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November 10, 2025<\/p>\n
2 min read<\/p>\n
Scientists See \u2018Eureka\u2019 Moments in Mathematicians\u2019 Chalkboard Writings<\/p>\n
Researchers spot the \u201ctipping point\u201d before mathematicians\u2019 moments of discovery<\/p>\n
By Matthew Hutson edited by Sarah Lewin Frasier<\/span><\/p>\n If you want to know when mathematicians are about to have a breakthrough, you don\u2019t need to look inside their heads. Just watch their movements at a chalkboard.<\/p>\n \u201cI\u2019ve always been super intrigued by this tension between how abstract and conceptual mathematics is, on the one hand, and then just how physical the actual activity of mathematics is,\u201d says Tyler Marghetis, a cognitive scientist at the University of California, Merced. He wondered whether he could use the \u201cmanual labor\u201d of math to deduce what was happening in someone\u2019s mind. In a recent study in the Proceedings of the National Academy of Sciences USA, Marghetis and his co-authors borrowed theoretical tools from other fields to show it\u2019s possible.<\/p>\n Complex systems sometimes abruptly change state. It can happen when metals become magnetic, when algae overtake a pond or when a horse goes from a walk to a trot. Often a period of instability precedes the tipping point. Some neuroimaging suggests that such a change also happens in the process of insight\u2014when the brain is stuck in a rut, wobbles and then finds the right track. This study illustrates that process at work.<\/p>\n If you’re enjoying this article, consider supporting our award-winning journalism by subscribing. By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.<\/p>\n The researchers recorded six mathematicians at chalkboards as they each spent about 40 minutes working on two math proofs and thinking aloud. Observers made a note each time a solver shifted attention to other parts of the board by writing, erasing or pointing at equations, diagrams, or other inscriptions. In this way, the mathematician and chalkboard together acted as what cognitive scientists would call one extended and semiobservable mind. The researchers also recorded exclamations of insight (\u201cI see!\u201d). By analyzing the data, they found that the places attention shifted to became significantly more unpredictable in the two minutes before a eureka moment. It\u2019s unclear where that unpredictability originated: Either a bubbling idea led solvers to connect puzzle pieces across the board, or solvers had grown frustrated and decided to physically forage for new connections, which sparked a solution. Perhaps it was a mixture of both.<\/p>\n \u201cI think it\u2019s a fun paper,\u201d says Santa Fe Institute physicist and mathematician Cristopher Moore, who studies complex systems and was not involved in the study. \u201cI only wish it helped me figure out how to have more insights,\u201d he adds with a laugh. He\u2019d like to see the study\u2019s statistical approach combined with deep interviews \u201cto build up a rich corpus of what mathematicians were thinking at the time.\u201d<\/p>\n Georgetown University psychologist Shadab Tabatabaeian, the paper\u2019s lead author, imagines a \u201ccool application\u201d of their method: someday computer interfaces that track mouse or eye movements might know when not to disturb someone on the brink of a breakthrough or when to toss a new idea their way.<\/p>\n If you enjoyed this article, I\u2019d like to ask for your support. Scientific American<\/span> has served as an advocate for science and industry for 180 years, and right now may be the most critical moment in that two-century history.<\/p>\n I\u2019ve been a Scientific American<\/span> subscriber since I was 12 years old, and it helped shape the way I look at the world. SciAm <\/span>always educates and delights me, and inspires a sense of awe for our vast, beautiful universe. I hope it does that for you, too.<\/p>\n If you subscribe to Scientific American<\/span>, you help ensure that our coverage is centered on meaningful research and discovery; that we have the resources to report on the decisions that threaten labs across the U.S.; and that we support both budding and working scientists at a time when the value of science itself too often goes unrecognized.<\/p>\n In return, you get essential news, captivating podcasts, brilliant infographics, can’t-miss newsletters, must-watch videos, challenging games, and the science world’s best writing and reporting. You can even gift someone a subscription.<\/p>\n There has never been a more important time for us to stand up and show why science matters. I hope you\u2019ll support us in that mission.<\/p>\n","protected":false},"excerpt":{"rendered":" November 10, 2025 2 min read Scientists See \u2018Eureka\u2019 Moments in Mathematicians\u2019 Chalkboard Writings Researchers spot the \u201ctipping point\u201d before mathematicians\u2019 moments of discovery By Matthew Hutson edited by Sarah Lewin Frasier If you want to know when mathematicians are about to have a breakthrough, you don\u2019t need to look inside their heads. Just watch<\/p>\n","protected":false},"author":1,"featured_media":32806,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[50],"tags":[18881,9610,8203,871,85,3407],"class_list":{"0":"post-32805","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-environment","8":"tag-chalkboard","9":"tag-inspiration","10":"tag-mathematicians","11":"tag-shows","12":"tag-strikes","13":"tag-writing"},"_links":{"self":[{"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=\/wp\/v2\/posts\/32805","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=32805"}],"version-history":[{"count":0,"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=\/wp\/v2\/posts\/32805\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=\/wp\/v2\/media\/32806"}],"wp:attachment":[{"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=32805"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=32805"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=32805"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}On supporting science journalism<\/h2>\n
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