A Meeting of Great Minds, Sophus Lie and John Nash throughout their Works

It is well known that Marius Sophus Lie (1842-1899) and John Forbes Nash (1928-2015) are great mathematicians. Sophus Lie comes from Norway and John Nash from United States of America. Their stories have certain resemblances and remarkable relations. This editorial would emphasize some of them. When they have started their university studies, their respective first interests were not mathematics.

That is to say, Lie has been in Astronomy and Nash in Chemical Engineering. Whereas,when they worked on mathematics, the first had Lobatchevski award in 1897 and the second, Nobel prize 1994 and Abel award 2015 (Niels Abel is the uncle of the wife of Sophus Lie: Anna Birch). In addition, their contributions in geometry are considerable, particularly in differential equations. Lie worked on transformation groups relative to partial differential equations, in other words, on Lie groups and on special non-associative algebras named Lie algebras.