Mathematicians who write like Vladimir Arnold

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SUMMARY

This discussion centers on the clarity of mathematical writing, specifically highlighting the works of V.I. Arnold as exemplary. Participants express a desire for math books that convey complex ideas with the same narrative clarity found in Arnold's texts. Recommendations include M.A. Armstrong's "Groups and Symmetry" and "Basic Topology," John Baez's expository articles, and George Shilov's "Elementary Real and Complex Analysis." Additionally, Sheldon Axler's "Linear Algebra Done Right" emphasizes the importance of engaging with mathematical texts in a meaningful way, while Tristan Needham's "Visual Complex Analysis" is noted for its exceptional clarity.

PREREQUISITES
  • Familiarity with mathematical notation and terminology
  • Understanding of mathematical exposition and clarity in writing
  • Knowledge of key mathematical texts and authors
  • Interest in mathematical pedagogy and communication
NEXT STEPS
  • Explore "Visual Complex Analysis" by Tristan Needham for its narrative style
  • Read "Linear Algebra Done Right" by Sheldon Axler to understand effective mathematical exposition
  • Investigate the works of John Milnor for clarity in advanced mathematics
  • Review the MathOverflow thread on similar mathematical texts for additional recommendations
USEFUL FOR

Mathematicians, educators, and students seeking to enhance their understanding of mathematical concepts through clear and engaging writing styles.

Snicker
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"What he needed was a notion, not a notation" ~ Gauss.​

I have a copy of several books by V.I. Arnold. If you have read him, then you would agree: He is one hell of a clear writer. His books contain some of the most technical information yet manages to read like novels. I want all my math books to be written with similar clarity.

Thus far, I have found a bit of Arnold in M.A. Armstrong (Groups and Symmetry and Basic Topology), John Baez (does not write a lot of books -- but a lot of expository articles), or George Shilov (Elementary Real and Complex Analysis, Linear Algebra, Functional Analysis).

Sheldon Axler, in the preface of Linear Algebra Done Right, claims that if one reads a page in a math book in under an hour, she is doing something wrong. He is correct, but I want a book in which I can read through it like a novel and understand the main points of the exposition without having to understand every little notational detail.

Therefore, do you know of any authors who, like V.I. Arnold, puts in that effort to make their books as clear as possible?
 
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