 That said, it is also the majority opinion that—with certain qualifications—Zeno’s paradoxes reveal some problems that cannot be resolved without the full resources of mathematics as worked out in the Nineteenth century (and perhaps beyond). This is not (necessarily) to say that modern mathematics is required to answer any of the problems that Zeno explicitly wanted to raise; arguably Aristotle and other ancients had replies that would—or should—have satisfied Zeno. (Nor shall we make any particular claims about Zeno’s influence on the history of mathematics.) However, as mathematics developed, and more thought was given to the paradoxes, new difficulties arose from them; these difficulties require modern mathematics for their resolution. These new difficulties arise partly in response to the evolution in our understanding of what mathematical rigor demands: solutions that would satisfy Zeno’s standards of rigor would not satisfy ours. Thus we shall push several of the paradoxes from their common sense formulations to their resolution in modern mathematics. (Another qualification: we shall offer resolutions in terms of ‘standard’ mathematics, but other modern formulations are also capable of dealing with Zeno, and arguably in ways that better represent his mathematical concepts.)