We Can Differentiate Numbers, Too

SummaryWe survey the history of the arithmetic derivative and more recent advances in research on this topic. Among other things, we discuss a few generalizations of the original arithmetic derivative and some arithmetic differential equations that are related to Goldbach’s conjecture and the twin prime conjecture. Our primary purpose is to give an overview of this field, but we also aim at providing supplementary material for an introductory course on discrete mathematics or number theory. Therefore, our survey contains ten exercises. Additional informationNotes on contributorsTimo TossavainenTimo Tossavainen (timo.tossavainen@ltu.se) is professor of mathematics education at Lulea University of Technology in Sweden. He received his Ph.D. in mathematics from Jyväskylä University, Finland, under the supervision of Pekka Koskela. He is interested in recreational mathematics, nonfiction literature, progressive rock, and cross-country skiing.Pentti HaukkanenPentti Haukkanen (pentti.haukkanen@tuni.fi) received his Ph.D. in mathematics from Tampere University, Finland, under the supervision of Seppo Hyyrö. Currently, he is university lecturer of mathematics at his alma mater. In his free time, he enjoys various sports and culture.Jorma K. MerikoskiJorma K. Merikoski (jorma.merikoski@tuni.fi) is emeritus professor of mathematics at Tampere University. He received his Ph.D. in mathematics from this university under the supervision of Seppo Hyyrö. Besides mathematics, he enjoys running, cross-country skiing, and literature.Mika MattilaMika Mattila (mika.mattila@tuni.fi) is university teacher of mathematics at Tampere University, where he also received his Ph.D. in mathematics under the supervision of Pentti Haukkanen. In addition to mathematics and some physical activities, he is interested in literature, movies, and retro console games.