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Although this has been valuable in a variety of applications, phenomena such as climate change have vastly increased the complexity of the systems that researchers would like to model. For instance, the ocean-climate-human system probably involves numerous feedbacks that are currently beyond mathematical models, as is the economic quantification of “ecosystem services”.1 This will require innovations in solving mathematical challenges such as finding solutions to complex and chaotic equations of fluid flow, and their integration with models that accurately reflect human behaviour and trends in other species’s movements and characteristics at a number of scales. Using higher-resolution data and more powerful computing resources to build and explore models will also improve our understanding.2 Programmes that ensure more equitable access to data and computational resources will bring much-needed depth and strength to these efforts.\n"},"title":"Nature","id":"openGraph_sub-topic/nature-1","image":{"id":"image_gesda-platform/banner/5-3-1-nature-25-2026_image__5.3.1_Nature_25_oy3lrc","url":"https://res.cloudinary.com/shapeable/image/upload/v1760163120/gesda-platform/banner/5-3-1-nature-25-2026_image__5.3.1_Nature_25_oy3lrc.webp","url2x":null,"thumbnails":{"card":{"id":"thumbnails-card-file_gesda-platform/banner/5-3-1-nature-25-2026_image__5.3.1_Nature_25_oy3lrc","url":"https://res.cloudinary.com/shapeable/image/upload/c_limit,w_480/v1760163120/gesda-platform/banner/5-3-1-nature-25-2026_image__5.3.1_Nature_25_oy3lrc.webp","url2x":"https://res.cloudinary.com/shapeable/image/upload/c_limit,w_960/v1760163120/gesda-platform/banner/5-3-1-nature-25-2026_image__5.3.1_Nature_25_oy3lrc.webp"},"small":{"id":"thumbnails-small-file_gesda-platform/banner/5-3-1-nature-25-2026_image__5.3.1_Nature_25_oy3lrc","url":"https://res.cloudinary.com/shapeable/image/upload/c_limit,h_64/v1760163120/gesda-platform/banner/5-3-1-nature-25-2026_image__5.3.1_Nature_25_oy3lrc.webp","url2x":"https://res.cloudinary.com/shapeable/image/upload/c_limit,h_128/v1760163120/gesda-platform/banner/5-3-1-nature-25-2026_image__5.3.1_Nature_25_oy3lrc.webp"}}}},"color":{"id":"65c55cbc9e947c438698a30d","name":"Black","value":"#292929","veryLightValue":"#D6D6D6"},"_schema":{"label":"Sub-Field","pluralLabel":"Sub-Fields"},"people":[]}},{"data":{"id":"68e792ff996e064174aade2a","path":"/sub-topics/machines","slug":"machines-1","name":"Machines","outlineNumber":"5.3.2","__typename":"SubTopic","typeLabel":"Sub-Field","openGraph":{"description":{"plain":"Recent progress in the development of AI and machine learning (ML) has led to numerous scientific, medical and even societal innovations that are set to improve the human experience. However, a range of significant challenges remain.5 Mathematicians are still seeking a clear theoretical understanding of exactly how and why AI and ML work,6 for example, with some models showing a mysterious ability to solve mathematical problems through guesswork in a manner that has yet to be understood. For this and other reasons, it is likely that AI will be most useful in its performance on tasks that are extremely challenging for human intelligence, and AI and human approaches to mathematics could ultimately be complementary rather than competitive.7\n"},"title":"Machines","id":"openGraph_sub-topic/machines-1","image":{"id":"image_gesda-platform/banner/5-3-2-machines-25-2026_image__5.3.2_Machines_25_nyrauc","url":"https://res.cloudinary.com/shapeable/image/upload/v1760163189/gesda-platform/banner/5-3-2-machines-25-2026_image__5.3.2_Machines_25_nyrauc.webp","url2x":null,"thumbnails":{"card":{"id":"thumbnails-card-file_gesda-platform/banner/5-3-2-machines-25-2026_image__5.3.2_Machines_25_nyrauc","url":"https://res.cloudinary.com/shapeable/image/upload/c_limit,w_480/v1760163189/gesda-platform/banner/5-3-2-machines-25-2026_image__5.3.2_Machines_25_nyrauc.webp","url2x":"https://res.cloudinary.com/shapeable/image/upload/c_limit,w_960/v1760163189/gesda-platform/banner/5-3-2-machines-25-2026_image__5.3.2_Machines_25_nyrauc.webp"},"small":{"id":"thumbnails-small-file_gesda-platform/banner/5-3-2-machines-25-2026_image__5.3.2_Machines_25_nyrauc","url":"https://res.cloudinary.com/shapeable/image/upload/c_limit,h_64/v1760163189/gesda-platform/banner/5-3-2-machines-25-2026_image__5.3.2_Machines_25_nyrauc.webp","url2x":"https://res.cloudinary.com/shapeable/image/upload/c_limit,h_128/v1760163189/gesda-platform/banner/5-3-2-machines-25-2026_image__5.3.2_Machines_25_nyrauc.webp"}}}},"color":{"id":"65c55cbc9e947c438698a30d","name":"Black","value":"#292929","veryLightValue":"#D6D6D6"},"_schema":{"label":"Sub-Field","pluralLabel":"Sub-Fields"},"people":[]}},{"data":{"id":"68e7941e996e064174aade41","path":"/sub-topics/society","slug":"society-1","name":"Society","outlineNumber":"5.3.3","__typename":"SubTopic","typeLabel":"Sub-Field","openGraph":{"description":{"plain":"Mathematics is central to much of the work carried out in the social sciences. Calculus underpins our understanding of economic systems; algebra and game theory define the forces at work when we model social interactions such as elections and responses to policy changes such as inter-state relations and healthcare provision; a deep grasp of statistics is vital to the task of anticipating future societal needs and ensuring that resource management is achieved effectively and efficiently. However, individual human behaviour resists mathematical modelling11 because of its complicated nature, including susceptibility to priming and framing effects that exert considerable influence on short timescales.\n"},"title":"Society","id":"openGraph_sub-topic/society-1","image":{"id":"image_gesda-platform/banner/5-3-3-society-25-2026_image__5.3.3_Society_25_sajzdr","url":"https://res.cloudinary.com/shapeable/image/upload/v1760163249/gesda-platform/banner/5-3-3-society-25-2026_image__5.3.3_Society_25_sajzdr.webp","url2x":null,"thumbnails":{"card":{"id":"thumbnails-card-file_gesda-platform/banner/5-3-3-society-25-2026_image__5.3.3_Society_25_sajzdr","url":"https://res.cloudinary.com/shapeable/image/upload/c_limit,w_480/v1760163249/gesda-platform/banner/5-3-3-society-25-2026_image__5.3.3_Society_25_sajzdr.webp","url2x":"https://res.cloudinary.com/shapeable/image/upload/c_limit,w_960/v1760163249/gesda-platform/banner/5-3-3-society-25-2026_image__5.3.3_Society_25_sajzdr.webp"},"small":{"id":"thumbnails-small-file_gesda-platform/banner/5-3-3-society-25-2026_image__5.3.3_Society_25_sajzdr","url":"https://res.cloudinary.com/shapeable/image/upload/c_limit,h_64/v1760163249/gesda-platform/banner/5-3-3-society-25-2026_image__5.3.3_Society_25_sajzdr.webp","url2x":"https://res.cloudinary.com/shapeable/image/upload/c_limit,h_128/v1760163249/gesda-platform/banner/5-3-3-society-25-2026_image__5.3.3_Society_25_sajzdr.webp"}}}},"color":{"id":"65c55cbc9e947c438698a30d","name":"Black","value":"#292929","veryLightValue":"#D6D6D6"},"_schema":{"label":"Sub-Field","pluralLabel":"Sub-Fields"},"people":[]}},{"data":{"id":"68e7956c996e064174aade5c","path":"/sub-topics/life","slug":"life-1","name":"Life","outlineNumber":"5.3.4","__typename":"SubTopic","typeLabel":"Sub-Field","openGraph":{"description":{"plain":"Whether for medical technologies such as diagnostic imaging, surgical intervention, prevention of infectious disease outbreaks and cancer treatment, or for biological applications in neuroscience, genomics and improving agricultural practices, mathematics plays a central role in our study of living systems.17\n"},"title":"Life","id":"openGraph_sub-topic/life-1","image":{"id":"image_gesda-platform/banner/5-3-4-life-25-2026_image__5.3.4_Life_25_dfa91r","url":"https://res.cloudinary.com/shapeable/image/upload/v1760163313/gesda-platform/banner/5-3-4-life-25-2026_image__5.3.4_Life_25_dfa91r.webp","url2x":null,"thumbnails":{"card":{"id":"thumbnails-card-file_gesda-platform/banner/5-3-4-life-25-2026_image__5.3.4_Life_25_dfa91r","url":"https://res.cloudinary.com/shapeable/image/upload/c_limit,w_480/v1760163313/gesda-platform/banner/5-3-4-life-25-2026_image__5.3.4_Life_25_dfa91r.webp","url2x":"https://res.cloudinary.com/shapeable/image/upload/c_limit,w_960/v1760163313/gesda-platform/banner/5-3-4-life-25-2026_image__5.3.4_Life_25_dfa91r.webp"},"small":{"id":"thumbnails-small-file_gesda-platform/banner/5-3-4-life-25-2026_image__5.3.4_Life_25_dfa91r","url":"https://res.cloudinary.com/shapeable/image/upload/c_limit,h_64/v1760163313/gesda-platform/banner/5-3-4-life-25-2026_image__5.3.4_Life_25_dfa91r.webp","url2x":"https://res.cloudinary.com/shapeable/image/upload/c_limit,h_128/v1760163313/gesda-platform/banner/5-3-4-life-25-2026_image__5.3.4_Life_25_dfa91r.webp"}}}},"color":{"id":"65c55cbc9e947c438698a30d","name":"Black","value":"#292929","veryLightValue":"#D6D6D6"},"_schema":{"label":"Sub-Field","pluralLabel":"Sub-Fields"},"people":[]}},{"data":{"id":"68e7a09d996e064174aaded8","path":"/sub-topics/digital-energy-innovations","slug":"digital-energy-innovations-1","name":"Digital energy innovations","outlineNumber":"3.1.2","__typename":"SubTopic","typeLabel":"Sub-Field","openGraph":{"description":{"plain":"Energy systems are changing from rigid, electromechanical structures to programmable, data-driven networks. 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The result should be a more flexible, integrated and democratised energy landscape.\n"},"title":"Digital energy 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