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Full title A Mathematician's Apology [permalink]
Language English
Author G. H. Hardy (author)
Categories Mathematics and science
Publication year 1940
Online version Link
Pages 52
Full title Asimov On Numbers [permalink]
Language English
Author Isaac Asimov (author)
Publisher Pocket Books
Categories Mathematics and science
Publication year 1978
ISBN 0-671-82134-2 [Amazon, B&N, Abe, Powell's]
Pages 275

This is a collection of essays by Asimov on numbers and mathematics. It discusses how we got the concept of zero (from India via the Arabs), exponents, factorials, aleph numbers (there are actually different kinds of infinities), pi, imaginary numbers, huge numbers (like googol, but that doesn't even scratch the surface), the metric system (yum), and a host of other stuff. It also has an essay on animals and their sizes.


As with most essay collections from Asimov, this one is a sure-fire good read. Asimov explains in detail (but not too painful detail) a lot of difficult mathematics, step by careful step. Unlike a lot of his other collections, this one feels a little miscellaneous, but that doesn't at all detract from its quality.

Images Back of Asimov On Numbers.Spine of Asimov On Numbers.Front of Asimov On Numbers.
Structure [Toggle visibility]
  • Introduction
    • 1. Nothing Counts
    • 2. One, Ten, Buckle My Shoe
    • 3. Exclamation Point!
    • 4. T-Formation
    • 5. Varieties of the Infinite
    • 6. A Piece of Pi
    • 7. Tools of the Trade
    • 8. The Imaginary That Isn't
    • 9. Forget It!
    • 10. Pre-fixing It Up
    • 11. The Days of Our Years
    • 12. Begin at the Beginning
    • 13. That's About the Size of It
    • 14. The Proton-Reckoner
    • 15. Water, Water, Everywhere—
    • 16. Up and Down the Earth
    • 17. The Isles of Earth
Full title Flatland: A Romance of Many Dimensions [permalink]
Language English
Author Edwin A. Abbott (author)
Categories Classic, mathematics, novel and science fiction
Publication year 1884
Online version Link
Pages 68

Flatland chronicles the adventure of A. Square, a being in Flatland. Flatland consists of only two dimensions, as opposed to Pointland, which consists of zero dimensions, Lineland, which consists of one dimension, and Spaceland (the one we inhabit), which consists of three dimensions. It describes at length the society in Flatland, and how they go about tasks that we Spacelanders find trivial. For instance, everyone is a Polygon. The more equal all its angles and the more sides it has, the higher its social rank. Lowest are women (or the Frailer Sex, as they are often called) who are mere Lines and have no chance of rising in rank. Then come the Triangles, which are men. Then Squares (of which the narrator, A. Square, is naturally a member), Pentagons, Hexagons, Heptagons, Octagons, etc. The more sides a Polygon has, the closer it gets to being a Circle. They're the top leaders of every aspect of Flatland's society.


Flatland is a classic, and even though it's written in the 1880s in Victorian English, it's still eminently readable (and funny). You might have to read a little carefully at first to get used to the age of the language, but once you've picked it up you'll have no trouble enjoying this excellent story.

Full title Flatterland: Like Flatland, only more so [permalink]
Language English
Author Ian Stewart (author)
Publisher Basic Books
Categories Mathematics, novel and science fiction
Publication year 2001
ISBN 978-0-7382-0675-2 [Amazon, B&N, Abe, Powell's]
Pages 294

Flatterland is sort of an unofficial sequel to Abbott's classic Flatland, written in modern non-Victorian English. Although Victorian English gave the original a pretty classy feel, Flatterland doesn't disappoint. Its aim is similar to that of the original: To explain new mathematical concepts to lay people in lay language.


The book succeeds brilliantly. It's filled with illustration to help visualize the concepts, and the stories around which the concepts are introduced are reminiscent of Alice's Adventures in Wonderland (well, the fact that chapters have names like The Topologist's Tea-Party and Along the Looking-Glass probably helps), and this gives the book a whimsical tone (that's a benefit). Here's a sample:

"Is Planiturth's universe built from mathematics? Or is mathematics built by the minds of Planiturthians? Planiturthian mathematicians would like to think that their universe is built from mathematics, but that's only natural, after all. Planiturthian physicists would like to think that the Planiturthian universe is built from physics. Planiturthian biologists would like to think that the Planiturthian universe is built from biology. Planiturthian philosophers would like to think that the Planiturthian universe is built from philosophy. (Let me tell you a secret: it is. The fundamental unit of the Planiturthian universe is the philosophon, a unit of logic so tiny that only a philosopher could hope to split it.)"

The book also ventures a little into physics, explaining things like the Schrödinger's cat, the double-slit experiment, time travel, and forces. But the meat of the book is mathematics.

Images Back of Flatterland.Spine of Flatterland.Front of Flatterland.
Structure [Toggle visibility]
  • From Flatland to Flatterland
  • 1 The Third Dimension
  • 2 Victoria's Diary
  • 3 The Visitation
  • 4 A Hundred and One Dimensions
  • 5 One and a Quarter Dimension
  • 6 The Topologist's Tea-Party
  • 7 Along the Looking-Glass
  • 8 Grape Theory
  • 9 What is a Geometry?
  • 10 Platterland
  • 11 Cat Country
  • 12 The Paradox Twins
  • 13 The Domain of the Hawk King
  • 14 Down the Wormhole
  • 15 What Shape is the Universe?
  • 16 No-Branes and P-Branes
  • 17 Flatterland
  • 18 The Tenth Dimension
Full title Mathematical Puzzles and Diversions [permalink]
Language English
Author Martin Gardner (author)
Publisher Penguin Books
Categories Mathematics and puzzle
Publication year 1965
Original publication year 1959
ISBN 0-14-02-0713-9 [Amazon, B&N, Abe, Powell's]
Pages 154

Based on articles written for Scientific American, every chapter has an addendum, explaining further points or elaborating new ones, and some chapters have letters from people sent in after the article in question was published.


An awesome book with lots of interesting things. Read the chapter titles in the Structures for a preview.

Images Back of Mathematical Puzzles and Diversions.Spine of Mathematical Puzzles and Diversions.Front of Mathematical Puzzles and Diversions.
Structure [Toggle visibility]
  • Introduction
  1. Hexaflexagons
  2. Magic with a Matrix
  3. Nine Problems
  4. Ticktacktoe, or Noughts and Crosses
  5. Probability Paradoxes
  6. The Icosian Game and the Tower of Hanoi
  7. Curious Topological Models
  8. The Game of Hex
  9. Sam Loyd: America's Greatest Puzzlist
  10. Mathematical Card Tricks
  11. Memorizing Numbers
  12. Nine More Problems
  13. Polyominoes
  14. Fallacies
  15. Nim and Tac Tix
  16. Left or Right?
  • References for Further Reading
Full title More Mathematical Puzzles and Diversions [permalink]
Language English
Author Martin Gardner (author)
Publisher Penguin Books
Categories Mathematics and puzzle
Publication year 1963
Original publication year 1961
ISBN 0-14-02-0748-1 [Amazon, B&N, Abe, Powell's]
Pages 186

This book is written in the same vein as Mathematical Puzzles and Diversions.


I truly loved this book. My favorite chapters are The Five Platonic Solids, Mazes, and Eleusis: The Induction Game.

Images Back of More Mathematical Puzzles and Diversions.Spine of More Mathematical Puzzles and Diversions.Front of More Mathematical Puzzles and Diversions.
Structure [Toggle visibility]
  • Introduction
  1. The Five Platonic Solids
  2. Tetraflexagons
  3. Henry Ernest Dudeney: England's Greatest Puzzlist
  4. Digital Roots
  5. Nine Problems
  6. The Soma Cube
  7. Recreational Topology
  8. Phi: The Golden Ratio
  9. The Monkey and the Coconuts
  10. Mazes
  11. Recreational Logic
  12. Magic Squares
  13. James Hugh Riley Shows, Inc.
  14. Nine More Problems
  15. Eleusis: The Induction Game
  16. Origami
  17. Squaring the Square
  18. Mechanical Puzzles
  19. Probability and Ambiguity
  • References for Further Reading
Full title Sphereland: A Fantasy About Curved Spaces and an Expanding Universe [permalink]
Language English
Authors Dionys Burger (author) and Cornelie J. Rheinboldt (translator)
Publisher Thomas Y. Crowell Company
Categories Mathematics and science fiction
Publication year 1968
Original publication year 1965
Pages 205

Somewhat of a sequel to Flatland, Sphereland continues in the same vein, explaining three dimensions to two-dimensional creatures. The pace and mode of writing is pretty similar to the original, and I very much liked that. The novel things that Sphereland does is two-dimensional space exploration and explaining a curved line to a one-dimensional being (and thus setting up the explanation for why two-dimensional beings would have problems understanding a plane curved into a sphere, and by extension how three-dimensional beings would have trouble understanding how to curve a sphere around a hyper-sphere).

Images Back of Sphereland.Spine of Sphereland.Front of Sphereland.
Structure [Toggle visibility]

A Look at FLATLAND A Fantasy About the Fourth Dimension by A. Square

  • 1 Flatland and Its Inhabitants
  • 2 Dream Vision of Lineland
  • 3 The Visit of the Sphere
  • 4 To the Land of Three Dimensions
  • 5 Dishonored

SPHERELAND A Fantasy About Curved Spaces and and Expanding Universe by A. Hexagon

  • PART I The Straight World
    • 1 Changed Times
    • 2 Easing of Class Consciousness
    • 3 Explorers' Trips
    • 4 The Trees, the Wildlife, and the Sea
    • 5 The Trip Around the World
    • 6 The Earth Is Round
    • 7 New Year's Eve
    • 8 The Sphere Reformed
  • PART II Congruence and Symmetry
    • 9 Pedigrees and Mongrels
    • 10 Little Red Riding Shoe
    • 11 A Magic Trick
    • 12 Vision of Lineland
    • 13 The Vertato Case
    • 14 Experiments in Spaceland
  • PART III Curved Worlds
    • 15 A Rumor
    • 16 The Visit
    • 17 Amazing Results
    • 18 An Impossible Problem
    • 19 Strange Triangles
    • 20 The Faculty
    • 21 Vision of Circleland
    • 22 Revelations by the Sphere
    • 23 Problems
    • 24 The Shortest Way
  • PART IV Expanding Worlds
    • 25 Distant Views
    • 26 Telemetry
    • 27 Increasing Distances
    • 28 Hunting for the Cause
    • 29 Expanding Circleland
    • 30 Expanding Sphereland
    • 31 Miracles in Spaceland
    • 32 Misunderstood
  • Index
Full title Letters to a Young Mathematician [permalink]
Language English
Author Ian Stewart (author)
Publisher Basic Books
Categories Mathematics and science
Series Art of Mentoring (11/14)
Publication year 2007
Original publication year 2006
ISBN 978-0-465-08232-2 [Amazon, B&N, Abe, Powell's]
Pages 203

Letters to a Young Mathematician is written as an update on G. H. Hardy's classic A Mathematician's Apology, but the book is not an exercise in apologetics.

"Attitudes change. No longer do mathematicians believe that they owe the world an apology."

It follows an imaginary girl, Meg, from her school years through her ensuing career, and each chapter is a letter to her at crucial steps in her career. Some parts are musings on math (pure vs applied) while others are specific career tips (solitary work vs collaboration). The book is virtually devoid of any actual math, so I think it's safe for mathophobes. In fact, for this very reason, it might even help to partially cure the phobia of those unfortunately inflicted.


I really liked the light-hearted way the book is written. Perhaps someone who is planning on embarking on a mathematical career would enjoy it even more.

Images Back of Letters to a Young Mathematician.Spine of Letters to a Young Mathematician.Front of Letters to a Young Mathematician.
Structure [Toggle visibility]
  • Preface
  • 1 Why Do Math?
  • 2 How I Almost Became a Lawyer
  • 3 The Breadth of Mathematics
  • 4 Hasn't It All Been Done?
  • 5 Surrounded by Math
  • 6 How Mathematicians Think
  • 7 How to Learn Math
  • 8 Fear of Proofs
  • 9 Can't Computers Solve Everything?
  • 10 Mathematical Storytelling
  • 11 Going for the Jugular
  • 12 Blockbusters
  • 13 Impossible Problems
  • 14 The Career Ladder
  • 15 Pure or Applied?
  • 16 Where Do You Get Those Crazy Ideas?
  • 17 How to Teach Math
  • 18 The Mathematical Community
  • 19 Pigs and Pickup Trucks
  • 20 Pleasures and Perils of Collaboration
  • 21 Is God a Mathematician?
  • Notes and References

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