Kathy O'Hara's constructive proof of the unimodality of the Gaussian polynomials

The best way to learn a topic is by teaching it. Similarly, the best way to understand a new proof is by writing an expository paper about it. This was the original motivation of the present paper. Once written, I thought that it would be nice if all the readers of this Monthly had the opportunity to savor this elegant proof. All the central ideas and constructions are O’Hara’s, but I have made a few minor improvements and shortcuts that I believe to make the argument clearer. I would like to thank Kathy O’Hara for stimulating conversations and correspondence.