Contents

Preface

1 “Sports and Pastimes, Done by Number”: Mathematical Tricks, Mathematical Games

The Well Spring of Sciences

Humfrey Baker, 1564

Mathematical Recreations

Henry van Etten, 1633

“How Prodigiously Numbers Do Increase”

William Leybourne, 1667

Profitable and Delightful Problems

Jacques Ozanam, 1708

Lotteries and Mountebanks

L. Despiau, 1801

Dodging the Mastodon and the Plesiosaurus

Henry Ernest Dudeney, 1917

“Plenty of Interesting Things to Be Discovered”

NRICH, 1998–2004

2 “Much Necessary for All States of Men”: From Arithmetic to Algebra

Addition and Subtraction

Robert Recorde, 1543

Multiplication and Division

Thomas Masterson, 1592

Reducing Fractions

John Tapp, 1621

Decimal Fractions

Edward Hatton, 1695

Extracting Square Roots

William Banson, 1760

The Rule of Three

Wardhaugh Thompson, 1771

The Rule of Three, in Verse

Nathan Withy, 1792

“The First Analysts”

Joseph Fenn, 1775

Quadratic Equations

The Popular Educator, 1855

Cubic Equations for the Practical Man

J. E. Thompson, 1931

3 “A Goodly Struggle”: Problems, Puzzles, and Challenges

The Ladies’ Diary

1798

The Girl’s Own Book

Lydia Marie Child, 1835

The Boy’s Own Magazine

1855

“The Analyst”

1874

Can You Solve It?

Arthur Hirschberg, 1926

Mathematical Challenges

1989

4 “Drawyng, Measuring and Proporcion”: Geometry and Trigonometry

Points and Lines

Robert Recorde, 1551

Squares and Triangles

Thomas Rudd, 1650

Pythagoras’s Theorem

Edmund Scarburgh, 1705

Trigonometrical Definitions

Edward Wells, 1714

The Resolution of Triangles

Hugh Worthington, 1780

Introduction to Spherical Geometry

Horatio Nelson Robinson, 1854

Napier’s Rules

Alan Clive Gardner, 1956

5 Maps, Monsters, and Riddles: The Worlds of Mathematical Popularization

The Athenian Mercury

1691–1697

Newton for the Ladies

Francesco Algarotti, 1739

Maps and Mazes

W. W. Rouse Ball, 1892

“Einstein’s Real Achievement”

Oliver Lodge, 1921

Riddles in Mathematics

Eugene P. Northrop, 1945

Fermat’s Last Theorem

Hans Rademacher and Otto Toeplitz, 1957

Where Does It End?

Dan Pedoe, 1958

Yamátárájabhánasalagám

Sherman K. Stein, 1963

Saddles and Soap Bubbles

Iakov Isaevich Khurgin, 1974

“The Monster” Unveiled

The Times, 1980

6 “To Ease and Expedite the Work”: Mathematical Instruments and How to Use Them

“Cards for the Sea”

Martín Cortés, 1561

Making a Horizontal Sundial

Thomas Fale, 1593

Speaking-Rods

Seth Partridge, 1648

Telescopes Refracting and Reflecting

The Juvenile Encyclopedia, 1800–1801

Scales Simple and Diagonal

J. F. Heather, 1888

Making a Star Clock

Roy Worvill, 1974

PC Astronomy

Peter Duffet-Smith, 1997

7 “How Fine a Mind”: Mathematicians Past

The Labyrinth and Abyss of Infinity

Voltaire, 1733

“It Must Have Commenced with Mankind”

Charles Hutton, 1796

Kepler’s Astronomical Publications

Robert Small, 1804

Isaac Newton, a Good and Great Man

Anonymous, 1860

Pythagoras and His Theorem

Thomas L. Heath, 1908

Seki Kōwa

David Eugene Smith and Yoshio Mikami, 1914

“Her Absolute, Incomparable Uniqueness”

B. L. van der Waerden, 1935

“One of Your Calculating Fits”

George Bernard Shaw, 1939

Analysis Incarnate

Carl Boyer, 1968

Hardy and Littlewood Rummage

Robert Kanigel, 1991

8 “By Plain and Practical Rules”: Mathematics at Work

High Marshal and Camp Master

Leonard Digges, 1579

The Practical Gauger

William Hunt, 1673

Geodæsia

John Love, 1688

Plain Sailing

Archibald Patoun, 1762

High-Pressure Engines

William Templeton, 1833

The Strength of Materials

Lucius D. Gould, 1853

Plumbing and Hydraulics

William H. Dooley, 1920

Automobiles and Printing

Samuel Slade and Louis Margolis, 1941

9 “The Speedier Expedition of Their Learning”: Thoughts on Teaching and Learning Mathematics

“To Have Their Children or Servants Instructed”

Humfrey Baker, 1590

Euclid with Algebra

Isaac Barrow, 1660

The Idea of Velocity

Leonhard Euler, 1760

Mathematical Toys

“Mrs Lovechild,” 1785

A Mother Explains Comets

Catherine Vale Whitwell, 1823

“Geometry without Axioms”

Thomas Perronet Thompson, 1833

The Game of Logic

Lewis Carroll, 1887

Higher Mathematics for Women

Mrs. Henry Sidgwick, 1912

A New Aspect of Mathematical Method

George Pólya, 1945

New Math for Parents

Evelyn Sharp, 1966

“Merely a Formal Statement of the Way We Think”

Robert E. Eicholz and Phares G. O’Daffer, 1964

Turtle Fun

Serafim Gascoigne, 1985

10 “So Fundamentally Useful a Science”: Reflections on Mathematics and Its Place in the World

The Myrrour of the Worlde

Gossuin of Metz, 1481

“A Very Fruitfull Praeface”

John Dee, 1570

“Geometry Is Improving Daily”

Joseph Glanvill, 1664

The Fifth Element

Edmund Scarburgh, 1705

Of Mathematics in General

Richard Sault, 1710

Lineal Arithmetic

William Playfair, 1798

Astronomy in New South Wales

Charles Stargard Rumker, 1825

The Advantages of Mathematics

William Barnes, 1834

Sylvester Contra Huxley

J. J. Sylvester, 1870

What a Mathematical Proposition Is

Cassius Jackson Keyser, 1929

The Character of Physical Law

Richard P. Feynman, 1965

Our Invisible Culture

Allen L. Hammond, 1978

11 The Mathematicians Who Never Were: Fiction and Humor

Spider-Men and Lice-Men

Margaret Cavendish, 1666

In the Court of Lilliput

“Captain Gulliver,” 1727

Automathes

John Kirkby, 1745

The Loves of the Triangles

John Frere, 1798

Master Senex the Astronomer

William Combe, 1815

An Ode to the Mathematics

Alfred Domett, 1833

“Some Veritable Urania”

Augusta Jane Evans, 1864

Fun

1863, 1870

A Sight of Thine Interior

Edwin A. Abbott, 1884

Scenes in the Life of Pythagoras

Geoffrey Willans and Ronald Searle, 1953

Bao Suyo

Kim Stanley Robinson, 1996

Index