There are many books which will generate enthusiasm for mathematics in a layman reader. Some of them are listed below:
1) One Two Three ... Infinity: Facts and Speculations of Science : George Gamow
Book by theoretical physicist George Gamow in $1947$, exploring some fundamental concepts in mathematics and science, but written at a level understandable by middle school students up through "intelligent layman" adults.
2) Fractals, Music, Hypercards and More ..., Mathematical Recreations
from SCIENTIFIC AMERICAN Magazine : Martin Gardner
3)Time Travel and Other Mathematical Bewilderments : Martin Gardner
4)The Universe in a Handkerchief : Martin Gardner
5)Men of Mathematics: E T Bell
Book on the history of mathematics written in $1937$ by the mathematician E. T. Bell. After a brief chapter on three ancient mathematicians, the remainder of the book is devoted to the lives of about forty mathematicians who worked in the seventeenth, eighteenth and nineteenth centuries. The emphasis is on mainstream mathematics following on from the work.
Men of Mathematics has inspired many young people, including the young John Forbes Nash Jr. and Freeman Dyson, to become mathematicians.
6)The Man Who Knew Infinity: A Life of the Genius Ramanujan : Robert Kanigel
Biography book of the Indian mathematician Srinivasa Ramanujan written in $1991$ by Robert Kanigel. The book gives a detailed account of his upbringing in India, his mathematical achievements and his mathematical collaboration with English mathematician G. H. Hardy. The book also reviews the life of Hardy and the academic culture of Cambridge University during early twentieth century.
7)A Beautiful Mind : Sylvia Nasar
Biography of Nobel Prize-winning economist and mathematician John Forbes Nash, Jr. by Sylvia Nasar. The book inspired a film by the same name, which was produced in 2001, directed by Ron Howard and starring Russell Crowe and Jennifer Connelly.
8)A Passion for Mathematics : Clifford A Pickover
9)Strange Brains and Genius : Clifford A Pickover
10)Surfing Through Hyperspace,Understanding Higher Universes in Six Easy Lessons: Clifford A Pickover
11)The Pattern Book, Fractals, Art and Nature : Clifford A pickover(editor)
12)The Mobius Strip : Clifford A Pickover
13)The Stars of Heaven, This book is dedicated to the triple alpha process and the number 7.6549: the reasons we are alive today,and smiling,on Earth : Clifford A Pickover
14)The Road to Reality: A Complete Guide to the Laws of the Universe: Roger Penrose
Book on modern physics by the British mathematical physicist Roger Penrose, published in $2004$.
It covers the basics of the Standard Model of particle physics, discussing general relativity and quantum mechanics, and discusses the possible unification of these two theories.
The book is just over $1100$ pages, of which the first $383$ are dedicated to mathematics—Penrose's goal is to acquaint inquisitive readers with the mathematical tools needed to understand the remainder of the book in depth.