We have had this discussion.
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I'm interestedd in non-standard analysis. The concept of infinitesimals always appeared fairly perplexing to me and the idea that you can do all that Newton, Leibniz, ... did with them in a rigorous way seems really interesting.
But... applications of non-standard analysis seem to be scarce and it doesn't seem to be an easy topic.
What do you think? If you studied non-standard analysis, did it pay off? Did it expand your understanding in a significant way?