The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities

by William Dunham

"Dunham writes for nonspecialists, and they will enjoy his piquantanecdotes and amusing asides -- Booklist

"Artfully, Dunham conducts a tour of the mathematical universe. . .he believes these ideas to be accessible to the audience he wantsto reach, and he writes so that they are." -- Nature

"If you want to encourage anyone's interest in math, get them TheMathematical Universe."
* New Scientist

Genres: Mathematics, Science, Nonfiction, History, Popular Science, Biography, Physics

320 pages, Paperback

First published January 1, 1994

About the author

An American writer who was originally trained in topology but became interested in the history of mathematics and specializes in Leonhard Euler. He has received several awards for writing and teaching on this subject.

Reviews

[Dimitrios · Rating 5 out of 5]

I really liked it, but i'm biased. When it comes to history of mathematics presented in an easy and fun to follow manner, i'm a sucker. The level of the book is not terribly high. Some parts require only to be aware of some ideas, others some familiarity with basic high school mathematics and some to have some previous experience. The most requiring subject to understand was differential and integral calculus to give you an idea. The contents include a lot of mathematical ideas, how they evolved, interesting stories about great mathematicians, interesting proofs. I highly recommend it

[Sohum · Rating 4 out of 5]

William Dunham's non-fiction book, The Mathematical Universe, is an enthralling book which takes readers on a journey through some of the most popular algebraic and geometric proofs, such as Runges Theorem and proving the value of pi. Despite its title and subject, the book was unexpectedly interesting as Dunham found a way to connect or relate these concepts of thought to any scholar's standard education. For instance, when discussing the differentiation of integrals, Dunham some how managed to relate the calculus involved in this process to basic polynomial fundamentals, which any educated middle-schooler should have knowledge of. In essence, Dunham has found a way to put complicated math concepts in terms in which even those with the most basic of educational backgrounds can understand, thereby expanding the range of the book's audience. However, when I checked this book out from my school's library, I had noticed that it had been untouched for an extended period of time, which was expected. Students would not often find this book interesting as they may not have a vested interest in mathematics, which is a recurring pattern with most students. Dunham, however still attempts to draw the attention of young students by placing comic strips or puns in his book, so that it may appeal to a younger audience. The most striking characteristic of this book was not the fact that it covered such wide branches of mathematics in a small amount of pages, but the fact that it placed it in terms in which any student could comprehend such concepts without being hindered by their lack of knowledge in mathematics when compared to college graduate.

[Ashar Malik · Rating 5 out of 5]

A very consice introduction to the mathematical world. Reads great. Definitely a must read.

[Martina Méndez · Rating 4 out of 5]

“La demostración por contradicción es una táctica lógica maravillosa. Al suponer lo contrario de lo que queremos demostrar, parece que ponemos en peligro nuestro objetivo final. Sin embargo, al terminar, la calamidad queda apartada”

Un libro relativamente sencillo, que se puede leer con fluidez y que despierta curiosidad en cualquier lector interesado. Recomiendo. Solo hacen falta matemáticas de bachillerato para entenderlo.

Mis tres partes favoritas del libro fueron las distintas demostraciones del Teorema de Pitágoras, la historia y resolución del Problema Isoperimétrico, y las aplicaciones del número e, la constante natural y misteriosa del universo.

[David · Rating 4 out of 5]

A solid, clear overview of mathematics, both simple and advanced. For anyone who wants a grounding in general math topics, this seems just about perfect. For someone who wants a more organized system, this will disappoint you (he jumps from topic to topic, based on the alphabet), and for someone like me who wants tougher questions answered ("what is Hilbert space?" "What is a Cauchy sequence?" etc.), this won't do much to help. But even though I realized it was the wrong book for my project, I kept reading it anyway because the author is clearly having so much fun. I'd heard that this was something of a classic, and now I know the reason.

[Raj Sharma · Rating 5 out of 5]

Most interesting popular Mathematics book. Parents of students wanting illustrious careers must read this book themselves and let their wards read it. This book can lay the path for young boys to become great mathematicians for the new world.

[Jose Moa · Rating 4 out of 5]

A understable book whith a background of high shool level;it is alphabeticlly ordered ,for example L for Leibnitz,E for Euler,D for diferential calculus ,P for prime number theorem and so on

[Greg · Rating 4 out of 5]

A delightful bite-sized journey through the history of mathematics. Mr. Dunham does a fantastic job choosing mathematical facts and figures to examine, and he is able to summarize the broad strokes of proofs in a way that preserves their beauty while sparing the reader the tedium of their rigor. Mr. Dunham is a splendid writer with a quick wit, and his love for the subject (both its science and its history) spills out of every page.

A half star is omitted because the format, though charming at first, becomes a little tedious after a few chapters because there is no logical progression in the way that the ideas are presented. Another half star is lost because one would expect an alphabetical journey to contain no less than 26 distinct chapters, but Mr. Dunham cheekily combines X and Y in a chapter on Cartesian coordinates.

Clearly these are not real complaints. Overall this was a very enjoyable book that is well suited to whet the appetite of anyone interested in mathematics. Math is an extremely beautiful subject that has been mutilated by public education (See A Mathematician's Lament by Paul Lockhart), but anyone who wishes to see the beauty, art, and majesty of the subject would do well to take a dip in the first few chapters of this book.

[Kelli · Rating 5 out of 5]

Maybe someone should revoke my ability to rate/review books now because I somehow LOVED THIS after fully expecting to hate it and find it boring after I bought it as a refresher on some math history.

It wasn’t boring at all! I read this in less than 48 hours and could barely put it down. Even though it was written in the 1990s it didn’t feel much outdated. The chapters were short enough to not feel intimidating and there were plenty of visual diagrams and pictures to help explain some of the concepts and proofs they mentioned. The organization was also really well done and I learned so much.

My favorite chapters were on the ancient beginnings of mathematics and reading through their logic and methods and all that was discovered before calculators and computers. However, one chapter was really, REALLY stupid- about how mathematicians typically look (bearded of course!) and dress (they don’t care about fashion!) and their special sense of humour (are you kidding me????)- and it was insane they included this chapter enforcing stereotypes and later only a single chapter about women in mathematics .... yikes... and so in reality this is 4.5 stars rounded up.

[Bryce Beale · Rating 4 out of 5]

This was an enjoyable and wandering read. It has been some time since I have touched mathematics, and this was just the sort of re-introduction I was looking for. Dunham somewhat artificially but also somewhat well attaches a concept from the practice or history of mathematics to each letter of the alphabet, which form the chapters of the book. This is a book that doesn't shy away from basic theorems in arithmetic, trigonometry, algebra, calculus, and number theory--there are lots of diagrams--but that is also directed toward the non-professional. Plus, Dunham is a rather witty writer. I very much enjoyed thinking God's thoughts after him in regard to our mathematical universe.

[Remo · Rating 5 out of 5]

Fantástico libro de divulgación sobre matemáticas, que me gustó tanto como el anterior del mismo autor, Viaje a través de los genios. En el libro se narran hechos curiosos, hechos determinantes, pruebas de teoremas que cambian el rumbos de las matemáticas, y el autor no tiene miedo de meterse en harina con bastante frecuencia y soltarte unas cuantas ecuaciones para mostrarte de qué te habla en ese momento.
Un capítulo por letra del abecedario, todos ellos fascinantes.

[elle · Rating 4 out of 5]

I read this as a teen with a love for maths but without a solid enough theoretical background to delve into more serious texts, so it was a joy to be introduced to some concepts I never even considered before in such a fun, accessible way. I remember finding this in my school library and falling in love, and it made me very happy during a rough time when I really appreciate the chance to lose myself in nerdy books :)

[Jason · Rating 4 out of 5]

Informative and easy to read, at least for a math brain. Some chapters may be harder if no or little higher math background. Most chapters were enjoyable, a couple i didn't care for because of the topic and not the author's skill.

[Ahmed Almatar · Rating 5 out of 5]

William Dunham, great as always!

[Dick Harding · Rating 4 out of 5]

I enjoyed this more than expected. It is a wide smattering of math and it's history. Some of the math seemed to be a bit beyond me but all in all I enoyed it.

[John Volpe · Rating 5 out of 5]

Awesome book! Definitely my favorite author.

[Dave · Rating 4 out of 5]

A very interesting and accessable book for the general audience.

[Dan · Rating 5 out of 5]

Loved the book. The history of mathematics without reading like textbook. Style is straight forward and great for using as a survey-level reference.

[Aleksandrof · Rating 5 out of 5]

Me ha conmovido. Poco más puedo decir. Libro de divulgación de enorme calidad, entretenido, accesible, profundo a veces, bien explicado. De interés universal.

[Jinwoo Chung · Rating 4 out of 5]

I tried a book related to math, since I never had a taste. It wasn't so bad, but stuff in this book can't really be helpful in real life unless you have some gift in math field (I think).

[Chelsea M · Rating 3 out of 5]

I liked the author's style - witty, but casual and disarming. The stories and analyses of the "background" behind histories and characters of mathematics fascinated me, but the mathematical ideas themselves were rather simple, most of it being at high-school level. I wish I had found this book a few years before, when these ideas were new to me.

[Faust0 · Rating 3 out of 5]

Unforgivable mistake of the kindle edition. Half of this book’s importance is the actual mathematics written, the other half being the story about that math. Thus, it is a massive mistake that in the kindle edition, the equations are written in a faint font and cannot be expanded to be read more clearly. It’s a pity because this book could otherwise have been given 4 or even 5 stars.

[Scott · Rating 4 out of 5]

A fascinating(and often humorous) look at the history of mathematics and the personalities involved in it's development. It's written to the non-mathematician, so don't let the subject matter dissuade you from reading it. Great book.

[Bonny · Rating 4 out of 5]

This is a great book to introduce some of history's fascinating and lesser-known mathematicians. I read it primarily for some background on Euler, but also found interesting information about Newton, Liebniz and others.

[Emma]

Because I couldn't write this for the work I had to do on it.
An alphabetised look on the whole of maths, as good as a work of fiction but with complicated maths as a storyline and 18th Century mathematicians as characters.

[Katie · Rating 4 out of 5]

Total nerd book but I liked it. :)

[Brett · Rating 4 out of 5]

Dunham really has a gift at making mathematics readable. Fun stuff.

[Jianliang · Rating 5 out of 5]

Very inspiring.

[Jennifer · Rating 4 out of 5]

Really enjoyable and enlightening book - does rather stretch a point or two on it's alphabetical nature but well put together

[John · Rating 4 out of 5]

Entertaining walk through a Mathematical alphabet of mathematics and mathematicians. Dense material yet easy read.