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PLATO’s Philosophy of Mathematics
PLATO (Πλάτων) was born around 428 B.C.E. in Athens (or Aigina?). He descended from an old, highly respected Athenian family.
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Doing Mathematics with 3D Pens: Five Years of Research on 3D Printing Integration in Mathematics Classrooms
Technology has the transformative potential to induce deep changes in thinking, learning, and doing mathematics. In this chapter, we discuss the...
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Bi-Lipschitz Characterization of Space Curves
In the paper Targino (Outer Lipschitz Geometry of Complex Algebraic Plane Curves. International Mathematics Research Notices, rnac202.
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On “Space” and “Geometry” in the Nineteenth Century
What did mathematicians mean by the words “space” and “geometry” in the nineteenth century? This chapter will try to answer this question, starting...
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Advice to a Young Mathematician Wishing to Enter the History of Mathematics
In this chapter, I will try to explain some basic issues in doing the history of mathematics, which seem almost self-evident though often not easy to...
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Experiments in Mathematics: Fact, Fiction, or the Future?
In this chapter, the possibility of experiments in mathematics is examined. A general scheme is proposed as a tool to handle the different forms of...
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Mathematics, the Human Mind, Verbal Language: Mathematics in Mind
In Chap. 1 we scoped out the domain of mathematics. In this chapter, we explore the complex...
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Kernels of Toeplitz operators on the Bergman space
A Coburn theorem says that a nonzero Toeplitz operator on the Hardy space is one-to-one or its adjoint operator is one-to-one. We study the...
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Nexus 20/21, Relationships Between Architecture and Mathematics: Part II
This letter from the editors introduces Vol. 24(3) of the Nexus Network Journal , which is the second special issue of selected papers from the Nexus...
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Daniele Barbaro and the Science of Mathematics
Daniele Barbaro is an interesting figure not only because he was working at a time which there was an ongoing debate that led to precisely a...
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On the Number of Irreducible Components of the Moduli Space of Semistable Reflexive Rank 2 Sheaves on the Projective Space
In 2017, Jardim, Markushevich, and Tikhomirov found a new infinite series of irreducible components of the moduli space of semistable nonlocally free...
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Solution of a Two-Facility Location Problem in a Space with Chebyshev Distance
AbstractThe work considers a minimax two-facility location problem in a multidimensional space with Chebyshev distance under interval constraints on...
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Thought Experiments in Mathematics: From Fiction to Facts
As in science and philosophy, thought experiments in mathematics link a problem to new epistemic resources that are unavailable in a given practice,...
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Mathematics takes First Priority
In Section 3.2 we saw how Hausdorff, at the beginning of his career, was still searching for orientation as a researcher. But soon he found his...
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The Origin of Mathematics in the Mind
Before starting our study of the topology of the thought and communications that the human mind creates as part of the Mathematics in Mind series we...
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Altering JS-Metric Space
In this paper, we introduce Altering JS-metric space and prove some results. We show that metric space, b-metric space, dislocated metric space, and...
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Nexus 20/21, Relationships Between Architecture and Mathematics
This letter from the editors commences by reporting on Nexus 20/21, the 13th international, interdisciplinary conference for architecture and...
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Problematic of Mathematics, Social Sciences, and Arts: A Ubiquitous Constructive Interaction in Algebraic Modeling
In this opening chapter, we reflect on the nature of mathematics and its contribution to society through two important ways of doing mathematics:...