Mathematics under the Microscope

Borovik, Alexandre

doi:10.1090/mbk/071

Cited by 22 publications

(9 citation statements)

References 93 publications

(139 reference statements)

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“…Example 1.1. 25 The centre of the graded ring If a group Γ is not abelian, then the centre of a Γ-graded ring may not be a graded subring. For example, let Γ = S 3 = {e, a, b, c, d, f } be the symmetric group of order 3, where…”

Section: Example 1123 Symmetric and Exterior Algebras As Z-graded Rmentioning

confidence: 99%

Graded Rings and Graded Grothendieck Groups

Hazrat

2016

118

185

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This study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra which has recently been adopted to classify the Leavitt path algebras. The book begins with a concise introduction to the theory of graded rings and then focuses in more detail on Grothendieck groups, Morita theory, Picard groups and K-theory. The author extends known results in the ungraded case to the graded setting and gathers together important results which are currently scattered throughout the literature. The book is suitable for advanced undergraduate and graduate students, as well as researchers in ring theory.

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Section: Example 1123 Symmetric and Exterior Algebras As Z-graded Rmentioning

confidence: 99%

Graded Rings and Graded Grothendieck Groups

Hazrat

2016

118

185

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“…And experiments show that in problems with multiple constraints evolution does not find an optimal, or even close to optimal, but just a survivable solution. 15 In short, the surviving solution could be in one of myriads of local optima, sufficiently good to ensure reasonably high probability of survival. Lucky strikes could be so rare that the huge search space and millions of years of evolution produce just one survivable solution, which, as a result, dominates the living world, and is perceived by us as something special.…”

Section: Some Further Comments On Mathematics and Evolutionmentioning

confidence: 99%

“…The deduction of Kolmogorov's seminal "5/3" Law for the energy distribution in turbulent fluid [34] is so simple that it can be done in a few lines using only school level algebra (that kind of derivation can be found in [15,Section 8.4]; I borrow some details from there).…”

Section: Once More About the Unreasonable Effectiveness Of Mathematic...mentioning

confidence: 99%

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A mathematician's view of the unreasonable ineffectiveness of mathematics in biology

Borovik¹

2021

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This paper discusses, from a mathematician's point of view, the thesis formulated by Israel Gelfand, one of the greatest mathematicians of the 20th century, and one of the pioneers of mathematical biology:There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness of mathematics in biology.Disclaimer. The author writes in his personal capacity and views expressed do not represent position of any other person, corporation, organisation, or institution.

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“…Why then do we talk about the mathematical revolution as incoming rather than well established? Why did a great mathematician I. M. Gelfand write, [1], Eugene Wigner wrote a famous essay on the unreasonable effectiveness of mathematics in natural sciences. He meant physics, of course.…”

Section: Mathematical Models In Biologymentioning

confidence: 99%

Foreword to BIOMATH 2017 Proceedings: Some comments on mathematical modelling and biomathematics.

Banasiak

2018

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Both biology and mathematics have existed as well established branches of science for hundreds of years and both, maybe not in a well defined way, have been with the humankind for a couple of thousands of years. Though nature was studied by the ancient civilizations of Mesopotamia, Egypt, the Indian subcontinent and China, the origins of modern biology are typically traced back to the ancient Greece, where Aristotle (384-322 BC) contributed most extensively to its development. Similarly, the ancient Babylonians were able to solve quadratic equation over four millennia ago and we can see the development of mathematical methods in all ancient civilisations, notably in China and on the Indian subcontinent. However, possibly again the Greeks were the first who studied mathematics for its own sake, as a collection of abstract objects and relations between them. Nevertheless, despite the fact that the development of such a mathematics has not required any external stimuli, an amazing feature of the human mind is that a large number of abstract mathematical constructs has proved to be very well suited for describing natural phenomena.This prompted Eugene Wigner to write his famous article The Unreasonable Effectiveness of Mathematics in the Natural Sciences, ...

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Mathematics under the Microscope

Cited by 22 publications

References 93 publications

Graded Rings and Graded Grothendieck Groups

Graded Rings and Graded Grothendieck Groups

A mathematician's view of the unreasonable ineffectiveness of mathematics in biology

Foreword to BIOMATH 2017 Proceedings: Some comments on mathematical modelling and biomathematics.

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