In 1953, mathematician Mauricio Peixoto, one of the founders of IMP (Institute of Pure and Applied Mathematics), began a pioneering study in the relatively new area of dynamic systems. By the end of the decade he had already proved that most differential equations in dimension two have a finite number of periodic solutions and are stable: solutions are not essentially affected when we change the equation a little.
American colleague Steve Smale soon became interested in these results. In work published in early 1960, he generalized the type of equations considered by Peixoto for larger dimensions and conjectured that these equations, which Frenchman René Thom called “Morse-Smale”, would still be most of all differential equations in any dimension.
But shortly thereafter, while visiting Impa to invite Peixoto and Elon Lages Lima, Smale received a letter from colleague Norman Levinson, dated February 20, who changed everything: Levinson had discovered, a long time ago, that there are many differential equations with infinite number of periodic solutions. Therefore, Smale’s conjecture could not be true! Read more (07/29/2025 – 23h00)
Source: Folha
I have worked in the news industry for over 10 years and have been an author at News Bulletin 247 for the past 5 years. I mostly cover technology news and enjoy writing about the latest gadgets and devices. I am also a huge fan of music and enjoy attending live concerts whenever possible.
