If the paper has been officially published, but mathematical errors are found, the first method is to contact the editor to withdraw the manuscript, correct the errors and publish it again. The second method is not to withdraw the manuscript, but to reissue a correction statement to explain the mistakes in the manuscript and apologize.

The above two methods can solve the problem of finding data errors after the publication of the paper.

When a small paper is published and the data is found to be wrong, we can cancel it and publish it again after revision.