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Walking with the Masters

Over the years, I have encountered thousands of children who had the potential to learn beautiful mathematics. But many of them never did. I think about these incidents as missed opportunities. After all, mathematics has led me to great joy in life. I wish this joy for more people.

One possible reason which prevented their growth is the lack of great teachers. This is not an accident but a statistical inevitability. The number of passionate teachers per capita is low in India and will remain low in the foreseeable future. Therefore the probability that a kid with great potential encounters an equally passionate teacher is also low.

This problem in pedagogy may be partially addressed using Abel's strategy. Norwegian mathematician Niels Henrik Abel was one of the most promising mathematicians of all time. Unfortunately, he died at the early age of 26. Among other things, when he was 16, he discovered proof of the binomial theorem that works for all numbers. At the age of 19, he showed that a quintic equation cannot be solved algebraically. When he was asked how he learned so much mathematics so fast, he responded, "by studying the masters, not their pupils."

Abel was referring to the books written by true masters of mathematics. Personally speaking, over the years I have become more and more convinced about Abel's strategy. Reading regular textbook-styled works is not only a waste of time, but it may also have a negative impact on an enthusiastic learner. On the other hand, reading a book written by a true master is like learning from him or her directly. It is an outstanding opportunity that none of us should miss.

Here are some of those walks with the masters, that have transformed my life and the way I do mathematics. You may use this list of beautiful mathematics books to stay inspired.

Class 1 to 5

  • Math from Three to Seven, The Story of a Mathematical Circle for Preschoolers
    Alexander K. Zvonkin
  • Math Circles for Elementary School Students
    by Natasha Rozhkovskaya

Class 6 to 8

  • Mathematics can be Fun by Yakov Perelman
  • Mathematical Circles, Russian Experience by Fomin
  • Algebra by Gelfund

Class 9 and above (in school)

  • Geometric Transformations Vol. I to IV by Yaglom
  • Geometry and the Imagination by Hilbert and Vossen
  • Calculus by Tarasov
  • Geometry Revisited by Coxeter
  • Intuitive Topology by Prasolov
  • Combinatorics by Krishnamurthy

Higher Mathematics

  • Three-dimensional Geometry and Topology by William Thurston
  • Trees by Serre
  • Analysis by Tao

Please be careful about using this list. It is not supposed to be a collection of exhaustive learning material for all possible topics. Use these books for inspiration. Moreover, I plan to update this list periodically. You may bookmark it for later use.

All the best.

Dr. Ashani Dasgupta

Cheenta

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