## Christian Gromoll / Mathematics

*“Bee School: What every honey bee learns in math class”*

SUMMARY

My idea is to interact with a small group of students by teaching them the mathematics of honey bee behavior through a weekly seminar on Grounds, and teaching them some practical aspects of bee keeping in my bee yard at my home.

INTRODUCTION

As a mathematician, I’m fascinated by honey bees. I keep several honey bee colonies so that I can watch as they overcome daunting challenges to survival: the acquisition, defense, and allocation of a number of different resources to enable successful overwintering and reproduction. Solving these problems requires sophisticated decision making, akin to the logic needed to run a manufacturing firm. How do bees do it? Their tiny brains are much too simple to understand the geometry of their honeycombs, or the correct allocation of foragers to blossom patches of varying quality. The answer is that each bee follows a simple set of rules, making certain basic decisions based on basic inputs. The aggregate effect of these decisions creates an emergent intelligence for the colony as a whole, able to react to a dynamic environment and achieve complex optimizations.

The mathematics of this emergent intelligence is amazing. I often use examples of honey bee behavior in my math classes, to illustrate certain applications of probability theory. Students love this, and usually draw the class off on a tangent with their follow-up questions about bees. The recent public awareness of honey bees is definitely reflected in our student body. I have always wanted to explore honey bee mathematics in more depth with a group of students, but have never had the right venue. I’m very excited to be among this year’s Mead Honored Faculty, which is the perfect opportunity to pursue this idea.

ACTIVITIES

The plan is for a small group of students to learn about the mathematics of honey bees. We’ll organize as a weekly seminar, reading papers from the scientific literature, and doing some mathematical modeling of bee behavior. Along the way, I’ll teach the students about bee keeping. The students will get plenty of face-to-face time with both me and the bees. We’ll have regular visits to my home to go out to the bee yard and work with the bees. In the Spring, we’ll start a new colony for the group. I’ll kick off the seminar in the Fall with a breakfast at my home, and conclude it in Spring with a dinner – both meals featuring honey, of course. I also plan to have a field trip in early Spring, to a larger apiary in the region.

SELECTION

In keeping with the small size of Professor Mead’s famous seminars, and to

keep the hands-on aspects of the seminar manageable, I’d like to select a small group of students, probably six, for this seminar. I hope to get a diverse group, a mathematician, a biologist, a computer scientist, etc. I’ll seek help from several colleagues in advertising the opportunity to students.

BUDGET

I’ll need veils and gloves for the students, as well as a bee hive, bees, and some miscellaneous items to start the group colony. $1500 will cover this. $500 for the two meals at my home, plus $500 to arrange the field trip yields a budget of $2500.

THANKS

I am delighted to be included in this year’s activities of the Mead Endowment, and would be honored to have my dream idea funded.