We are literally up to our ears in magnets: the headphones many of us wear are coil-driven ferromagnets. The first electric generators (dynamos) were also based on permanent magnets, and we attach postcards to our refrigerators with magnets.  But what are the simplest conditions under which magnetism can occur? Surprisingly, the answer to this basic conceptual question is still under debate. Magnetism arises in strongly interacting systems of fermions, which are notoriously difficult to simulate numerically. Approximate pictures [1,2] developed eighty years ago proposed that strong interactions may be sufficient, but exact calculations show these models to fail in one-dimensional systems, for instance [3]. Nature provides us with crystalline materials (such as nickel and iron) that are "itinerant" ferromagnets, but is the crystal an essential ingredient? We will review some of the history of this question, and discuss how ultra-cold atoms might  weigh in on the debate [4]. We then present strong evidence that magnetism emerges in a strongly interacting ultra-cold gas [5].

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[2] E. Stoner, Philos. Mag. 15 , 1018 (1933).
[3] E. Lieb, D. Mattis, Phys. Rev. 125 , 164 (1962).
[4] L. J. LeBlanc, J. H. Thywissen, A. Burkov, and A. Paramekanti, Phys. Rev. A 80 , 013607 (2009).
[5] G-B Jo, Y-R Lee, J-H Choi, C. A. Christensen, T. H. Kim, J. H. Thywissen, D. E. Pritchard, and W. Ketterle, Science 325 , 1521 (2009).