The self-chosen remit of my blog is “Updates on my research and expository papers, discussion of open problems, and other maths-related topics”.  Of the 774 posts on this blog, I estimate that about 99% of the posts indeed relate to mathematics, mathematicians, or the administration of this mathematical blog, and only about 1% are not related to mathematics or the community of mathematicians in any significant fashion.

This is not one of the 1%.

Mathematical research is clearly an international activity.  But actually a stronger claim is true: mathematical research is a transnational activity, in that the specific nationality of individual members of a research team or research community are (or should be) of no appreciable significance for the purpose of advancing mathematics.  For instance, even during the height of the Cold War, there was no movement in (say) the United States to boycott Soviet mathematicians or theorems, or to only use results from Western literature (though the latter did sometimes happen by default, due to the limited avenues of information exchange between East and West, and former did occasionally occur for political reasons, most notably with the Soviet Union preventing Gregory Margulis from traveling to receive his Fields Medal in 1978 EDIT: and also Sergei Novikov in 1970).    The national origin of even the most fundamental components of mathematics, whether it be the geometry (γεωμετρία) of the ancient Greeks, the algebra (الجبر) of the Islamic world, or the Hindu-Arabic numerals $0,1,\dots,9$, are primarily of historical interest, and have only a negligible impact on the worldwide adoption of these mathematical tools. While it is true that individual mathematicians or research teams sometimes compete with each other to be the first to solve some desired problem, and that a citizen could take pride in the mathematical achievements of researchers from their country, one did not see any significant state-sponsored “space races” in which it was deemed in the national interest that a particular result ought to be proven by “our” mathematicians and not “theirs”.   Mathematical research ability is highly non-fungible, and the value added by foreign students and faculty to a mathematics department cannot be completely replaced by an equivalent amount of domestic students and faculty, no matter how large and well educated the country (though a state can certainly work at the margins to encourage and support more domestic mathematicians).  It is no coincidence that all of the top mathematics department worldwide actively recruit the best mathematicians regardless of national origin, and often retain immigration counsel to assist with situations in which these mathematicians come from a country that is currently politically disfavoured by their own.

Of course, mathematicians cannot ignore the political realities of the modern international order altogether.  Anyone who has organised an international conference or program knows that there will inevitably be visa issues to resolve because the host country makes it particularly difficult for certain nationals to attend the event.  I myself, like many other academics working long-term in the United States, have certainly experienced my own share of immigration bureaucracy, starting with various glitches in the renewal or application of my J-1 and O-1 visas, then to the lengthy vetting process for acquiring permanent residency (or “green card”) status, and finally to becoming naturalised as a US citizen (retaining dual citizenship with Australia).  Nevertheless, while the process could be slow and frustrating, there was at least an order to it.  The rules of the game were complicated, but were known in advance, and did not abruptly change in the middle of playing it (save in truly exceptional situations, such as the days after the September 11 terrorist attacks).  One just had to study the relevant visa regulations (or hire an immigration lawyer to do so), fill out the paperwork and submit to the relevant background checks, and remain in good standing until the application was approved in order to study, work, or participate in a mathematical activity held in another country.  On rare occasion, some senior university administrator may have had to contact a high-ranking government official to approve some particularly complicated application, but for the most part one could work through normal channels in order to ensure for instance that the majority of participants of a conference could actually be physically present at that conference, or that an excellent mathematician hired by unanimous consent by a mathematics department could in fact legally work in that department.

With the recent and highly publicised executive order on immigration, many of these fundamental assumptions have been seriously damaged, if not destroyed altogether.  Even if the order was withdrawn immediately, there is no longer an assurance, even for nationals not initially impacted by that order, that some similar abrupt and major change in the rules for entry to the United States could not occur, for instance for a visitor who has already gone through the lengthy visa application process and background checks, secured the appropriate visa, and is already in flight to the country.  This is already affecting upcoming or ongoing mathematical conferences or programs in the US, with many international speakers (including those from countries not directly affected by the order) now cancelling their visit, either in protest or in concern about their ability to freely enter and leave the country.  Even some conferences outside the US are affected, as some mathematicians currently in the US with a valid visa or even permanent residency are uncertain if they could ever return back to their place of work if they left the country to attend a meeting.  In the slightly longer term, it is likely that the ability of elite US institutions to attract the best students and faculty will be seriously impacted.  Again, the losses would be strongest regarding candidates that were nationals of the countries affected by the current executive order, but I fear that many other mathematicians from other countries would now be much more concerned about entering and living in the US than they would have previously.

It is still possible for this sort of long-term damage to the mathematical community (both within the US and abroad) to be reversed or at least contained, but at present there is a real risk of the damage becoming permanent.  To prevent this, it seems insufficient for me for the current order to be rescinded, as desirable as that would be; some further legislative or judicial action would be needed to begin restoring enough trust in the stability of the US immigration and visa system that the international travel that is so necessary to modern mathematical research becomes “just” a bureaucratic headache again.

Of course, the impact of this executive order is far, far broader than just its effect on mathematicians and mathematical research.  But there are countless other venues on the internet and elsewhere to discuss these other aspects (or politics in general).  (For instance, discussion of the qualifications, or lack thereof, of the current US president can be carried out at this previous post.) I would therefore like to open this post to readers to discuss the effects or potential effects of this order on the mathematical community; I particularly encourage mathematicians who have been personally affected by this order to share their experiences.  As per the rules of the blog, I request that “the discussions are kept constructive, polite, and at least tangentially relevant to the topic at hand”.