The Education of a Mathematician by Philip Davies

This book is different from most other books for the mathematics layman. It is a very tangible and personal journey of the author from the 1930’s to end of the 20 century. In general I found it a very readable book on mathematics as well as mathematics education. There is also philosophy discussions in the book.

The author is a professional mathematician who gives his personal experience and what it means to be a mathematician with his travels to various countries.

The author discuss some really important questions such as the future role of mathematics and it applications. Also he reflects back at how mathematics has affected all of us in the past.

The last chapter describes the authors’ talk at the ‘The International Congress of Mathematicians’ in August 1998 given in Berlin. I really like this chapter with subheading such as Male vs Female Mathematics and Soft Mathematics vs Traditional Mathematics.

My only reservation is that it was hard to follow in places as the author is also a philosopher. 

Review of The Mathematical Universe by William Dunham

This is a popular mathematics book for the layman. The author has succeeded in writing interesting articles in mathematics which are laid out alphabetically. Dunham discusses the problems and personalities in the history of mathematics. If you want a student hooked into mathematics then this the book they should read.

The technical mathematics in the book are excellently described in simple terms that the average layman can understand. Dunham really does bring mathematics to live in this book.

Initially I was reluctant to purchase a book which is mapped out in alphabetic order. However Dunham managed to make the progression from one chapter to the next seamless. Chapter 1 is on arithmetic and the last chapter called Z is on complex numbers. 

The book is very well organised and has good quality writing style – well expressed, clarity, coherence etc. Dunham has struck the right balance between writing thoroughly and for the amateur or non-professional. Illustrations are sprinkled throughout the book and the author has used these with dramatic effect.

I would recommend this book to any student or teacher of mathematic as well as for non mathematicians.

Kuldeep Singh 

1st Feb 2012

The Story of Mathematics by Anne Rooney

27 December 2011

This book is full of interesting facts on the history of mathematics such as where our symbols + , – , = and square root originated from. There are also details of mathematics of the 20^th Century such as fractals and fuzzy logic. In places the book is fascinating reading such as ‘Pascal’s Triangle is called Khayyam’s Triangle in Iran.’ A student doing mathematics would find this book intriguing and learn some entertaining facts about the history of the subject.

The author has made good use of colour in diagrams but the diagrams are not referenced. There is also no caption for tables.

The layout of some details is rather peculiar. For example page 27 of the book claims that minus sign was first used by Johannes Widmann but does not mention who Widmann is until page 130.

In general the book is full of interesting facts but does lack detail in places. I think it would have been a better book with fewer facts but more details and mathematics about some of these facts.

I personally do not like the text layout in two columns per page. It just doesn’t flow as well as a traditional one column per page book. Additionally it is confusing in places with various diagrams and boxed information on the same page. However I can see the advantage of being a portable book of 208 pages, something that you can fit into your pocket.

Font size of the comprehensive index is rather small with three columns to the page.

Even with these reservations I would recommend this book to any student or layman who is interested in the history of mathematics.

Kuldeep Singh

Femininity, Mathematics and Science, 1880-1914

This is an excellent account of the history of women in the academic world of mathematics, science and engineering between 1880 and 1914.

Jones focuses on the barriers women faced at the turn of the 19^th century such as the scientific laboratory which was seen as a harsh environment for women. These labs were places of manliness and heroism. An example is Cavendish Laboratory at Cambridge which is named after Henry Cavendish who passed electric current through his own body. Even Darwin had theorised that women’s intellect was not on par with men and women were lower down the evolutionary scale, closer to animals. The author also provides an interesting history of the suffragette’s movement.

Jones has concentrated on two particular women, Hertha Ayrton and Grace Young, who both attended Girton College Cambridge to study mathematics. The author states that Hertha was the first Jewish woman to enter Cambridge and that she renounced Judaism so that she could assimilate into the middle class scientific society. Both women took the mathematical tripos examination at Cambridge with Hertha Ayrton opting for the applied mathematics route whilst Grace chose pure mathematics.

The author describes how by the end of the 19^th century men were deserting the mathematics tripos for natural sciences tripos which consequently made this masculine in character. However the new women’s colleges (Girton and Newnham) retained their preferences for mathematics.

The author makes a really fascinating point on the use of language in mathematics (something I did not realise) . ‘The feminised language distinguished pure mathematics from the applied and helped women to feel comfortable within the discipline’. Her she is referring to proofs being elegant and theorems - beautiful. Jones gives some really interesting definitions of pure mathematics such as ‘Mathematics is absolute knowledge, permanent and unchanging over time’. The author goes on to say ‘Around 1900 Pure Mathematics prided itself on being uncontaminated by the real world’.

Jones highlights how mathematics was changing by the end of the 19^th century. It was moving away from algebraic geometry to a more abstract area such as set theory and Gottingen in Germany led the way. Gottingen was the leading centre for mathematics by the end of the 19^th century. Grace Young moved to Gottingen between 1900 and 1908 and became a member of the Gottingen Mathematics Club. By this time it was not unusual to see a small group of women in Gottingen mathematics lectures. However the author highlights some serious impediments on women because there were severe lack of academic openings for women in Germany as well as England.

Grace’s work at Gottingen had an enormous influence on the development of Cambridge mathematics according to the author. Her and her husband were at the forefront of the new mathematical analysis.

Hertha Aryton’s research at Central College London was in arc lights being used for search lights, street lights and other public lighting. When her husband died in 1908 she had no further dealing with Central College London.

Jones states that women encountered fewer obstacles in infiltrating mathematics as it did not necessarily require an institutional base. Hertha required a lab whilst Grace needed pencil, desk and access to a mathematical education.

In general this book is an excellent history of the barriers faced by women in academic circles around the 1900’s. I was not aware of such rich history and there are very few books in this particular field. I particularly liked the rare photographs in the book and would have preferred to have more of these. Also the author has made good use of graphs by highlighting the number of male and female students taking the mathematics and natural sciences triposes. My only gripe would be the cost of the book at £55. I think this book should be within the financial budgets of students.

I only found a couple of typos. On page 40 it should say 1890’s not 1990’s. On page 169 it should say 23 mathematical problems rather than 123 mathematical problems.

Kuldeep Singh

Review of Linear Algebra and its Applications by D.C. Lay

The most obvious benefit of this particular book is its size. At fewer than five hundred pages it is a comparatively light book. Despite its compact nature, it does include some clear and helpful illustrations, and features some interesting applications
However, the layout is far from appealing, and at first glance can be confusing. The answers to the random exercises can be difficult to locate, and the solutions are often too brief to be of any use. In general the proofs are difficult to follow because they are in compact notation, and like many books of this type, it makes little provision for students struggling to remember previously mentioned results and definitions. In some cases a theorem is stated on page X and then the proof of this theorem is given on page X+2 without restating the theorem. This means the reader is constantly flicking between pages X and X+2. The inclusion of repeated theorems would not hamper the confident mathematician, but would be invaluable to a less self assured student.
There seems to be little attempt made to inspire the reader, and its approach is largely clinical and less personal.

Review of Elementary Linear Algebra by Larson and Edwards

This book has an attractive layout, with its theorems and definitions clearly and repetitively presented in highlighted boxes. It is easy to follow and could certainly prove useful to a weak student.
However, many results are stated without providing proof, leaving the student to produce the proof as part of the exercise. Underpinning this type of mathematics with proof is certainly a fundamental part of the education process, but in my experience many students find this an intimidating step. I believe it is vital that students have proofs demonstrated repeatedly, until they become confident enough to formulate their own. This book could undoubtedly benefit from the inclusion of more examples.
In addition, there is a noticeable lack of illustrations, giving the book a very dense feel.
Generally speaking, while this book might provide a valuable handbook for some students, I don’t believe its style engages the attention of the reader and it doesn’t attempt to provide a thorough explanation of linear algebra.

Review of ‘Recountings’ by Joel Segel

This is a fascinating history of mathematics at MIT covering the period of post WWII to the present. It gives a detailed account of how mathematics at MIT was converted from a service department for engineers to the high class research department over this period.
This is a book for the layman and also academics who work in such environments. Many mathematics departments throughout the world could do well be investing in this book and emulating a lot of the work done at MIT. The book highlights that the main reason for the transformation was by hiring some of best mathematicians in the world.
The book has a different style to mathematics books for the layman in the sense that it is based on a collection of interviews with 12 members of MIT and the widow of Norman Levison.
The author highlights some well known stories about the men (apart from the first interview which is with Fagi Levison all the other 12 interviews are with men) in mathematics at MIT such as how they were hooked into the institute from other organisations. Additionally the book highlights the arguments within the department between pure and applied mathematicians.
My main reservations regarding the book are:
• It contains no index. This is a serious omission.
• The book does not read well in places and it should have been more thoroughly reviewed.
Generally it was a good joy to read this book and definitely worth buying.
Kuldeep Singh

Review of ‘The Unfinished Game’ by Keith Devlin

I really enjoyed reading this book. It is an excellent account of the history of probability theory. It is essentially a correspondence between the two great French mathematicians, Fermat and Pascal.
The book has an interesting hook with the opening paragraph being a letter sent by Pascal to Fermat. The basis of this correspondence asks ‘how should we divide the stakes if a particular game is incomplete’. This lays the ground work for probability theory.
I liked the style of the author and the way he dipped into some straightforward mathematics in this book.
The history is particularly appealing with the explanation of how Graunt developed his mortality tables. It also goes on to state that Newton’s first great mathematical discovery, the binomial theorem, is based on Pascal’s triangle. Additionally the book explains with entertainment detail the personalities of Fermat and Pascal.
There are also some very fascinating applications of probability mentioned in the book such as how the repeated use of Bayes theorem predicted an attack on the pentagon and also the explanation of why DNA profiling is so reliable.
However the book has the following shortcomings:
It should have stated the dates of birth and death of all the mathematicians mentioned in the book.
On page 83 the author misses the first Fermat prime 3.
The last sentence in the second paragraph on page 102 should say ‘bet 24 to 40, that is 3 to 5, that a sixteen year old will die before the age thirty six’.
This is a book for anybody interested in history of mathematics or mathematics in general. You do not need to be a mathematician to appreciate this book.
Overall I would say this is a very successful book and would recommend anybody interested in mathematics or history of mathematics to purchase this book.