{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T06:44:08Z","timestamp":1792565048047,"version":"4.5.0"},"reference-count":92,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T00:00:00Z","timestamp":1792540800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Artif. Intell."],"abstract":"<jats:p>Artificial intelligence (AI) in healthcare relies on diverse mathematical frameworks, yet their contributions to model development, evaluation, interpretability, and clinical translation remain fragmented. This systematic review synthesized the classical and emerging mathematical foundations underpinning healthcare AI and examined major methodological and application trends. Following PRISMA 2020 guidelines, studies published between January 2016 and June 30, 2026, were identified through systematic searches of Scopus, Google Scholar, and PubMed\/MEDLINE, with searches conducted using Harzing\u2019s Publish or Perish v8 where applicable. Bibliometric analysis was performed using VOSviewer, while methodological quality was assessed using an adapted JBI-based framework and AMSTAR-2 for systematic reviews. Of 653 records identified, 147 studies met the eligibility criteria. Non-mutually exclusive mathematical-domain coding identified linear algebra in 100\/147 studies (68.0%), calculus and optimization in 91\/147 (61.9%), and probability and statistics in 79\/147 (53.7%), highlighting their roles in data representation, learning, optimization, inference, uncertainty quantification, and validation. A separate mutually exclusive classification of dominant methodological themes identified explainable and trustworthy AI in 24\/147 studies (16.3%), statistics and learning theory in 23\/147 (15.6%), probability and Bayesian methods in 23\/147 (15.6%), calculus and optimization in 19\/147 (12.9%), and linear algebra in 15\/147 (10.2%). Radiology and medical imaging were the leading healthcare application (24.3%), while classification and diagnosis were the most frequent clinical task (17.1%). Overall, healthcare AI is supported by an interconnected mathematical ecosystem. Emerging approaches, including graph neural networks, Transformers, and quantum machine learning, require stronger external validation, standardized benchmarking, and rigorous evaluation for reliable clinical translation.<\/jats:p>","DOI":"10.3389\/frai.2026.1995929","type":"journal-article","created":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T05:59:45Z","timestamp":1792562385000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Mathematical foundations of artificial intelligence in healthcare: a systematic review"],"prefix":"10.3389","volume":"9","author":[{"given":"Yuliana","family":"Jim\u00e9nez-Gaona","sequence":"first","affiliation":[{"name":"Departamento de Qu\u00edmica y Producci\u00f3n, Universidad T\u00e9cnica Particular de Loja","place":["Loja, Ecuador"]},{"name":"Theoretical and Experimental Epistemology Lab, School of Optometry and Vision Science, University of Waterloo","place":["Waterloo, ON, Canada"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vasudevan","family":"Lakshminarayanan","sequence":"additional","affiliation":[{"name":"Theoretical and Experimental Epistemology Lab, School of Optometry and Vision Science, University of Waterloo","place":["Waterloo, ON, Canada"]},{"name":"Department of Systems Design Engineering, Physics, and Electrical and Computer Engineering, University of Waterloo","place":["Waterloo, ON, Canada"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2026,10,21]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/j.inffus.2021.05.008","article-title":"A review of uncertainty quantification in deep learning: techniques, applications and challenges","volume":"76","author":"Abdar","year":"2021","journal-title":"Inf. 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