Hello:   
      
   In Volume 2 of my books, I briefly discuss a classical quintic equation like:   
      
   P1: x^5+ 15 x +12=0   
      
    Such equations are treated in most of abstract algebra textbooks using Galois   
   Theory and by explicit resolvant sextic.   
      
   However, I have noted a class type polynomials, i.e. those having as a class   
   related to same type differential equations, such as Riccati and Bernoulli.   
      
   It was noted that p1 is a transformation away from a member of class   
   polynomial.   
      
   We see solutions in the book. It is different than those obtained by Galois   
   Theory, however numerically the same.   
      
   It was not a chance to get more into quintic solving of Volume 2, since   
   solving differential equations got most of the PDF files.   
      
   But there is no doubt that future mathematicians need to identify such basis   
   for polynomials as class polynomials rooted in Riccati.   
      
   Personally, I think Galois Theory is ill structured with regard to polynomial   
   solving.   
      
   Also new solutions of polynomials and old ones (in algebra) give us new   
   identities equations in mathematics.   
      
   Now, as I have mentioned in my book DNA OF Mathematics, science need to be   
   free from academic power struggles.   
      
   I hope the American Math Society seriously look into freedom of science and   
   this new math in the coming months ahead.   
      
   Sincerely   
      
   Dr.Mehran Basti   
      
   Basti05b@aol.com   
      
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