Critique
Despite the elegance and appeal of some aspects of non-standard analysis, there has been skepticism in the mathematical community about whether the nonstandard machinery adds anything that cannot easily be achieved by standard methods. These criticisms notwithstanding, however, there is no controversy about the mathematical validity of the approach and the results of non-standard analysis. Bishop's critique of NSA and of Keisler's elementary calculus book based on Robinson's theory is documented at Criticism of non-standard analysis#Bishop's criticism.
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