Popular Mathematical Writings
Arnold is well known for his lucid writing style, combining mathematical rigour with physical intuition, and an easy conversational style of teaching. His writings present a fresh, often geometric approach to traditional mathematical topics like ordinary differential equations, and his many textbooks have proved influential in the development of new areas of mathematics. However, Arnold's books have been criticized for supporting the theory with statements meant to teach an intuitive understanding, without providing the tools necessary to prove these statements.
Arnold was an outspoken critic of the trend towards high levels of abstraction in mathematics during the middle of the last century. He had very strong opinions on how this approach—which was most popularly implemented by the Bourbaki school in France—initially had a negative impact on French, and then later other countries', mathematical education. Arnold's sharp critique of the Bourbaki approach was in turn criticized by other mathematicians.
Read more about this topic: Vladimir Arnold
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