1964; \url{doi:10.1109/MSPEC.1964.6500770})].
For the entire collection see [Zbl 1484.68015].Prior analytics (\(\sim\)350 BCE)https://zbmath.org/1528.680032024-03-13T18:33:02.981707Z"Aristotle"https://zbmath.org/authors/?q=ai:aristotle.Reprinted from [\textit{Aristotle}, Prior analytics. Translated from the Greek, with introduction, notes, and commentary by Robin Smith. Indianapolis, IN etc.: Hackett Publishing Co. (1989; Zbl 0726.01003)].
For the entire collection see [Zbl 1484.68015].An investigation of the laws of thought on which are founded the mathematical theories of logic and probabilities (1854)https://zbmath.org/1528.680042024-03-13T18:33:02.981707Z"Boole, George"https://zbmath.org/authors/?q=ai:boole.georgeReprinted from [\textit{G. Boole}, An investigation of the laws of thought. On which are founded the mathematical theories of logic and probabilities. Reprint of the 1854 original. Cambridge: Cambridge University Press (2009; Zbl 1205.03003)].
For the entire collection see [Zbl 1484.68015].As we may think (1945)https://zbmath.org/1528.680052024-03-13T18:33:02.981707Z"Bush, Vannevar"https://zbmath.org/authors/?q=ai:bush.vannevarReprint of [the author, Atlantic Monthly 176, 112--124 (1945)].
For the entire collection see [Zbl 1484.68015].Mathematical problems (1900)https://zbmath.org/1528.680062024-03-13T18:33:02.981707Z"Hilbert, David"https://zbmath.org/authors/?q=ai:hilbert.davidReprinted from [\textit{D. Hilbert}, Bull. Am. Math. Soc. 8, 437--479 (1902; JFM 33.0976.07)].
For the entire collection see [Zbl 1484.68015].The education of a computer (1952)https://zbmath.org/1528.680072024-03-13T18:33:02.981707Z"Hopper, Grace Murray"https://zbmath.org/authors/?q=ai:hopper.graceReprint of [the author, in: ACM '52: Proceedings of the 1952 ACM national meeting (Pittsburgh), May 1952, 243--249 (1952; \url{doi:10.1145/609784.609818})].
For the entire collection see [Zbl 1484.68015].On the shortest spanning subtree of a graph and the traveling salesman problem (1956)https://zbmath.org/1528.680082024-03-13T18:33:02.981707Z"Kruskal, Joseph B. jun."https://zbmath.org/authors/?q=ai:kruskal.joseph-b-junReprint of [the author, Proc. Am. Math. Soc. 7, 48--50 (1956; Zbl 0070.18404)].
For the entire collection see [Zbl 1484.68015].The true method (1677)https://zbmath.org/1528.680092024-03-13T18:33:02.981707Z"Leibniz, Gottfried Wilhelm"https://zbmath.org/authors/?q=ai:leibniz.gottfried-wilhelmReprint of a translation by Lloyd Strickland (2020) of a manuscript held by G. W. Leibniz Bibliothek, Hanover.
For the entire collection see [Zbl 1484.68015].A logical calculus of the ideas immanent in nervous activity (1943)https://zbmath.org/1528.680102024-03-13T18:33:02.981707Z"McCulloch, Warren"https://zbmath.org/authors/?q=ai:mcculloch.warren-s"Pitts, Walter"https://zbmath.org/authors/?q=ai:pitts.walterReprint of [the authors, Bull. Math. Biophys. 5, 115--133 (1943; Zbl 0063.03860)].
For the entire collection see [Zbl 1484.68015].Sketch of the analytical engine (1843). With notes by the translator, Ada Augusta, Countess of Lovelacehttps://zbmath.org/1528.680112024-03-13T18:33:02.981707Z"Menabrea, L. F."https://zbmath.org/authors/?q=ai:menabrea.f-lReprinted from [\textit{L. F. Menabrea}, Sketch of the analytical engine invented by Charles Babbage, Esq. London: Taylor and Francis (1843)].
For the entire collection see [Zbl 1484.68015].A symbolic analysis of relay and switching circuits (1938)https://zbmath.org/1528.680122024-03-13T18:33:02.981707Z"Shannon, Claude"https://zbmath.org/authors/?q=ai:shannon.claude-elwoodReprint of [the author, Trans. Am. Inst. Electr. Eng. 57, No. 12, 713--723 (1938; \url{doi:10.1109/T-AIEE.1938.5057767})].
For the entire collection see [Zbl 1484.68015].On computable numbers, with an application to the Entscheidungsproblem (1936)https://zbmath.org/1528.680132024-03-13T18:33:02.981707Z"Turing, Alan Mathison"https://zbmath.org/authors/?q=ai:turing.alan-mReprint of [the author, Proc. Lond. Math. Soc. (2) 42, 230--265 (1936; Zbl 0016.09701; JFM 62.1059.03)].
For the entire collection see [Zbl 1484.68015].Computing machinery and intelligence (1950)https://zbmath.org/1528.680142024-03-13T18:33:02.981707Z"Turing, Alan Mathison"https://zbmath.org/authors/?q=ai:turing.alan-mReprint of [the author, Mind 59, No. 236, 433--460 (1950; \url{doi:10.1093/mind/LIX.236.433})].
For the entire collection see [Zbl 1484.68015].First draft of a report on the EDVAC (1945)https://zbmath.org/1528.680152024-03-13T18:33:02.981707Z"von Neumann, John"https://zbmath.org/authors/?q=ai:von-neumann.johnReprinted from [the author, IEEE Ann. Hist. Comput. 15, No. 4, 27--75 (1993; Zbl 0944.01510)].
For the entire collection see [Zbl 1484.68015].The best way to design an automatic calculating machine (1951)https://zbmath.org/1528.680162024-03-13T18:33:02.981707Z"Wilkes, Maurice"https://zbmath.org/authors/?q=ai:wilkes.maurice-vincentReprint of [the author, Microprocess. Microprogramm. 8, No. 3--5, 141--144 (1981; \url{doi:10.1016/0165-6074(81)90018-1})].
For the entire collection see [Zbl 1484.68015].Do we have any viable solution to the measurement problem?https://zbmath.org/1528.810212024-03-13T18:33:02.981707Z"Adlam, Emily"https://zbmath.org/authors/?q=ai:adlam.emily-christineSummary: Wallace has recently argued that a number of popular approaches to the measurement problem can't be fully extended to relativistic quantum mechanics and quantum field theory; Wallace thus contends that as things currently stand, only the unitary-only approaches to the measurement problem are viable. However, the unitary-only approaches face serious epistemic problems which may threaten their viability as solutions, and thus we consider that it remains an urgent outstanding problem to find a viable solution to the measurement problem which can be extended to relativistic quantum mechanics. In this article we seek to understand in general terms what such a thing might look like. We argue that in order to avoid serious epistemic problems, the solution must be a single-world realist approach, and we further argue that any single-world realist approach which is able to reproduce the predictions of relativistic quantum mechanics will most likely have the property that our observable reality does not supervene on dynamical, precisely-defined microscopic beables. Thus we suggest three possible routes for further exploration: observable reality could be approximate and emergent, as in relational quantum mechanics with the addition of cross-perspective links, or observable reality could supervene on beables which are not microscopically defined, as in the consistent histories approach, or observable reality could supervene on beables which are not dynamical, as in Kent's solution to the Lorentzian classical reality problem. We conclude that once all of these issues are taken into account, the options for a viable solution to the measurement problem are significantly narrowed down.Twenty years of EUROPT, the EURO working group on continuous optimizationhttps://zbmath.org/1528.900012024-03-13T18:33:02.981707Z"Cafieri, Sonia"https://zbmath.org/authors/?q=ai:cafieri.sonia"Tchemisova, Tatiana"https://zbmath.org/authors/?q=ai:tchemisova.tatiana-v"Weber, Gerhard-Wilhelm"https://zbmath.org/authors/?q=ai:weber.gerhard-wilhelmSummary: EUROPT, the Continuous Optimization working group of EURO, celebrated its 20 years of activity in 2020. We trace the history of this working group by presenting the major milestones that have led to its current structure and organization and its major trademarks, such as the annual EUROPT workshop and the EUROPT Fellow recognition.EUR\(O\)pt, the continuous optimization working group of EURO: from idea to maturityhttps://zbmath.org/1528.900022024-03-13T18:33:02.981707Z"Illés, Tibor"https://zbmath.org/authors/?q=ai:illes.tibor"Terlaky, Tamás"https://zbmath.org/authors/?q=ai:terlaky.tamasSummary: This brief note presents a personal recollection of the early history of EUR\(O\)pt, the Continuous Optimization Working Group of EURO. This historical note details the events that happened before the formation of EUR\(O\)pt Working Group and the first five years of its existence. During the early years EUR\(O\)pt Working Group established a conference series, organized thematic EURO Mini conferences, launched the EUR\(O\)pt Fellow program, developed an effective rotating management structure, and grown to a large, matured, very active and high impact EURO Working Group.Error detecting and error correcting codes (1950)https://zbmath.org/1528.940012024-03-13T18:33:02.981707Z"Hamming, R. W."https://zbmath.org/authors/?q=ai:hamming.richard-wesleyReprint of [the author, Bell Syst. Tech. J. 29, No. 2, 147--160 (1950; Zbl 1402.94084)].
For the entire collection see [Zbl 1484.68015].