Two events in my life significantly influenced my career choice.
Since I dutifully complied with all that was expected of me, I was generally regarded as a good student. I did well in mathematics in first year algebra because I could follow rules, but found them very rigid, and I resented the fact that we were penalized if we attempted to reach a result by some different approach. Originality or creativity were strongly discouraged.
In my sophomore year, however, something new and very exciting happened. We started studying Euclidean geometry. Here, we had a set of axioms -- self-evident truths -- and based on these, and some hypotheses, we were able to establish a variety of fascinating theorems. It was all reasonable and logical, and no one was requiring that I follow some rules I didn't understand. I loved the subject and tried to obtain results beyond those assigned.
One day, we came to a theorem for which an indirect proof was given. I wondered why we couldn't prove the result directly, tried to do so, and found a proof that worked, except when the geometric figures involved were positioned in a certain way. I decided that I had found the reason for the indirect proof and didn't feel a need to raise the question further.
Some time later, we had a similar problem involving the same geometric figures, where, again, an indirect proof was given. This time, the teacher pointed out that the problem could also be solved directly, and outlined a proof that was essentially the one I had discovered earlier. I then raised the question of the difficulty that arose when the figures were positioned differently. The teacher had an immediate response, ``You have an axiom that states that geometric figures can be moved in space without affecting their properties.'' Incredible! It was an axiom that we had not used and I had forgotten all about it. What a beautiful subject! Everything fell into place so neatly!
I entered college with great uncertainty about a major. I didn't know what I could do with mathematics. About the only career option in that area, as far as I was aware, was school teaching, and I knew I didn't want to be a school teacher -- if for no other reason than the fact that, as a woman, I would not be allowed to marry and remain a teacher -- at least in public schools in my area, and I knew no other.
Physics was suggested to me as a subject with greater career options and a good alternative to mathematics. My select high school, restricted to girls, did not offer physics. In college, however, I enrolled in a freshman physics course to consider it as a possible major.
In one of our early labs, we were to do the standard experiment of scattering iron filings on the lab table, placing a magnet in their midst, and noting how the filings align about each pole. Everyone in the class did the experiment very readily -- everyone, that is, except for me. My iron filings refused to follow the expected pattern, and instead, kept arranging themselves in bizarre formations. One after another of my classmates, realizing what I was experiencing, came over to offer advice, and to watch the strange results. Finally, the entire class, including the instructor, was gathered around, with everyone trying to explain why my iron filings were so uncooperative. One observant girl finally solved the mystery. She pulled out a drawer that was directly under my work space, and, believe it or not, it was full of magnets!
That episode brought to mind my experience in the geometry class. I concluded that, in mathematics, we have control over our assumptions -- if they are poor, our results will not be good, but we know what we are working with; in physics, there may be factors that are completely unknown to us, but can distort our results and unbeknownst to us, make them invalid.
That drawer of magnets determined for me that I loved mathematics and it would be my major, regardless of my need to be practical and to select a field with a greater number of more reasonable career options.
Web editor's note: The title of this section was changed to include the author's middle name.