Princeton University;

DIMACS (Center for Discrete Mathematics & Theoretical Computer Science), Rutgers University; and

University of Colorado at Colorado Springs

*“This quarterly journal, started by Alexander Soifer at the University of Colorado at Colorado Springs, specializes in geometry and combinatorics, but what really distinguishes it from the field is attitude!”*

— Paul Kainen, 1991

*“Dear Alex, Finally got around to reading the October Geombinatorics, which contains more than the usual supply of gems – the bits by Vizing and Alon were worth more than a year’s subscription,if it’s not too crass to put a money value on great mathematics, and why should it be, art is sold for money all the time …”*

— Peter D. Johnson, Dec. 18, 1995

**1. CONCEPTION**

In the spring of 1990 I formulated some problems and conjectures in Euclidean Ramsey Theory, and I wanted to share them with a few colleagues, at least with Paul Erdös, Ron Graham and Branko Grünbaum. How would one do this? Writing several long mathematical letters, but this would take months! Sending Xerox copies, but this would seem to be so impersonal, that I do not know why anyone would read them, let alone think them! :) And so one day in June of 1990 I called Branko Grünbaum and proposed a solution to this dilemma:

– What do you think about publishing a small lively journal devoted entirely to problem posing essays, work in progress, so that instead of a half a dozen letters to colleagues we would write just one essay?

– There are problem sections in many journals, but I do not know a journal completely devoted to open problems. Did you have in mind any limitations?

– How about geometry of combinatorial flavor, Geombinatorics?

– A good idea; let us try it.

– But I will need your essays – in every issue.

– OK, I’ll try.

Now you know “the rest of the story” of the conception of Geombinatorics, which was born a year later, in June 1991, when its first issue came out. It was tiny, and contained just two essays – by Branko and I. But the volume doubled in the second issue, when Paul Erdös and John Isbell joined the two of us. And then it took off.

So what is Geombinatorics? What sets it apart from other journals?

**2. LIVE MATHEMATICS**

Academic journals remind me old cemeteries. They publish (bury?), with a great deal of respect, completed research, solved problems. Moreover, the publications appear a couple or more years after research was completed. By then the results ought to be of not much interest not only to the readers but even to their own authors: years passed, and an active mathematician would likely be working on something else!

Geombinatorics is, perhaps, the only publication entirely dedicated to research in progress. This is a place to enjoy live mathematics!

In a sense, it is a white conspiracy of a relatively small number of active subscribers throughout the world, with an explicit goal of doing geometric combinatorics and sharing with each other their new problems, ideas, their work in progress when it still interests them – and therefore may inspire others.

And once an issue of the journal is out, it is picked up and further disseminated to hundreds of thousands of other mathematicians by Mathematical Reviews, Zentralblatt für Mathematik, and Mathematics Abstracts.

**3. INCLUSIVENESS & ACCESSIBILITY**

Essays in Geombinatorics are written to be read, read by a broad spectrum of active mathematicians, from bright high school and undergraduate college students to research mathematicians. Problems we publish have classical clarity. Indeed, anyone could understand our problems – the trick is to solve them :-). Essays are expected to present the history of the problem, partial results, author’s conjectures, and bibliography.

There is a popular belief that young students have to be kept away from starting to work on open problems. We reject this discrimination based on young age and provide young readers with a place where they can take off and sail into their own research. In fact, the doctoral thesis of Paul O’Donnell from Rutgers University grew out of a few of his early essays on chromatic number of the plane, all of which appeared on the pages of Geombinatorics. Paul O’Donnell’s last essay [1] that appeared in the year 2000, solved an old and well known problem posed in 1976 by Paul Erdös about existence of arbitrarily large girth 4-chromatic unit distance graphs. They exist, Paul proved!

We do have young subscribers. Moreover, we have high school and undergraduate authors. The high school student from Vermont Thomas Pietraho said it best (letter of August 29, 1991):

“Although I have not solved any of the problems (not yet, that is), I know that I’ll gain a lot from items such as these… And if the Muses grant me their aid, I’ll be more than swift to send you my solutions.”

**4. COMBINATORIAL AND DISCRETE GEOMETRY**

A small publication cannot cover the breadth of today’s mathematics. Thus, Geombinatorics from its inception has focused on Combinatorial and Discrete Geometry and related areas. We encourage mathematicians in other areas to start similar lively publications.

But we do not build fences and do not seat on them either. Geombinatorics has published (my) historical research on P. J. H. Baudet, Van der Waerden and Isai Schur, as well as reminiscences about Paul Erdös and Branko Grünbaum by their many collaborators and colleagues.

In some instances we are even ready to come to the rescue of folks in other creative endeavors. When the acclaimed Russian poet Evgeny Evtushenko complained during his talk at Colorado College that nobody was willing to publish his latest controversial poem, I offered him pages of Geombinatorics!

**5. EPILOGUE**

We have a web page:

https://www.geombina.uccs.edu/

It includes Contents of every issue for the first 12 years, Authors’ Index, and the Editorial Board. Prospective authors can find there Submission Rules and Copyright Form.

The success of Geombinatorics is due to many colleagues from all over the world who have for ten years contributed their thoughts and their aspirations to this quarterly. Some maturity manifested itself when Mathematical Reviews and Zentralblatt für Mathematik came on board and pronounced Geombinatorics to be their “publication of high density” (which meant that all Geombinatorics articles in their final form would be reviewed).

— Paul Erdös in Colorado Springs

Problem posing style of Geombinatorics has very much been inspired by Paul Erdös’s 20+ problem-posing articles and his countless problem-posing talks. Paul served as an Editor of Geombinatorics. Moreover, he cared about our journal: he contributed 15 essays to the 21 issues of “Geombinatorics” that appeared during his life.