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Purpose: This paper aims to identify the current situation of higher education institutions in Spain regarding the introduction of the Sustainable Development Goals in the classroom, and what is the role of mathematics in this task. Design/methodology/approach: A review is made of how the concept of sustainability has evolved in higher education, its gradual introduction in the University and the way in which this subject is approached in the field of mathematics. Findings: The study concludes that higher education has a key role to play in designing strategies that lead to the global sustainability of the planet. This implies major changes in degree curricula, assessment, competences and teacher training. Cross-disciplinarity and interdisciplinarity between different subjects within the same degree is a strategy for students to analyse the Sustainable Development Goals using mathematical techniques. Social implications: The University as an institution must train socially responsible professionals who are aware of the importance of promoting a sustainable world. Changes should be made to introduce values in the classroom that promote and encourage sustainability. Training should be seen as a continuous process that leads to the preparation of professionals committed to society and nature and who develop strategies aimed at improving the planet through values. Originality/value: Through practical activities, the Sustainable Development objectives can be analysed from several subjects of the same degree, emphasising the interdisciplinary and transversal nature that should be the central axis of higher education. Each subject can develop a strategy for change in favour of sustainability that will be reinforced and increased by working together on the proposed teaching practice. In this way, the contents of the different subjects are not isolated, but rather the student can see how there is an interrelationship between them and with real life. [ABSTRACT FROM AUTHOR]