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It is a pleasant surprise to him (the pure mathematician) and an added problem if he finds that the arts can use his calculations, or that the senses can verify them, much as if a composer found that sailors could heave better when singing his songs.
In J. R. Newman (ed.), The World of Mathematics, New York: Simon and Schuster, 1956.
Loci: Convergence
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A Locally Compact REU in the History of Mathematics: Involving Undergraduates in Research
Advice
You can do this! Pursuing research in the history of mathematics with undergraduates is very possible and very rewarding. Tailor your project to your resources and your interests. You may not be close to the Library of Congress, but you are probably close to some major research library. Find out about private libraries and collections in your area. Use the Internet; learn about Google Books. Come up with questions you want to answer, and start investigating. You never know where it might lead you.
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Mayfield, Betty and Kimberly Tysdal, "A Locally Compact REU in the History of Mathematics: Involving Undergraduates in Research," Loci (February 2009), DOI: 10.4169/loci003263