Problems for Mathematicians, Young and Old

Problems for Mathematicians, Young and Old presents 93 mathematical problems designed to challenge readers at various skill levels. The problems span multiple areas including algebra, analysis, geometry, and logic. Each problem is self-contained and includes background information needed for understanding the challenge. Solutions are provided separately in the back of the book, allowing readers to work through problems at their own pace. The collection reflects Halmos's experience both as a mathematician and as an educator at multiple universities. Problems range from introductory exercises suitable for students to complex challenges that will interest professional mathematicians. The book stands as an example of how mathematical education can combine rigor with accessibility, presenting problems that develop both technical skills and mathematical intuition.

Readers describe this as a collection of mathematics problems ranging from basic algebra to advanced concepts. Most are puzzles rather than formal proofs. Likes: - Clear, concise problem statements - Problems build on each other in difficulty - Solutions provided but not immediately visible - Mix of classic problems and original ones - Useful for self-study and teaching Dislikes: - Some find the difficulty jumps too steep - A few problems have unclear wording - Solutions can be terse and hard to follow - Limited explanations of underlying concepts Ratings: Goodreads: 4.0/5 (48 ratings) Amazon: 4.1/5 (12 ratings) "Perfect for keeping your problem-solving skills sharp" - Math teacher review on Amazon "Some gems here but prepare to struggle" - Goodreads reviewer "Would benefit from more detailed solutions" - Mathematics Stack Exchange user The book connects with both students and professional mathematicians as a source of intellectual challenge.

Mathematical Puzzles and Diversions by Martin Gardner This collection presents mathematical problems and recreational puzzles that encourage creative problem-solving approaches through logic, geometry, and number theory.

What Is Mathematics? by Richard Courant The text connects fundamental mathematical concepts through a series of problems that build from basic principles to complex mathematical ideas.

How to Solve It by George Pólya The book outlines problem-solving strategies through mathematical examples that demonstrate systematic approaches to mathematical thinking.

The Art and Craft of Problem Solving by Paul Zeitz This text presents problem-solving techniques through challenging mathematical problems that range from elementary to advanced topics.

A Moscow Math Circle by Sergey Dorichenko The book contains week-by-week mathematical problems from Moscow's mathematical circles that develop problem-solving skills through careful progression of concepts.

🔹 Paul Halmos was known for introducing the "end of proof" symbol ■ (called a halmos or tombstone) into common mathematical usage 🔹 The book contains 100 problems ranging from elementary to advanced, with Halmos specifically stating that some problems are meant to be unsolvable - teaching readers that knowing when a problem cannot be solved is as valuable as solving one 🔹 Halmos wrote more than 40 mathematical books and papers, and was celebrated for his clear, engaging writing style that made complex mathematical concepts more accessible 🔹 The problems in this book were collected over decades of Halmos's teaching career at the University of Chicago, University of Michigan, and several other prestigious institutions 🔹 Despite being a renowned mathematician, Halmos initially failed his first PhD qualifying exam at the University of Illinois, demonstrating that even brilliant mathematicians face setbacks in their journey