Beyond Infinity: An Expedition to the Outer Limits of Mathematics (edição 2017)

Read the Wikipedia article on Hilbert's hotel and Infinite series and you'll learn much more than this book has to offer. The rest is just the author fawning over how quirky and zany she is. That and cutesy stories about children and her childhood. You will be puking rainbows by chapter 3. She also replaced the boring counting of apples with eating cake - truly ground breaking.

The best way by which it conveys infinity is by how many times you get to read about her "10 print 20 goto 10" program. ( )

There are some big numbers out there, footballers earn a jaw dropping amount per year, for what I am not entirely sure… The global economy is around US$107.5 trillion, there are approximately seven quintillion, five hundred quadrillion grains of sand on the earth and it is thought that there are 10 times as many stars as that. All of these numbers are frankly huge, enormous, gargantuan even, but compared to ∞ they are a mere drop in the ocean. In this book, Eugenia Cheng takes us on a journey to the outer reaches of the mathematical universe to contemplate the slightly abstract concept that is infinity. In it she poses various questions about this number, asking if 1 ∞ is larger than ∞ 1, are some infinities larger than others, can you fit an infinite number of people in Hilbert's Hotel and when does a number start becoming irrational.

Thankfully this book has lots of diagrams as Cheng sets about explaining the concepts of infinity, from the very simplest right up to the most detailed. I found most of it straightforward, but occasionally it was fairly tough going. When trying to get your head around infinity has challenged mathematicians for ages so it is not going to be easy for us mere mortals. Cheng endeavours to keep the prose readable, however, someone who has not picked up a maths book since school might struggle with this, but most of the time she gets the concepts across clearly. Overall a good introduction to infinity. ( )

Eugenia Cheng ha un modo molto personale di parlare di matematica: nel suo libro precedente paragonava la teoria delle categorie al cucinare dolci, qui il viaggio verso l'infinito è costellato di ricordi di vita personale. Il lettore che sappia già un po' di cose sulla teoria degli infiniti forse non troverà molto di nuovo; il libro in fin dei conti si limita a sfiorare i problemi posti dalla teoria cantoriana. Il neofita invece troverà un grande vantaggio, perché Cheng batte moltissimo sulla constatazione che non possiamo fare matematica dell'infinito con le regole solite, e soprattutto mostra esplicitamente dove e come queste regole saltano. In questo modo si evitano tutti i danni dell'approccio scolastico tipico "si deve fare così", che rende la matematica troppo simile a una collezione di articoli di legge da imparare a memoria. (Sì, anche in diritto le leggi non nascono dal nulla ma hanno un razionale: ma ci siamo capiti). ( )

Infinity is a confusing topic, and I think Ms. Cheng did a brilliant job of delivering it in an interesting, fun, engaging way. Yes, at times I didn't quite understand, but given the topic that's acceptable--I certainly understood more than I expected to, and that's all on her.

At the very least, I'm glad I don't have to move people from a one floor hotel with an infinite number of rooms, to a two floor hotel, each of which has an infinite number of rooms, and that's something prior to reading that I didn't realize I was grateful for.

(Note: 5 stars = rare and amazing, 4 = quite good book, 3 = a decent read, 2 = disappointing, 1 = awful, just awful. There are a lot of 4s and 3s in the world!) ( )

As someone else already said, it is better if you're already interest in mathematics. It's pretty intelligible for a high school senior. ( )