Scientific life in lower-and-middle-income countries presents a number of unique challenges for the professors, postdocs, and students living and working in them, most of which have to do with isolation, high travel expenses and conference registration fees, and limited access to research funding. While naturally not all of the problems which researchers in lower-and-middle-income countries face can be solved by researchers working in countries with a more robust scientific infrastructure, there are nonetheless many things which may be done, both individually and institutionally, which can help to mitigate these problems and create a more inclusive, equitable, and integrated mathematical world. I have included a number of concrete suggestions in the following list, roughly in order of my view of their importance.
Referee papers from mathematicians working in developing countries, even - or especially - if you don't know the authors and/or any of the authors' institutional affiliations.
Refereeing papers from mathematicians in developing countries is one of the most important things one can do to support mathematics in lower-and-middle-income countries, and it doesn't involve travel or grant money! Please consider dedicating a percentage of your refereeing time to papers with authors based in the developing world.
(For journal editors) Ensure that there is an "online first" publication option which assigns a DOI to all articles and publishes them online very shortly after they're accepted. (And for online-only publications, make sure that all articles are assigned DOIs.)
In many developed countries, from the moment a paper is accepted, it may be counted towards hiring, tenure, and promotion decisions. Unfortunately, this is not true in many developing countries, where an online publication (with a DOI) is often the minimum necessary for the publication to be counted in a professional evaluation. Waiting several years between acceptance and publication, which is common for mathematics journals, including many prestigious ones, is simply not an option for many scientists working in developing countries, especially younger scientists, and if a journal does have such a long backlog and no "online first" publication, it becomes impractical for us to submit articles there. Similarly, a publication in an online journal, no matter how prestigious, which does not assign DOIs to their articles may not count as a publication in some countries' scientific evaluations (like in Mexico) simply because of the lack of a DOI. If you are on the editorial board of a journal, please make sure the journal assigns DOIs to all of its articles and that the articles are published online with this DOI as soon as possible after acceptance.
(Mainly for computer scientists and applied mathematicians) De-emphasize the importance of conference proceedings, and encourage and emphasize publication in journals.
There are many, many reasons to do this - less frenetic, higher quality reviewing, resulting in higher-quality papers, being a big one - but the one which affects researchers in developing countries most acutely is that we simply don't have the funding to pay for an author to pay for the registration fees and/or physically travel to a conference every time we want to have a paper published in a prestigious venue. Requiring attendance at a conference as a prerequisite for publication in a 'high-impact' proceedings has the de-facto effect of devaluing a lot of good work which gets done in places where we can't afford to "pay to play", as well as sidelining the people who do it. To make matters worse, computer science and applied math conferences which do offer virtual presentation options often have registration fees which are themselves prohibitively expensive.
Collaborate with researchers in developing countries.
Expanding one's collaboration network to include faculty in developing countries is another one of the best ways a researcher from a developed country can participate in the development of science in the the developing world, but it often takes a conscious decision to seek it out (and perhaps some failed attempts) before it happens.
Cite authors in developing countries.
Publication metrics are often given an importance in developing countries which is much greater even than it is in the developed world, typically in an (overzealous) attempt to make evaluation of researchers "objective", and these metrics can very directly affect hiring, promotion, and salary decisions, so citation counts (unfortunately) really matter. Also, citing papers with authors in the developing world helps to let their colleagues know that their work is noticed abroad, which can be important for one's general professional development at home. Of course, one has an ethical obligation to cite the papers whose techniques one uses directly, but there is somewhat more flexibility in the literature review or discussion sections of articles. When in doubt, aim to be inclusive in one's citations. Similarly, if you're visiting an institution in a developing country to give a talk, it's nice to mention it if someone at that institution or in that country has work in the same or a related topic. You can't assume that an author's colleagues have any idea what they do or that they know whether it's interesting or important to people elsewhere, even when those colleagues and the author are at the same institution, and a brief comment in a talk from a visitor can help to communicate this.
Visit and give talks and workshops at institutions in developing countries,
Invite mathematicians from developing countries to give talks in seminars and events that you organize (and help with their travel expenses),
Organize events in developing countries,
It's much cheaper for us to go to an event nearby than to attend one far away, and this also helps to avoid problems with visas. Local expenses for the conferences are also typically a fraction of what they would be in the US, Canada, or Europe, which additionally helps funding for organizing the conference go farther.
Include hybrid options in the events that you organize,
Reduce event registration fees for professors, postdocs, and students based in developing countries,
Include mathematicians from developing countries to participate as co-Principal Investigators in grants,
Hire post-docs who obtained their degrees in institutions in developing countries,
Offer salary and lodging support for sabbaticals for mathematicians based in developing countries who would like to spend a semester or year at your institution,
The structure of salary support for sabbaticals in the US and elsewhere is typically that the base institution will cover a percentage of a professor's base salary, and that the host institution will cover another percentage. This is fine if you're a professor in the US visiting another institution in the US, but if your base salary is more typical of those in developing countries (in Mexico, for instance, the range is roughly between about 1/7 to 1/3 of a typical US professor salary, and Mexico is in good shape compared to many countries in Latin America), this arrangement makes it difficult or impossible to do sabbaticals in countries in the developed world. If direct salary support is impossible for some reason, try to at least offer support for lodging, health insurance, and a per diem.
If you are an editor of a journal with a pay-for-open-access option, make sure there are (significantly) reduced rates and/or fee wavers for authors based in developing countries,
Co-advise students studying in developing countries,
Recruit and accept students with undergraduate or Master's degrees from institutions in developing countries into doctoral programs,
This is more subtle and difficult than it first appears. Different countries have different grading systems, most countries have less grade inflation than the US and Canada, and there are vast differences between countries in what is considered a "good" recommendation letter, so it's not always easy - and often very difficult - to make fair comparisons between students from a country whose educational system is unfamiliar and one from your home country. Also, application fees can be prohibitive for students from developing countries and their families, and taking the GRE can involve an expensive trip to a testing center in some other city, and sending the results involves increased costs which increases the burden on students and their families. Increasing the number of acceptances in a systematic way typically requires a decision to recruit from certain places, and then to familiarize oneself with the grading and evaluation practices there, so that fair comparisons are more likely to be made. Reduced application fees would also be helpful.
Donate to organizations - such as the International Mathematical Union (IMU), the Unión Matemática de América Latina y el Caribe (UMALCA), and the African Mathematical Union (AMU) - which support mathematics in developing countries,
Lobby to get your local mathematical professional society (such as the AMS, LMS, or EMS) to support events in developing countries and fund mathematicians to travel between their institution and yours,
The LMS and EMS both have programs in Africa. I would love to see more, but it's a great start. The AMS has nothing comparable, although they do help support some of the large, regional meetings, such as the Mathematical Congress of the Americas, of which there isn't anything comparable in Europe.
Become involved in the governance and administration of organizations such as the IMU, UMALCA, or AMU, which support mathematicians in developing countries.