Patterns, Pictures, and Predictions: Mapping Mathematical Worlds

Bharath Sriraman ()
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Bharath Sriraman: University of Montana – Missoula, Department of Mathematical Sciences

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 1-18 from Springer

Abstract: Abstract Mathematical practice has undergone a profound transformation over the past several decades. Once dominated by symbolic manipulation and axiomatic deduction, the discipline now routinely integrates visualization, computation, and data-driven experimentation as central methodological components. This chapter examines how experimental mathematics, computational techniques, and visual reasoning have reshaped both pure and applied domains, dissolving long-standing boundaries between them. Through case studies drawn from number theory, epidemiology, topology, sports analytics, and formal verification, we illustrate how computation generates conjectures, visualization guides intuition and proof, and data grounds theoretical models. Rather than serving as auxiliary tools, these methods now constitute a unified mathematical practice in which patterns, pictures, and predictions jointly produce understanding.

Keywords: Computational mathematics; Visualization; Experimental mathematics; Mathematical modeling; Data-driven methods; Conjecture generation; Formal verification; Machine learning in mathematics; Uncertainty quantification; Interdisciplinary mathematics (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-16368-4_95

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DOI: 10.1007/978-3-032-16368-4_95

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