Combinatorics

In this appendix, I provide brief biographical sketches of the mathematicians whose names have arisen in this book.

Numerous mathematicians, with a wide diversity of backgrounds and identities, work in the field of combinatorics. Some (including many of those from the most marginalised backgrounds) have focused their attention on math education, generally providing significant support and inspiration to students. One example of this is that a number of the first Black people (and particularly the first Black women) to receive PhDs in mathematics in North America, went on to teach at Historically Black Colleges. Typically they would have heavy teaching loads, and little if anything in the way of research expectations. Some focus on writing books, or popular articles of mathematics, or on mathematical outreach to children. Such people may have a huge influence on the field, but are not often actively involved in research, so do not make discoveries or prove results that fit easily into a book such as this. Indigenous mathematicians likewise feel heavy pressures to teach, mentor, and serve their communities, that often limit the time they have for research.

It is important to acknowledge that underrepresentation is not accidental, and that systemic barriers as well as overt discrimination, harassment, and bullying have all contributed to it. Mathematicians continue to grapple with these issues.

Without leaving out anyone whose work seemed important to understanding the key topics of this book, I have tried to include results by people with diverse backgrounds and identities. It is often not apparent from someone's name whether or not they come from an underrepresented population, so I hope to make you aware of some of these mathematicians' identities through these sketches. There are likely to be other aspects to their identities that I remain unaware of. I hope that you may find some of these people relatable, and possibly inspirational.

Perhaps even more than mathematicians in other fields of research, combinatorists like to collaborate. We enjoy working together, and encourage our students to develop research skills through collaborations also. This has been a broader change to mathematical culture over time: mathematicians used to be much rarer and more isolated, so worked on their own a lot more than they typically do now. Particularly in the very recent context, it's therefore usual for someone's most significant piece of work to have been written in conjunction with others. This means that finding a theorem or object that has been named after a woman, for example, is challenging: her best work may have been completed with other researchers, and will bear their names as well. Please don't take this as a sign that women (or other underrepresented groups) haven't made important contributions!

Names are listed in alphabetical order, but this comes with some caveats. Following the style guides I found, medieval Arabic names are alphabetised under the first name. When the indefinite article “Al-” is part of the first name, it is ignored in the alphabetising. Chinese names have been alphabetised by the family name. The order in which Chinese family names and given names are used has varied over time and through contexts, so is not consistent in this book. The medieval Zhu Shijie is referred to as such (his family name is Zhu); the modern Ming-Yao Xu publishes (when he writes in English) with his name in this order (his family name is Xu).

I have endeavoured to contact all of the living mathematicians included below, for approval and confirmation of the information I am including. Many of them responded very helpfully, for which I am extremely grateful. If you believe that something is inaccurate or should not be included, please do not hesitate to contact me so we can sort this out. Any errors are my own.

I am deeply indebted to Laci Babai who carefully read many of these sketches. Laci provided a great deal of clarification and additional information, and even provided suggestions for beautiful and carefully-constructed wording that I have adopted gratefully. To avoid filling the sketches with quotation marks and repeated references to Laci, this general acknowledgment stands in lieu of specific attribution for the many phrases and even paragraphs that he generously offered. In particular, without his knowledge of the Hungarian context and of the numerous Hungarian mathematicians listed below (most if not all of whom he knows or has known), these sketches would contain numerous misunderstandings and inaccuracies.