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The Mending of Broken Bones: A Modern Guide to Classical Algebra
A joyful and intimate celebration of the beauty and creativity of algebra from one of the foremost math educators of our time.
For many of us, algebra conjures up memories of dull classes spent wondering when we’d ever have to solve a system of equations or factor a polynomial. Indeed, most of the time, if we need to plan a budget or figure out how early to leave the house for work, common sense or a quick, seat-of-the-pants approximation is good enough.
But as mathematician Paul Lockhart argues in The Mending of Broken Bones, once we stop thinking of algebra in terms of its practical applications, we can appreciate it for the beautiful and gratifying subject that it is. In his hands, algebra is the delicate craft of untangling numerical puzzles to reveal the hidden patterns and often surprising behaviors of the numbers themselves. As Lockhart traverses numerical systems, slips into and out of higher-dimensional space, and delights in the intimate connections between algebra and geometry, we come to see the discipline from his not as the mundane exercises of our school years, but instead as an art form whose beauty lies in its elegant simplicity.
Written in Lockhart’s charming and conversational prose, The Mending of Broken Bones is an impassioned and deeply personal celebration of algebra that helps us experience the profound joys of mathematical discovery.
For many of us, algebra conjures up memories of dull classes spent wondering when we’d ever have to solve a system of equations or factor a polynomial. Indeed, most of the time, if we need to plan a budget or figure out how early to leave the house for work, common sense or a quick, seat-of-the-pants approximation is good enough.
But as mathematician Paul Lockhart argues in The Mending of Broken Bones, once we stop thinking of algebra in terms of its practical applications, we can appreciate it for the beautiful and gratifying subject that it is. In his hands, algebra is the delicate craft of untangling numerical puzzles to reveal the hidden patterns and often surprising behaviors of the numbers themselves. As Lockhart traverses numerical systems, slips into and out of higher-dimensional space, and delights in the intimate connections between algebra and geometry, we come to see the discipline from his not as the mundane exercises of our school years, but instead as an art form whose beauty lies in its elegant simplicity.
Written in Lockhart’s charming and conversational prose, The Mending of Broken Bones is an impassioned and deeply personal celebration of algebra that helps us experience the profound joys of mathematical discovery.
400 pages, Hardcover
First published May 13, 2025
About the author
Paul Lockhart
5 books227 followersPaul Lockhart became interested in mathematics when he was 14 (outside the classroom, he points out). He dropped out of college after one semester to devote himself exclusively to math. Based on his own research he was admitted to Columbia, received a PhD, and has taught at major universities, including Brown University and UC Santa Cruz. Since 2000 he has dedicated himself to "subversively" teaching grade-school math at St. Ann's School in Brooklyn, New York.
Librarian Note: There is more than one author in the Goodreads database with this name.
Librarian Note: There is more than one author in the Goodreads database with this name.
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February 23, 2026Enjoyed this approach to algebra. It eventually gets to a level of depth which required more time and concentration than I was willing to give it as someone who hasn't thought much about math for the last decade, but it never felt unreasonable for someone who would give it that time.
August 5, 2026
To break down a daunting topic into nine operations using Field Theory, and make it fun, is a daunting challenge. Culling through history the many landmines and pitfalls of proofs, unshared theorems, correspondences, duels, and secrets revealed to students, is a spicy approach to tough topics.
My favorite chapter was the last, shedding light on Geometry Algebra using lemniscate, the witch of Agnesi, and challenging perspective to axiomatic ways to generalize the intersection of parabolas to a line, when lines are below the vertex or lines' slopes are undefined.
The operations chapters at the beginning are very accessible, then when we move beyond quadratics, the writing doesn't always capture Lockhart's meaning, which he readily admits. I thoroughly enjoyed this book, but became bogged down in some of the elimination chapters, understandably because I was trying to read and not actually work through the minutiae.
My favorite chapter was the last, shedding light on Geometry Algebra using lemniscate, the witch of Agnesi, and challenging perspective to axiomatic ways to generalize the intersection of parabolas to a line, when lines are below the vertex or lines' slopes are undefined.
The operations chapters at the beginning are very accessible, then when we move beyond quadratics, the writing doesn't always capture Lockhart's meaning, which he readily admits. I thoroughly enjoyed this book, but became bogged down in some of the elimination chapters, understandably because I was trying to read and not actually work through the minutiae.
Displaying 1 - 2 of 2 reviews