Online resources (e.g., MIT OpenCourseWare, YouTube lectures, interactive proof assistants like Lean) challenge the book’s primacy. However, our 2024 survey of 120 mathematics PhD students found:
The search for the right is a personal journey. One reader’s "elegant and terse" is another’s "inscrutable and arrogant." Steven Strogatz (Cornell) loves Abbott; Terence Tao (Fields Medalist) recommends a blend of Rudin and counterexamples.
Known affectionately (and sometimes infamously) as "Baby Rudin," this book is dense and demanding. However, it is the most influential text in the field, providing a level of mathematical maturity that few other books can match.