Looking for a neat technical book on mathematics/physics as a gift

dexter

A good friend of mine has been very kind to me through university, and he's just come to the very end of his PhD in mathematics. I know his area was analysis, and he did some mathematical physics too. I'm looking to give him a really nice book on one of these topics, mathematical physics would be really cool too. Something along the lines of "Road to Reality" by Penrose, or the Feynman lectures (he already has both of these). Thanks for any advice, I'd really appreciate it.

TychoCelchuuu

I would actually suggest a more generic gift: the chances of him getting to the end of a PhD without owning the majority of books about his field that he wants to own are pretty slim. You're likely to duplicate something he already has if you hew too closely to this specific interest.

Chop Logic

BAM

http://www.amazon.com/gp/aw/d/0802778135/ref=redir_mdp_mobile

GAME OVER.

I can personally guarentee any true science/math nerd would love this book, it's one of the best books I own, and the odds of him having it already are really small.

Lepton

May I recommend:

http://www.amazon.com/Pleasure-Finding-Things-Out-Richard/dp/0465023959/ref=sr_1_1?s=books&ie=UTF8&qid=1327922143&sr=1-1

or

http://www.amazon.com/s/ref=nb_sb_noss?url=search-alias=stripbooks&field-keywords=God+invented+the+integers&x=0&y=0

Pure Din

omg, I know this isn't a book, but if your friend is at all a person who loves desk things check this out: http://bathsheba.com/

I would love one of those things as a phd present and I'm not even doing my phd in math.

Cobell

My vote is for Godel, Escher, Bach

http://www.amazon.com/Gödel-Escher-Bach-Eternal-Golden/dp/0465026567/ref=sr_1_1?s=books&ie=UTF8&qid=1328030930&sr=1-1

Clipse

As TychoCelchuuu said, trying to give him a book in his field is going to be a minefield since he almost certainly owns or is familiar with the renowned works in that area. I think you should veer towards general mathematics texts, and there are two different tacks you can take there:

Non-technical novels:
A Mathematician's Apology by G.H. Hardy is probably the single most important non-technical work regarding mathematics; the only reason I don't simply tell you "buy this!" is that I'm worried he would already have it -- I studied math, and most of my colleagues had read this book as an undergrad or earlier.
The Man Who Loved Only Numbers by Paul Hoffmann is a superb biography of one of the most influential (and eccentric) mathematicians of the 20th century (Paul Erdos). It's a phenomenal read and less well-known than the previous recommendation.

General (but interesting!) Technical works:
Mathematics and Plausible Reasoning by Polya is a fairly well-known text that touches upon aesthetics of mathematics without veering too far into philosophy or pop-sci (as such texts are wont to do). There is also a second volume of this released a few years ago which I am not familiar with and cannot vouch for.
Proofs from The Book by Martin Aigner is a collection of incredibly elegant proofs from a wide variety of fields. In addition to being generally very good (I discovered this book as a grad student and was nevertheless impressed by many of the proofs presented), it makes an excellent pairing with "The Man Who Loved Only Numbers", as the title is a reference to Erdos' myth of a Book which contains the most elegant proof of every theorem.

dexter

Thank you all for your advice, greatly appreciated. I was aware of the fact he might very well own a lot of the books I might think to buy him - but I do know him relatively well and I know mates of his who can drop subtle questions for me.

Clipse, I found your technical works suggestions especially interesting. Thank you very much, I think both those books would be a fantastic gift and right up his ally!