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Jacobian conjecture remains open

Lately some
papers were posted on the arXiv
claiming to solve the plane Jacobian conjecture. Fortunately, T.T. Moh took
the time to crack these attempts and posted the mistakes they made also
on the arXiv : Comment on a Paper by
Yucai Su On Jacobian Conjecture
and Comment on a Paper by
Kuo, Parusinski and Paunescu On Jacobian Conjecture
. Both papers are
only 2 pages long but are fun reading.

This note
was written on Oct 10, 2005 and was sent to the authors. At once
they replied to insist that they are correct, which was natural.
After a month we checked the website of Parusinski,
and found that a new sentence ”The proof contains some gaps in
section 7” by the authors without mentioning any objection by

So, the plane Jacobian conjecture remains
open, at least for now..

As for Kuo and his
collaborators, we believe that they have a good taste of
mathematics, and wish that they will push the analytic method deeper
to solve the Jacobian Conjecture.

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