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
Famous quotes containing the words popular, mathematical and/or writings:
“Fifty million Frenchmen can’t be wrong.”
—Anonymous. Popular saying.
Dating from World War I—when it was used by U.S. soldiers—or before, the saying was associated with nightclub hostess Texas Quinan in the 1920s. It was the title of a song recorded by Sophie Tucker in 1927, and of a Cole Porter musical in 1929.
“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)
“Even in my own writings I cannot always recover the meaning of my former ideas; I know not what I meant to say, and often get into a regular heat, correcting and putting a new sense into it, having lost the first and better one. I do nothing but come and go. My judgement does not always forge straight ahead; it strays and wanders.”
—Michel de Montaigne (1533–1592)