History of Mathematics

Hilbert's axiomatic approach was an optimistic take over on the side of the logical foundations. It was also a response to various restrictive views of mathematics supposedly bounded by the reaches of epistemic elements in mathematics. A complete axiomatization should be able to exclude epistemic or ontic elements from mathematical theorizing, according to Hilbert. This exclusion is not necessarily a logicism in similar form to Frege's or Dedekind's projects. That is, intuition can still have a role in mathematical reasoning. Nevertheless, (...) this role is to be given a structural orientation with the help of explications of the underlying logic of axiomatization. (shrink)

Tatiana Ehrenfest-Afanassjewa was an important physicist, mathematician, and educator in 20th century Europe. While some of her work has recently undergone reevaluation, little has been said regarding her groundbreaking work on dimensional analysis. This, in part, reflects an unfortunate dismissal of her interventions in such foundational debates by her contemporaries. In spite of this, her work on the generalized theory of homogeneous equations provides a mathematically sound foundation for dimensional analysis and has found some appreciation and development. It remains to (...) provide a historical account of Ehrenfest-Afanassjewa's use of the theory of homogeneous functions to ground (and limit) dimensional analysis. We take as a central focus Ehrenfest-Afanassjewa's contributions to a debate on the foundations of dimensional analysis started by physicist Richard Tolman in 1914. I go on to suggest an interpretation of the more thoroughgoing intervention Ehrenfest-Afanassjewa makes in 1926 based on this earlier context, especially her limited rehabilitation of a "theory of similitude" in contradistinction to dimensional analysis. It is shown that Ehrenfest-Afanassjewa has made foundational contributions to the mathematical foundations and methodology of dimensional analysis, our conception of the relation between constants and laws, and our understanding of the quantitative nature of physics, which remain of value. (shrink)

The reception of Newton's Principia in 1687 led to the attempt of many European scholars to ‘mathematicise' their field of expertise. An important example of this ‘mathematicisation' lies in the work of Irish-Scottish philosopher Francis Hutcheson, a key figure in the Scottish Enlightenment. This essay aims to discuss the mathematical aspects of Hutcheson's work and its impact on British thought in the following centuries, providing a case in point for the importance of the interactions between mathematics and philosophy throughout time.

Husserl’s Philosophy of Mathematical Practice explores the applicability of the phenomenological method to philosophy of mathematical practice. The first section elaborates on Husserl’s own understanding of the method of radical sense-investigation (Besinnung), with which he thought the mathematics ofhis time should be approached. The second section shows how Husserl himself practiced it in tracking both constructive and platonistic features in mathematical practice. Finally, the third section situates Husserlian phenomenology within the contemporary philosophy of mathematical practice, where the examined styles are (...) more diverse. Husserl’s phenomenology is presented as a method, not a fixed doctrine, applicable to study and unify philosophy of mathematical practice and the metaphysics implied in it. In so doing, this Element develops Husserl’s philosophy of mathematical practice as a species of Kantian critical philosophy and asks after the conditions of possibility of social and self-critical mathematical practices. (shrink)

Set-theoretic potentialism is one of the most lively trends in the philosophy of mathematics. Modal accounts of sets have been developed in two different ways. The first, initiated by Charles Parsons, focuses on sets as objects. The second, dating back to Hilary Putnam and Geoffrey Hellman, investigates set-theoretic structures. The paper identifies two strands of open issues, technical and conceptual, to clarify these two different, yet often conflated, views and categorize the potentialist approaches that have emerged in the contemporary debate. (...) The final outcome is a taxonomy that should help researchers navigate the rich landscape of modal set theories. (shrink)

One of the general criteria G. H. Hardy identifies and discusses in his famous essay A Mathematician’s Apology (Cambridge University Press, Cambridge, 1940) by which a mathematician’s patterns must be judged is seriousness. This article focuses on one of Hardy’s examples of a non-serious theorem, namely that 8712 and 9801 are the only numbers below 10000 which are integral multiples of their reversals, in the sense that 8712 = 4·2178, and 9801 = 9·1089. In the context of a discussion of (...) generality, which he considers an essential quality of seriousness, he explains that there is nothing in this example which “appeals much to a mathematician” and that it is “not capable of any significant generalization.” Interestingly, since the publication of the Apology, more than a dozen papers—including one by the renowned mathematician Neil Sloane—have been published that discuss generalizations of Hardy’s example. By identifying the most important aspect of Hardy’s notion of generality, it is argued that, contrary to the views of several researchers, Hardy’s claim regarding the non-capability of any significant generalization is still tenable. Furthermore, this case study is presented and discussed as an example of the multifaceted nature of mathematical interest. (shrink)

The cognitive basis of geometry is still poorly understood, even the ‘simpler’ issue of what kind of representation of geometric objects we have. In this work, we set forward a tentative model of the neural representation of geometric objects for the case of the pure geometry of Euclid. To arrive at a coherent model, we found it necessary to consider earlier forms of geometry. We start by developing models of the neural representation of the geometric figures of ancient Greek practical (...) geometry. Then, we propose a related model for the earliest form of pure geometry – that of Hippocrates of Chios. Finally, we develop the model of the neural representation of the geometric objects of Euclidean geometry. The models are based on the hub-and-spoke theory. In our view, the existence of specific models opens the possibility of addressing the relationship between geometric figures and geometric objects, in a novel way, in terms of their neural representation. (shrink)

Brouwer’s intuitionism was a far-reaching attempt to reform the foundations of mathematics. While the mathematical community was reluctant to accept Brouwer’s work, its response to later-developed brands of intuitionism, such as those presented by Hermann Weyl and Arend Heyting, was different. The paper accounts for this difference by analyzing the intuitionistic versions of Brouwer, Weyl, and Heyting in light of a two-tiered model of the body and image of mathematical knowledge. Such a perspective provides a richer account of each story (...) and points to a possible connection between the community’s reaction and the changes each mathematician had proposed. (shrink)

The year 2023 celebrates the 125th anniversary of the birth of Mark Yakovlevich Vygodsky, a famous Soviet mathematician and pedagogue, one of the founders of the Soviet school of the history of mathematics. Not only the scientist's scientific achievements, but also his significant contribution to pedagogical theory and practice, allow us to describe him as a significant scientific figure of the twentieth century. His mathematics textbooks and reference books are reprinted almost annually, so that his ideas continue to influence educational (...) and scientific practice to this day. This article is the second in a series of publications prepared by the author, who is the great-grandson of M.Y. Vygodsky. This research presents previously unpublished scientific results and discoveries concerning the life and work of the scholar. Firstly, based on archival data and family memories, detailed facts about his origins, young years and his development as a scientist are presented. At the same time, a rather complete chronology of M.Y. Vygodsky's scientific activity and personal life is compiled. Secondly, for the first time, a complete list of his main scientific contributions has been prepared, which makes it possible to assess the talent and the scale of his academic achievements. The presented results may be useful for prospective scientific and historical studies. In the modern context, it seems valuable to present a picture of M.Y. Vygodsky's life and work, as he was an interdisciplinary researcher and in this he was ahead of his time. In our changing world, contemporary challenges require the same interdisciplinarity to solve complex problems, and a fresh look at the life and work of a scholar like M.J. Vygodsky can stimulate inspiration in the modern researcher, student, and anyone seeking development and awareness. (shrink)

This article aims at identifying the sources of fols. 395r and 686r-686v of the Codex Atlanticus. These anonymous folios, inserted in Leonardo da Vinci’s notebooks, do not deal with the duplication of the cube proper, nor do they derive from Giorgio Valla’s De expetendis et fugiendis rebus (1501), as has been claimed. They deal specifically with the extraction of the cube root by geometric methods. The analysis of the sources by the tracer method reveals that these fragments are taken from (...) the Practica geometrie by Leonardo Fibonacci (1220) and, more precisely, from a volgarizzamento that appears in the Praticha d’arismetrica by Benedetto da Firenze (1463). Leonardo could have consulted this text in one of his two Florentine periods, around 1463-1482 or around 1503-1506. (shrink)

Brouwer’s intuitionistic program was an intriguing attempt to reform the foundations of mathematics that eventually did not prevail. The current paper offers a new perspective on the scientific community’s lack of reception to Brouwer’s intuitionism by considering it in light of Michael Friedman’s model of parallel transitions in philosophy and science, specifically focusing on Friedman’s story of Einstein’s theory of relativity. Such a juxtaposition raises onto the surface the differences between Brouwer’s and Einstein’s stories and suggests that contrary to Einstein’s (...) story, the philosophical roots of Brouwer’s intuitionism cannot be traced to any previously established philosophical traditions. The paper concludes by showing how the intuitionistic inclinations of Hermann Weyl and Abraham Fraenkel serve as telling cases of how individuals are involved in setting in motion, adopting, and resisting framework transitions during periods of disagreement within a discipline. (shrink)

The classification of algebraic surfaces by the Italian School of algebraic geometry is universally recognized as a breakthrough in 20th-century mathematics. The methods by which it was achieved do not, however, meet the modern standard of rigor and therefore appear dubious from a contemporary viewpoint. In this article, we offer a glimpse into the mathematical practice of the three leading exponents of the Italian School of algebraic geometry: Castelnuovo, Enriques, and Severi. We then bring into focus their distinctive conception of (...) rigor and intuition. Unlike what is often assumed today, from their perspective, rigor is neither opposed to intuition nor understood as a unitary phenomenon – Enriques distinguishes between small-scale rigor and large-scale rigor and Severi between formal rigor and substantial rigor. Finally, we turn to the notion of mathematical objectivity. We draw from our case study in order to advance a multi-dimensional analysis of objectivity. Specifically, we suggest that various types of rigor may be associated with different conceptions of objectivity: namely, objectivity as faithfulness to facts and objectivity as intersubjectivity. (shrink)

Ein Beispiel für die Rezeption und Fortführung der schopenhauerschen Logik findet man in den Mathematiklehrbüchern Friedrich Adolph Wilhelm Diesterwegs (1790–1866), In diesem Aufsatz werden die historische und systematische Dimension dieser Anwendung von Logikdiagramme auf die Mathematik skizziert. In Kapitel 2 wird zunächst die frühe Rezeption der schopenhauerschen Logik und Philosophie der Mathematik vorgestellt. Dabei werden einige oftmals tradierte Vorurteile, die das Werk Schopenhauers betreffen, in Frage gestellt oder sogar ausgeräumt. In Kapitel 3 wird dann die Philosophie der Mathematik und der (...) Logik Schopenhauers vorgestellt. Es wird gezeigt, dass Schopenhauers Logikdiagramme auf Ideen der Mathematiker Leonhard Euler (1707–1783), Bernhard Friedrich Thibaut (1775–1832) und Franz Ferdinand Schweins (1780–1856) zurückgehen und dass Schopenhauer diese Logikdiagramme auch bereits zur Analyse mathematischer Begriffe verwendet. Kapitel 4 beschäftigt sich mit der Schopenhauer-Rezeption Diesterwegs. Es wird die Frage behandelt, inwieweit Diesterweg in der Mathematik von Schopenhauer beeinflusst war und welche Rolle dieser Einfluss auf sein Verständnis von Logik und Mathematik hatte. In Kapitel 5 wird schließlich gezeigt, dass Diesterweg die schopenhauersche Begriffsanalyse der Mathematik mit Hilfe von Logikdiagrammen aufgreift und weiterführt. Da Diesterweg einer der einflussreichsten Pädagogen und Mathematikdidaktiker des 20. Jahrhunderts war, ist anzunehmen, dass sich Spuren dieser Methode noch heute finden lassen. Inwiefern dies wahrscheinlich ist, wird in der Zusammenfassung (Kapitel 6) thematisiert. (shrink)

Open Court began publishingThe Monistin 1890 as a journal“devotedto the philosophy of science”that regularly included mathematics. The audiencewas understood to be“cultured people who have not a technical mathematicaltraining”but nevertheless“have a mathematical penchant.”With these constraints,the mathematical content varied from recreations to logical foundations, but every-one had something to say about non-Euclidean geometry, in debates that rangedfrom psychology to semantics. The focus in this essay is on the contested value ofmathematical expertise in legitimating what should be considered as mathematics.While some mathematicians urgedThe (...) Monistto uphold disciplinary standards ofgeometrical reasoning, authors opposed tonon-Euclidean geometry aligned theirreasoning with practical applications, universal know-how, and nonhierarchicaldemocracy. As one contributorinquired,“How isthe professional expert betterfit-ted to see more lucidly in dealing with the elements of geometry than any otherperson of good geometric faculty?”. (shrink)

The paper examines Yankov’s contribution to the history of mathematical logic and the foundations of mathematics. It concerns the public communication of Markov’s critical attitude towards Brouwer’s intuitionistic mathematics from the point of view of his constructive mathematics and the commentary on A.S. Esenin-Vol’pin program of ultra-intuitionistic foundations of mathematics.

The paper examines the main points of Yankov’s hypothesis on the rise of Greek mathematics. The novelty of Yankov’s interpretation is that the rise of mathematics is examined within the context of the rise of ontological theories of the early Greek philosophers, which mark the beginning of rational thinking, as understood in the Western tradition.

The paper explores Hermann Weyl’s turn to intuitionism through a philosophical prism of normative framework transitions. It focuses on three central themes that occupied Weyl’s thought: the notion of the continuum, logical existence, and the necessity of intuitionism, constructivism, and formalism to adequately address the foundational crisis of mathematics. The analysis of these themes reveals Weyl’s continuous endeavor to deal with such fundamental problems and suggests a view that provides a different perspective concerning Weyl’s wavering foundational positions. Building on a (...) philosophical model of scientific framework transitions and the special role that normative indecision or ambivalence plays in the process, the paper examines Weyl’s motives for considering such a radical shift in the first place. It concludes by showing that Weyl’s shifting stances should be regarded as symptoms of a deep, convoluted intrapersonal process of self-deliberation induced by exposure to external criticism. (shrink)

Bernard Bolzano (1781–1848) is commonly thought to have attempted to develop a theory of size for infinite collections that follows the so-called part–whole principle, according to which the whole is always greater than any of its proper parts. In this paper, we develop a novel interpretation of Bolzano’s mature theory of the infinite and show that, contrary to mainstream interpretations, it is best understood as a theory of infinite sums. Our formal results show that Bolzano’s infinite sums can be equipped (...) with the rich and original structure of a non-commutative ordered ring, and that Bolzano’s views on the mathematical infinite are, after all, consistent. (shrink)

The paper discusses Peano's defense and application of permanence of forms as a principle of mathematical practice. (Dedicated to the memory of Mic Detlefsen.).

It has been argued in relation to Old Babylonian mathematical procedure texts that their validity or correctness is self-evident. One “sees” that the procedure is correct without it having, or being accompanied by, any explicit arguments for the correctness of the procedure. Even when agreeing with this view, one might still ask about how is the correctness of a procedure articulated? In this work, we present an articulation of the correctness of ancient Egyptian and Old Babylonian mathematical procedure texts – (...) mathematical texts presenting the solution of problems. We endeavor to make explicit and explain how and why the procedures are reliable over and above the fact that their correctness is intuitive. (shrink)

The purpose of this work is to address the relation existing between ancient Greek practical geometry and ancient Greek pure geometry. In the first part of the work, we will consider practical and pure geometry and how pure geometry can be seen, in some respects, as arising from an idealization of practical geometry. From an analysis of relevant extant texts, we will make explicit the idealizations at play in pure geometry in relation to practical geometry, some of which are basically (...) explicit in definitions, like that of segments in Euclid’s Elements. Then, we will address how in pure geometry we, so to speak, “refer back” to practical geometry. This occurs in two ways. One, in the propositions of pure geometry. The other, when applying pure geometry. In this case, geometrical objects can represent practical figures like, e.g., a practical segment. (shrink)

Archimedes’ statics is considered as an example of ancient Greek applied mathematics; it is even seen as the beginning of mechanics. Wilbur Knorr made the case regarding this work, as other works by him or other mathematicians from ancient Greece, that it lacks references to the physical phenomena it is supposed to address. According to Knorr, this is understandable if we consider the propositions of the treatise in terms of purely mathematical elaborations suggested by quantitative aspects of the phenomena. In (...) this paper, we challenge Knorr’s view, and address propositions of Archimedes’ statics in their relation to physical phenomena. (shrink)

Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss (...) and Eisenstein, and a sophisticated proof using algebraic number theory, due to Hilbert. Philosophers have yet to look carefully at such explanatory disagreements in mathematics. I do so here. According to the view I defend, there are two important explanatory virtues—depth and transparency—which different proofs (and other potential explanations) possess to different degrees. Although not mutually exclusive in principle, the packages of features associated with the two stand in some tension with one another, so that very deep explanations are rarely transparent, and vice versa. After developing the theory of depth and transparency and applying it to the case of quadratic reciprocity, I draw some morals about the nature of mathematical explanation. (shrink)

In Bertrand Russell's 1903 Principles of Mathematics, he offers an apparently devastating criticism of the neo-Kantian Hermann Cohen's Principle of the Infinitesimal Method and its History (PIM). Russell's criticism is motivated by his concern that Cohen's account of the foundations of calculus saddles mathematics with the paradoxes of the infinitesimal and continuum, and thus threatens the very idea of mathematical truth. This paper defends Cohen against that objection of Russell's, and argues that properly understood, Cohen's views of limits and infinitesimals (...) do not entail the paradoxes of the infinitesimal and continuum. Essential to that defense is an interpretation, developed in the paper, of Cohen's positions in the PIM as deeply rationalist. The interest in developing this interpretation is not just that it reveals how Cohen's views in the PIM avoid the paradoxes of the infinitesimal and continuum. It also reveals some of what is at stake, both historically and philosophically, in Russell's criticism of Cohen. (shrink)

The “four-color” theorem seems to be generalizable as follows. The four-letter alphabet is sufficient to encode unambiguously any set of well-orderings including a geographical map or the “map” of any logic and thus that of all logics or the DNA plan of any alive being. Then the corresponding maximally generalizing conjecture would state: anything in the universe or mind can be encoded unambiguously by four letters. That admits to be formulated as a “four-letter theorem”, and thus one can search for (...) a properly mathematical proof of the statement. It would imply the “four colour theorem”, the proof of which many philosophers and mathematicians believe not to be entirely satisfactory for it is not a “human proof”, but intermediated by computers unavoidably since the necessary calculations exceed the human capabilities fundamentally. It is furthermore rather unsatisfactory because it consists in enumerating and proving all cases one by one. Sometimes, a more general theorem turns out to be much easier for proving including a general “human” method, and the particular and too difficult for proving theorem to be implied as a corollary in certain simple conditions. The same approach will be followed as to the four colour theorem, i.e. to be deduced more or less trivially from the “four-letter theorem” if the latter is proved. References are only classical and thus very well-known papers: their complete bibliographic description is omitted. (shrink)

David Lindsay Roberts. Republic of Numbers: Unexpected Stories of Mathematical Americans through History. ix + 244 pp., bibl., index. Baltimore: Johns Hopkins University Press, 2019. $29.95 (cloth); ISBN 9781421433080. E-book available. Julian Havil. Curves for the Mathematically Curious: An Anthology of the Unpredictable, Historical, Beautiful, and Romantic. xx + 259 pp., apps., refs., index. Princeton, N.J./Oxford: Princeton University Press, 2019. $29.95 (cloth); ISBN 9780691180052. E-book available. David S. Richeson. Tales of Impossibility: The Two-Thousand-Year Quest to Solve the Mathematical Problems of (...) Antiquity. xii + 436 pp., notes, refs., index. Princeton, N.J./Oxford: Princeton University Press, 2019. $29.95 (cloth); ISBN 9780691192963. E-book availabl. (shrink)

This book offers insights relevant to modern history and epistemology of physics, mathematics and, indeed, to all the sciences and engineering disciplines emerging of 19th century. This research volume is the first of a set of three Springer books on Lazare Nicolas Marguérite Carnot’s (1753–1823) remarkable work: Essay on Machines in General (Essai sur les machines en général [1783] 1786). The other two forthcoming volumes are: Principes fondamentaux de l’équilibre et du mouvement (1803) and Géométrie de position (1803). Lazare Carnot (...) – l'organisateur de la victoire – in Essai sur le machine en général (1786) assumed that the generalization of machines was a necessity for society and its economic development. Subsequently, his new coming science applied to machines attracted considerable interest for technician, as well, already in the 1780’s. With no lack in rigour, Carnot used geometric and trigonometric rather than algebraic arguments, and usually went on to explain in words what the formulae contained. His main physical– mathematical concepts were the Geometric motion and Moment of activity–concept of Work . In particular, he found the invariants of the transmission of motion (by stating the principle of the moment of the quantity of motion) and theorized the condition of the maximum efficiency of mechanical machines (i.e., principle of continuity in the transmission of power). While the core theme remains the theories and historical studies of the text, the book contains an extensive Introduction and an accurate critical English Translation – including the parallel text edition and substantive critical/explicative notes – of Essai sur les machines en général (1786). The authors offer much-needed insight into the relation between mechanics, mathematics and engineering from a conceptual, empirical and methodological, and universalis point of view. As a cutting–edge writing by leading authorities on the history of physics and mathematics, and epistemological aspects, it appeals to historians, epistemologist–philosophers and scientists (physicists, mathematicians and applied sciences and technology). (shrink)

From 1908 to 1916, articles supporting the axiom of choice were scant. The situation changed in 1916, when Wacław Sierpiński published a series of articles reviving the debate. The posterity of the axiom of choice as we know it would be unimaginable without Sierpiński’s efforts.

The purpose of this work is to address what notion of geometrical object and geometrical figure we have in different kinds of geometry: practical, pure, and applied. Also, we address the relation between geometrical objects and figures when this is possible, which is the case of pure and applied geometry. In practical geometry it turns out that there is no conception of geometrical object.

In his well-known paper on Euclid’s geometry, Ken Manders sketches an argument against conceiving the diagrams of the Elements in ‘semantic’ terms, that is, against treating them as representations—resting his case on Euclid’s striking use of ‘impossible’ diagrams in some proofs by contradiction. This paper spells out, clarifies and assesses Manders’s argument, showing that it only succeeds against a particular semantic view of diagrams and can be evaded by adopting others, but arguing that Manders nevertheless makes a compelling case that (...) semantic analyses ought to be relegated to a secondary role for the study of mathematical practices. (shrink)

Relying upon a very close reading of all of the definitions given in Euclid’s Elements, I argue that this mathematical treatise contains a philosophical treatment of mathematical objects. Specifically, I show that Euclid draws elaborate metaphysical distinctions between substances and non-substantial attributes of substances, different kinds of substance, and different kinds of non-substance. While the general metaphysical theory adopted in the Elements resembles that of Aristotle in many respects, Euclid does not employ Aristotle’s terminology, or indeed, any philosophical terminology at (...) all. Instead, Euclid systematically uses different types of definition to distinguish between metaphysically different kinds of mathematical object. (shrink)

in this paper we return to Marshall Clagett’s view about the existence of an ancient Greek geometry of motion. It can be read in two ways. As a basic presentation of ancient Greek geometry of motion, followed by some aspects of its further development in landmark works by Galileo and Newton. Conversely, it can be read as a basic presentation of aspects of Galileo’s and Newton’s mathematics that can be considered as developments of a geometry of motion that was first (...) conceived by ancient Greek mathematicians. (shrink)

Albert Lautman (b. 1908–1944) was a philosopher of mathematics whose views on mathematical reality and on the philosophy of mathematics parted with the dominant tendencies of mathematical epistemology of the time. Lautman considered the role of philosophy, and of the philosopher, in relation to mathematics to be quite specific. He writes that: ‘in the development of mathematics, a reality is asserted that mathematical philosophy has as a function to recognize and describe’ (Lautman 2011, 87). He goes on to characterize this (...) reality as an ‘ideal reality’ that ‘governs’ the development of mathematics. The relation between mathematical problems as they arise in the historical development of mathematics and the solutions that are provided to these problems by mathematicians, in the form of new mathematical theories, definitions or axioms, are governed by a what Lautman characterises as a dialectics of mathematics. The aim of this paper is to give an account of this Lautmanian dialectic and of how it can be understood to govern the development of solutions to mathematical problems. (shrink)

Mathematics has always been a core part of western education, from the medieval quadrivium to the large amount of arithmetic and algebra still compulsory in high schools. It is an essential part. Its commitment to exactitude and to rigid demonstration balances humanist subjects devoted to appreciation and rhetoric as well as giving the lie to postmodernist insinuations that all “truths” are subject to political negotiation. In recent decades, the character of mathematics has changed – or rather broadened: it has become (...) the enabling science behind the complexity of contemporary knowledge, from gene interpretation to bank risk. Mathematical understanding is all the more necessary for future jobs, as well as remaining, as ever, a prophylactic against the more corrosive philosophical views emanating from the humanities. (shrink)

The influence of religious beliefs to several leading mathematicians in early Soviet years, especially among members of the Moscow Mathematical Society, had drawn the attention of militant Soviet marxists, as well as Soviet authorities. The issue has also drawn significant attention from scholars in the post-Soviet period. According to the currently prevailing interpretation, reported purges against Moscow mathematicians due to their religious inclination are the focal point of the relevant history. However, I maintain that historical data arguably offer reasons to (...) cast reasonable doubts on this interpretation. In this paper, by reviewing the relevant literature, I raise some methodological and philosophical concerns, in an attempt to contribute to a better understanding of the issue. I maintain that an efficient line of reasoning is to discuss issues in the context of their making, taking into consideration the specific features of each era’s culture. Thus, by focusing on P.A. Nekrasov’s case, I attempt to point to an alternative interpretation, in which the different treatment of religious inclined mathematicians by Soviet authorities is explained in the context of the ideological confrontation between two contrasting worldviews, as part of the ongoing class war in the several phases of Soviet history. (shrink)