The Jacobian Conjecture is a mathematical problem that was first proposed by Italian mathematician Luigi Cremona in 1868. It deals with the invertibility of polynomial mappings in several variables.
Yes, the Jacobian Conjecture is still an open problem in mathematics. Despite numerous attempts by mathematicians over the years, a general proof or counterexample has yet to be found.
The Jacobian Conjecture is significant because it has connections to many different areas of mathematics, such as algebra, geometry, and topology. It also has practical applications in fields such as robotics and computer vision.
Over the years, there have been many partial results and special cases of the Jacobian Conjecture that have been proven. However, a complete solution to the conjecture has not yet been found.
There is currently no official prize or recognition for solving the Jacobian Conjecture. However, it is considered to be one of the most challenging open problems in mathematics, and its solution would likely be met with great acclaim in the mathematical community.