The paper examines global space making and geopolitics in higher education. After reviewing global ontology and spatiality, globalisation (worldwide convergence and integration), and the interactions of the national and global scales, it examines the changing geopolitical order on an historical basis. It moves from the long impact of the colonial inheritance to the high point of neocolonial Euro-American globalisation in the 1990s (‘the end of history’), to global multi-polarisation and the spread of capacity in higher education and science in the 2000s and after, to the tempestuous decade after 2015 and the present Euro-American (Western) nativist revolt against cross-border connections, and the U.S. strategy of decoupling from China, both of which closely affect the contemporary geopolitics of universities and science. Global multiplicity in agency, culture and identity, especially the rapid rise of China and the longer erosion of the colonial order, plus the neoliberal immiseration of Euro-American populations, have triggered Western pushback against the 1990-2015 phase of globalisation. This pushback has taken form in a shift from normative internationalisation and cosmopolitanism to widespread assertions of singular national identity, nativist resistance to migration that has disrupted cross-border student mobility in many countries, and partial breakdown in relations between the U.S. and China in political economy and in science and technology. In government bordered nation-state identity and strategy are being more sharply asserted and multilateralism is weaker. The U.S. decoupling with China is associated with the reworking of bottom-up global scientific cooperation by techno-nationalism and national security politics, with negative implications for the Humboldtian university practices of university autonomy and academic freedom.