{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T00:25:50Z","timestamp":1785198350075,"version":"3.55.0"},"reference-count":115,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T00:00:00Z","timestamp":1782259200000},"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. Cognit."],"abstract":"<jats:p>\n                    The more advanced the symbolic mathematics, the more impenetrable the meaning. This is particularly evident in quantum theory, where symbolic formalisms foreground states and objects. An alternative diagrammatic approach, Quantum Picturalism (QPic), privileges structure, relation, and transformation. As a category theoretic formalism, it supports reasoning through the composition of visually represented quantum processes, a distinction that not only concerns representation but also shapes how quantum phenomena are conceptualized, opening new educational possibilities and ways of knowing. The choice of formalism\u2014algebraic or diagrammatic\u2014is not neutral, but embodies underlying ontological commitments that shape which structural features of quantum phenomena\u2014such as states vs. relations; objects vs. transformations\u2014are made accessible. This paper examines the epistemological, cognitive, and educational significance of non-symbolic thought in mathematics, and in quantum mechanics in particular, using QPic as a guiding example. We raise a central question: can quantum processes be represented in ways that align more naturally with human cognition? What is new here is showing how the epistemological and cognitive aspects of non-symbolic formalism are brought into pedagogical practice. Such paradigm largely benefits from the\n                    <jats:italic>language of thought<\/jats:italic>\n                    hypothesis alongside theories of embodied cognition, dual coding, and conceptual metaphor theory to articulate a holistic framework in which multiple, interacting conceptual systems underpin understanding. Drawing on historical precedents\u2014from Euclidean geometry to Leibniz's universal calculus of thought\u2014we contend that human intuition works more naturally within relational and visual frameworks, particularly those that help complex ideas to be seen and manipulated as structured wholes. The broader impact of this paradigm lies in democratizing access to quantum innovation and rethinking what it means to\n                    <jats:italic>understand<\/jats:italic>\n                    the quantum world, offering an inclusive entry point into it.\n                  <\/jats:p>","DOI":"10.3389\/fcogn.2026.1790789","type":"journal-article","created":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T05:45:52Z","timestamp":1782279952000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Beyond symbolic algebra with quantum picturalism"],"prefix":"10.3389","volume":"5","author":[{"given":"Selma","family":"D\u00fcndar-Coecke","sequence":"first","affiliation":[{"name":"Neurossance","place":["Oxford, United Kingdom"]},{"name":"Centre for Educational Neuroscience, King's College London","place":["London, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lia","family":"Yeh","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Oxford","place":["Oxford, United Kingdom"]},{"name":"Department of Computer Science and Technology, University of Cambridge","place":["Cambridge, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Emmanuel","family":"Pothos","sequence":"additional","affiliation":[{"name":"Department of Psychology, City University","place":["London, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad Hamza","family":"Waseem","sequence":"additional","affiliation":[{"name":"Clarendon Laboratory, Department of Physics, University of Oxford","place":["Oxford, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bob","family":"Coecke","sequence":"additional","affiliation":[{"name":"Perimeter Institute","place":["Waterloo, ON, Canada"]},{"name":"Wolfson College, University of Oxford","place":["Oxford, United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2026,6,24]]},"reference":[{"key":"B1","first-page":"415","article-title":"\u201cA categorical semantics of quantum protocols,\u201d","volume-title":"Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS)","author":"Abramsky","year":"2004"},{"key":"B2","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1016\/B978-0-444-52869-8.50010-4","article-title":"Categorical quantum mechanics","volume":"2","author":"Abramsky","year":"2009","journal-title":"Handb. 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