## Finding Fibonacci, by Keith Devlin – a review

This book was sent to me by the publisher as a review copy.

I have a terrible admission to make. I came to this book with a paltry knowledge of Fibonacci (Leonardo of Pisa). The knowledge that I thought that I had was quickly shown in fact to be incorrect, so I was largely starting with a blank slate (Fibonacci did not discover the Fibonacci sequence, nor would he be terribly happy to know that in the popular psyche, this is what he is famous for).

In fact, this book is not really about Fibonacci (Devlin has another book about him). This is a book about the writing of a book, and about Devlin’s process of uncovering the history and importance of what Fibonacci had accomplished. It is a book about the research of the history of mathematics, and as such, it is a lovely tale: one of fortuitous moments of discovery, and of frustrations of searching for manuscripts.…

The concept of proof by contradiction refers to taking a statement and assuming the opposite is true. When assuming the opposite is true we begin to further examine the our ‘opposite’ statement and reach to a conclusion which doesn’t add up or in simple terms is absurd.

Take the case:

Statement: There are infinite number of prime numbers.

Using the concept of proof by contradiction, we will assume the opposite is true.

If an integer (2) divides an integer (6) we say that 2 divides 6 or 2|6. In a more general sense we can say that if any integer ‘a’ divides any other integer ‘b’ then a|b.

Prime numbers: it is an integer (n ≥ 2) that has exactly two positive factors (1 and itself).

eg. 2, 3, 5 …

Composite numbers: it is an integer (n ≥ 2) that has more than two positive factors.

eg. 4, 6, 8 …

Fundamental Theorem of Arithmetic: Every integer n ≥ 2 has a unique (exactly one) prime factorization.…

## The best writing on mathematics 2016, edited by Mircea Pitici – a review

This book was sent to me by the publisher as a review copy.

http://press.princeton.edu/images/j10953.gif

It is not easy to write a review for an anthology of writings, but I think that in such cases what is best discussed is the choice of writing and its range, both topically and in terms of level. In this case we have some 30 short essays, covering a huge range of topics, as well as a real breadth of complexity. I will highlight some of my particular favourites, though I should say from the outset that I really enjoyed reading just about everything in this book. There were perhaps two or three posts which didn’t resonate with me, but out of 30, that is pretty good, given my personal tastes.

The collection starts with a lovely essay discussing the interplay between the teaching, and the practice of mathematics, and in particular the role of rigour, formality and proof in these two somewhat separate directions.…