Everyone has their own approach to problem solving:

"Like his thesis adviser Dr. Kolmogorov, Dr. Arnold had an unusual approach when he got stuck on a problem. Writing in the Russian online newspaper Gazeta.ru, his former students Askold Khovanskii and Yuli Ilyashenko recalled that Dr. Arnold would ski for 25 miles or more, wearing nothing more than swim trunks."

I knew him only through his books, but both 'Ordinary Differential Equations' and 'Mathematical Methods of Classical Mechanics' were highly influential - the use of geometric methods was a breath of fresh air at the time I read them.