Mathematics : History & Philosophy

Luitzen Egbertus Jan Brouwer is a remarkable figure, both in the development of mathematics and in wider Dutch history. A mathematical genius with strong mystical and philosophical leanings, he advocated a constructivistic, more human view of mathematics and science. A sophisticated analysis of a crucial era of mathematical research, this book is an important insight into the life of one of its most fascinating characters. - ;Luitzen Egbertus Jan Brouwer is a remarkable figure, both in the development of mathematics and in wider Dutch history. A mathematical genius with strong mystical and philosophical leanings, he advocated the intuitionist view of mathematics and science as a constructive mental activity. This drew him into a discussion with David Hilbert, the leading advocate of the formalist school, about the nature of mathematics, a debate which made Brouwer a legend during his lifetime. He also. contributed significantly to research in topology, and was a member of the socio- linguistic Signific Circle. As well as his diverse mathematical interests he had a great impact in wider Dutch society. His keen sense of justice made him a party in many conflicts, both scientific and political. He would often be involved in controversial issues, such as the campaign to undo the boycott of German scientists, and this made him a figure both of admiration and embarrassment in his native Holland. Although his abilities won him offers from prestigious universities such as Berlin and G--ouml--;ttingen, he. preferred to stay in Amsterdam, so that he could pursue a life of quiet unconventionality in the artist community at Laren. This book, the second in a two volume set, provides a sophisticated analysis of this crucial era of mathematical research, but also gives an important insight into the wider life of one of the most fascinating characters involved. - ;...the author has achieved an enormous task ... for the first time, we now have a full and detailed picture of some of more...

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Chemistry, physics and biology are by their nature genuinely difficult. Mathematics, however, is man-made, and therefore not as complicated. Two ideas form the basis for this book: 1) to use ordinary mathematics to describe the simplicity in the structure of mathematics and 2) to develop new branches of mathematics to describe natural sciences. Mathematics can be described as the addition, subtraction or multiplication of planes. Using the exponential scale the authors show that the addition of planes gives the polyhedra, or any solid. The substraction of planes gives saddles. The multiplication of planes gives the general saddle equations and the multispirals. The equation of symmetry is derived, which contains the exponential scale with its functions for solids, the complex exponentials with the nodal surfaces, and the GD (Gauss Distribution) mathematics with finite periodicity. Piece by piece, the authors have found mathematical functions for the geometrical descriptions of chemical structures and the structure building operations. Using the mathematics for dilatation; twins, trillings, fourlings and sixlings are made, and using GD mathematics these are made periodic. This description of a structure is the nature of mathematics itself. Crystal structures and 3D mathematics are synonyms. Mathematics are used to describe rod packings, Olympic rings and defects in solids. Giant molecules such as cubosomes, the DNA double helix, and certain building blocks in protein structures are also described mathematically. more...

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Logic, mathematical knowledge and objects are explored alongside reason and intuition in the exact sciences. more...

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This text discusses the great philosophers and the importance of mathematics to their thought. It includes topics such as: the mathematical image; platonism; picture-proofs; applied mathematics; Hilbert and Godel; knots and nations; definitions; and picture-proofs and Wittgenstein. more...

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Introduction: One by Number. 1. Platonic Cosmology on Plotinian Terms. Ennead VI.6 and the Timaeus. Origin of Multiplicity in Plotinus. Plotinus' apostasies and Numenius' stasis. The Universe as Degrees of Separation from the One. 2. Multiplicity as Number. Surfacing from "the Neopythagorean Underground". Outward and Inward Direction of Multiplicity in VI.6. Multiplicity as Effluence and Unity. 3. "The Number of Infinity". Plato's Position. Aristotle's Criticism of Plato and the Platonists. Plotinus' Answer. 4. Number and Substance. Plotinus' Three Hypotheses about Number in the Intelligible Realm. Is Substantial Number Discrete and Incidental?. The Whole Number of Beings. The Substantial and Monadic Number. 5. Number and the Universe. Substantial Number and the One. Substantial Number and the Absolute Being. Substantial Number and Intellect. Substantial Number and Beings. Substantial Number and the Complete Living Being. Soul and Number. The Unfigured Figure of Soul's Dance. 6. Unity of Thought and Writing. Porphyry and the Enneads. Enneads VI.6. "Six Along with the Nines". Conclusion: In Defense of Plato. Bibliography. Index of Names and Subjects. Index Locorum more...

Price: $74.00