Archives for March 2023

This section is useful because I review how the author uses evidence and examples to build credibility and to explain concepts. This could be nice for my book as I could work with these strategies.

The author goes about building arguments in a well- organized and systematic manner. Throughout the book he gives the achievements and stories of numerous wonderful mathematicians, scientists and philosophers, which he then uses in the last chapter to forward his argument about the answer to the questions posed by Wigner’s Enigma. These include the concepts applications of Knot theory, Einstein’s use of Reimannian geometry, the accuracy of Newton’s laws of gravitation and of Einstein’s laws of general/ special relativity, etc.

◦Even within chapters, the author gives numerous examples as evidence for statements and clarifications. One example would be citing the Tetraktys as the symbol of perfection to show the Pythagoreans’ love for numbers.

◦He also gives a number of quotations from renowned personalities so as to cite authority in his book. A few examples would include those by Newton, Descartes, Alexander Pope, Daniel Dafoe. This may also be done to clarify someone’s stance about a particular question, such as Max Tegmark’s belief that the universe is mathematics, G.H. Hardy’s Platonic views, etc.

◦He also gives a number of excerpts from the books of many personalities discussed so as to clarify what stance those personalities supported or to explain certain principles. For example, an excerpt from Newton’s Principia or The Mathematical Principles of Natural Philosophy to show hints of how he adopted Descartes’ methods of scientific reasoning in establishing mathematical principles to describe the cosmos. He also used excerpts from Jakob Bernoulli’s Ars Conjectandi to show the principle of probability and the Law of Large Numbers.

◦The author also gives stories in order to explain a few facts, such as those of Archimedes’ traps that showed his knowledge of practical applications of mathematics, and that of Kurt Godel about his American citizenship to show his curiosity.

◦In a few instances, the author also gives pictures of the frontispieces of treatises like that of the Ars Conjectandi and also a number of figures to explain concepts like String Theory, etc.

◦Once all the evidence was gathered, at the end of a chapter, the author progressed logically to draft questions that were answered in later chapters and to show transitions in mathematics, for example, the author shows the relationship between logic and Mathematics by explaining the contributions of de Morgan, George Boole, etc., explains how Euclidean geometry was challenged by giving examples of Riemannian elliptic geometry, Russian Nikolai Ivanovich Lobachevsky’s hyperbolic geometry, etc.

This section helps in learning about the central ideas of a book that has a very similar audience and purpose. Reviewing the central ideas gives me points to include in my introduction.

This book revolves around the mystery of the omnipresence of mathematics. It discusses different perspectives of how to answer the question of the “unreasonable effectiveness of mathematics” as put forward in Wigner’s Enigma. It shows how mathematics evolved from the Pythagoreans’ love of numbers, to Descartes’ analytical methods, and from Newton’s laws of gravitation to Einstein’s theory of general relativity.

◦This book seeks to answer the question of whether mathematics is a discovery or an invention and also aims to explain the active and passive powers of mathematics, active powers referring to the accuracy with which mathematical laws can be created to model nature for specific purposes, and passive powers being mathematical laws created for non- practical purposes that find practical application a long time after their invention or discovery.

◦This book also subtly shows how knowledge is gained irrespective of age, profession, nationality, etc. It shows how the act of gaining knowledge does not require specialization in a particular field but only requires a genuine interest. Through examples of Boole, Grassman, Godel, etc.

◦It also shows the interdisciplinarity of the sciences, mathematics and philosophy and how mathematics permeates through each of these. Even Quetelet acknowledged the fact that advancement in the Sciences leads them to further their deep relationship with Mathematics.

In order to better research mathematical books, I read Is God a Mathematician and made a small book review/ analysis. Here is a summary:

◦This book centers around Wigner’s enigma and through various instances of the passive and active effectiveness of mathematics it finally presents the author’s views on the “passive effectiveness of mathematics.”

◦It also shows the radical ways of thinking that have laid the foundations of the present. It shows that no idea is false or true until proven to be either.

◦It also shows the achievements of the three mathematicians the author considered mathematics to be incomplete without, namely Archimedes, Galileo and Descartes. He also gives the achievements in and the contributions to mathematics, of many other mathematicians like Newton, Boole, Leibniz, and so on.

INTRODUCTION (with new things highlighted)

This reference list is for my book on the Collatz Conjecture. It includes what references I have used for my research and how they are important. I wrote it in the format given to us in class because I felt that it was short and detailed at the same time, allowing for quickly going through a reference while writing the book and for finding information. The first paragraph contains four sentences about the information and the second paragraph explains how I could use it. I included this information because it is most relevant according to me.

The last reference is a clubbed one (19-22) because I felt that all the references contributed to the same topic in my book and it would be repetitive to write them separately. I also wrote a book analysis/ review for Is God a Mathematician? It is a book I took up as my Spring Reading and I wrote the review for my research given the similarity in audience and purpose with my book. I will release the Spring Reading as a separate section in the Notebook.

I found important information about the mathematical nature of the Collatz Conjecture and about illustration. However, I did not find much about the applications part of my book. My research might have to shift slightly towards non-mathematical websites or papers so that I can understand my readers. AB 1 -10 enclosed in document AB-v1 were scored.

I added AB-v2 with AB 11-22 and focused not only on the mathematics, but also on articles about writing books.