History of Mathematics in Hungary until the 20th Century

1992 ◽  
Author(s):  
Barna Szénássy
Keyword(s):  
20Th Century ◽  
History Of Mathematics ◽  
History Of

scholarly journals A short remark on Gödel incompleteness theorem and its self-referential paradox from Neutrosophic Logic perspective

2019 ◽  
pp. 21-26
Author(s):  
V. Christianto ◽  
◽  
◽  
F. Smarandache
Keyword(s):  
20Th Century ◽  
History Of Mathematics ◽  
The Self ◽  
Incompleteness Theorem ◽  
Aristotelian Logic ◽  
Binary Logic ◽  
Neutrosophic Logic ◽  
History Of ◽  
Incompleteness Theorems ◽  
Modern Mathematics

It is known from history of mathematics, that Gödel submitted his two incompleteness theorems, which can be considered as one of hallmarks of modern mathematics in 20th century. Here we argue that Gödel incompleteness theorem and its self-referential paradox have not only put Hilbert’s axiomatic program into question, but he also opened up the problem deep inside the then popular Aristotelian Logic. Although there were some attempts to go beyond Aristotelian binary logic, including by Lukasiewicz’s three-valued logic, here we argue that the problem of self-referential paradox can be seen as reconcilable and solvable from Neutrosophic Logic perspective. Motivation of this paper: These authors are motivated to re-describe the self-referential paradox inherent in Godel incompleteness theorem. Contribution: This paper will show how Neutrosophic Logic offers a unique perspective and solution to Godel incompleteness theorem.

scholarly journals Proof of Fermat's Last Theorem By Infinite Descent

2020 ◽  
Author(s):  
Djamel Himane
Keyword(s):  
20Th Century ◽  
Elementary Function ◽  
Mathematical Problem ◽  
History Of Mathematics ◽  
Peano Arithmetic ◽  
Basic Principles ◽  
Fermat's Last Theorem ◽  
Fermat’S Last Theorem ◽  
History Of ◽  
Infinite Descent

Fermat's last theorem, one of the most challenging theories in the history of mathematics, has been conjectured by French lawyer Pierre de Verma in 1637. Since then, it wasconsidered the most difficult and unsolvable mathematical problem. However, more than three centuries later, a first proof was proposed by the British mathematician Andrew Wiles in 1994, relying on 20th-century techniques. Wiles's proof is based on elliptic (oval) curves that were not available at the time when the theory was first proposed. Most mathematicians argued that it was impossible to prove Fermat's theorem according to basic principles of arithmetic, though Harvey Friedman's grand conjecture states that mathematical theorems, including Fermat's Last Theorem, can be solved in very weak systems such as the Elementary Function Arithmetic (EFA). Friedman's grand conjecture states that "every theorem published in the journal, Annals of Mathematics, whose statement involves only finitary mathematical objects (i.e., what logicians call an arithmetical statement) can be proved in EFA, which is the weak fragment of Peano Arithmetic based on the usual quantifier free axioms for 0,1,+,x, exp, together with thescheme of induction for all formulas in the language all of whose quantifiers are bounded." *

scholarly journals Academician Jonas Kubilius: works dedicated to the history of Lithuanian mathematics

2021 ◽  
Vol 62 ◽  
pp. 13-21
Author(s):  
Juozas Banionis
Keyword(s):  
Probability Theory ◽  
20Th Century ◽  
History Of Mathematics ◽  
Book Series ◽  
Informal Group ◽  
Mathematical School ◽  
Mathematics History ◽  
History Of ◽  
The 19Th Century ◽  
Fourth Book

The rise of the Lithuanian mathematical school in the second half of the 20th century is associated with the development of probability theory and its application, and the foundations of that school were insightfully laid by the famous Lithuanian mathematician Jonas Kubilius. However, the academician also had a second vocation – the history of mathematics. At the end of the 20th century, he purposefully researched the mathematical legacy of the poet, bishop A. Baranauskas, recognizing him as the first Lithuanian mathematician researcher of the second half of the 19th century. At the beginning of the 21st century, J. Kubilius undertook a detailed implementation of the idea of a work in the history of Lithuanian mathematics. For this purpose, an informal group of specialists was convened, the content of the work was planned, and the research-based book series ``From the History of Lithuanian Mathematics'' was published. The fourth book in this series, Mathematics in Lithuanian Higher Education Institutions in 1921–1944, presents the research of an academic who reveals the situation of mathematics in universities in Kaunas and Vilnius. In addition, the memoirs of mathematics history by J. Kubilius, dedicated to mathematicians Z. Žemaitis, G. Žilinskas and V. Statulevičius, should be mentioned. The article, at the end of which fragments of the author's memories are presented, is dedicated to the centenary of the birth of Academician J. Kubilius.

Visual Thinking in Mathematics

Philosophy ◽  
2019 ◽  
Author(s):  
Jessica Carter
Keyword(s):  
20Th Century ◽  
Euclidean Geometry ◽  
18Th Century ◽  
History Of Mathematics ◽  
Mathematical Practice ◽  
Visual Representations ◽  
Visual Thinking ◽  
General Acceptance ◽  
History Of ◽  
Euclid’S Elements

In contemporary philosophy, “visual thinking in mathematics” refers to studies of the kinds and roles of visual representations in mathematics. Visual representations include both external representations (i.e., diagrams) and mental visualization. Currently, three main areas and questions are being investigated. The first concerns the roles of diagrams, or the diagram-based reasoning, found in Euclid’s Elements. Second is the epistemic role of diagrams: the question of whether reasoning based on diagrams can be rigorous. This debate includes the question of whether beliefs based on visual input can be justified, and whether visual perception may lead to mathematical knowledge. The third observes that diagrams abound in (contemporary) mathematical practice, and so tries to understand the role they play, going beyond the traditional debates on the legitimacy of using diagrams in mathematical proofs. Looking at the history of mathematics, one will find that it is only recently that diagrammatic proofs have become discredited. For about 2,000 years, Euclid’s Elements was conceived as the paradigm of (mathematical) rigorous reasoning, and so until the 18th century, Euclidean geometry served as the foundation of many areas of mathematics. One includes the early history of analysis, where the study of curves draws on results from (Euclidean) geometry. During the 18th and 19th centuries, however, diagrams gradually disappear from mathematical texts, and around 1900 one finds the famous statements of Pasch and Hilbert claiming that proofs must not rely on figures. The development of formal logic during the 20th century further contributed to a general acceptance of a view that the only value of figures, or diagrams, is heuristic, and that they have no place in mathematical rigorous proofs. A proof, according to this view, consists of a discrete sequence of sentences and is a symbolic object. In the latter half of the 20th century, philosophers, sensitive to the practice of mathematics, started to object to this view, leading to the emergence of the study of visual thinking in mathematics.

History of Mathematics of the Early 20th Century: The Role of Transition

2008 ◽  
pp. 1295-1360
Author(s):  
Leo Corry ◽  
Della Fenster ◽  
Joachim Schwermer
Keyword(s):  
20Th Century ◽  
History Of Mathematics ◽  
Early 20Th Century ◽  
History Of

scholarly journals Uma ‘Aritmética Para Ensinar’ no Curso Primário: Orientações nos Manuais para o Ensino de Multiplicação

2018 ◽  
Vol 11 (1) ◽  
pp. 64
Author(s):  
Viviane Barros Maciel
Keyword(s):  
Mathematics Education ◽  
Primary School ◽  
20Th Century ◽  
History Of Mathematics ◽  
Early 20Th Century ◽  
Doctoral Research ◽  
Training History ◽  
History Of ◽  
And Training ◽  
Over Time

Como se dá o processo de constituição de uma aritmética para ensinar no curso primário a partir da leitura de orientações dadas aos professores nos manuais pedagógicos (1880 – 1970)? Buscando por respostas a esta questão maior, a pesquisa de doutorado traz um primeiro resultado tendo como foco as orientações para o ensino de multiplicação. Que multiplicação para ensinar se configura no final do século XIX e início do século XX nos manuais pedagógicos? Para tanto, a pesquisa se pautou em autores que colocam os saberes no centro das profissões de ensino e de formação. A extração de elementos a partir da análise das orientações nos manuais e a ligação destes com o que os referenciais denominam ‘saberes para ensinar’ proporcionaram uma leitura da multiplicação para ensinar que se estabelece no período. A perspectiva é de que ao longo do tempo, com a análise de outros manuais e de outros saberes a ensinar, o processo de constituição de uma aritmética para ensinar possa ser revelado.Palavras-chave: aritmética escolar; formação de professores; história da educação matemáticaAbstractHow does happen the constitution process of a ‘arithmetic for teaching’ in the primary school fron the reading of guidelines given to the teachers in manuals teaching (1880 – 1970) ? Looking for answers to this larger question, the doctoral research brings a first result focused guidelines for teaching multiplication. That multiplication for teaching is configured in the late 19th and early 20th century teaching manuals? Thus, the research was based on authors who prioritize knowledge and put them at the heart of the profession of teaching and training. The extraction of elements from the analysis of the guidelines in the manuals and the connection with what the references are called ‘ savoirs pour enseigner ‘ provided a reading of multiplication to teach that is established in the period. It is thought to be possible that over time, with the analysis of other manuals and other knowledges to teaching, the establishment of a arithmetic for teaching process can be revealed.Keywords: school arithmetic; teacher training; history of mathematics education.

The history of Tatar mathematics education

2020 ◽  
pp. 129-142
Author(s):  
Ildar Safuanov
Keyword(s):  
Mathematics Education ◽  
20Th Century ◽  
19Th Century ◽  
History Of Mathematics ◽  
Arabic Language ◽  
Mathematical Education ◽  
Modern Times ◽  
History Of ◽  
Three Stages ◽  
The 19Th Century

The history of mathematics education of the Tatar nation from Medieval to modern times is described. Three stages of the development of mathematical education in Tatar schools are traced: 1) Mathematical education in Arabic language (up to the last decades of the 19th century); 2) Mathematical education in old Turk-Tatar language with terminology mostly in Arabic (second half of 19th century and the beginning of 20th century); 3) Mathematical education in modern Tatar language (from the beginning of the 20th century, especially after the October revolution). Keywords: history, mathematics education, Tatar language

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