I was at a conference in Germany where Faugère presented his work. The room was stunned, but didn't understand. Hendrik Lenstra asked me to spend several days with Faugère, then give an expository talk. My marching orders: Assume nothing: groups, rings, fields.

I ended up lecturing on Gröbner Bases and Faugère's algorithm to an audience that included Buchberger and Faugère. Faugère appreciated my efforts. Buchberger was like a shook up soda bottle; he made a twenty minute speech during the question period.

I coauthored the computer algebra system Macaulay, that first introduced Gröbner Bases to algebraic geometry, opening up the field to applications. At the time there was a separate community in France studying "standard bases", from which I learned a lot. Their focus was on power series not polynomials, but the translation is easy.

Algebraic geometry is a great subject, and computerizing it was a noble cause, but it thrust me into a backwater where the difference between polynomials and power series is considering significant. I got out.