Black holes as a mathematical question
Elena Giorgi studies mathematical aspects of general relativity at Columbia University. Her work asks whether mathematical descriptions of black holes remain stable when slightly disturbed. She explains the issue through a pendulum: a balanced position can be a valid mathematical solution yet fall apart under a small disturbance.
How a proof develops
Giorgi describes simplifying a problem until she can make progress, then trying to remove those simplifying assumptions. Removing just one can change the problem enough that the earlier method no longer works. Discussions with advisers and other researchers help with this process; a proof is not presented as a single uninterrupted flash of insight.
Interest alongside doubt
Asked about belonging, she describes continuing doubts about her abilities, rather than a moment when uncertainty ended. Wanting to understand a problem keeps her engaged. Meeting women mathematicians during her doctorate and postdoctoral work helped her imagine doing excellent mathematics while also having other interests and a family life.
One decision at a time
Giorgi wishes younger people felt less pressure to plan an entire career at fifteen. Studying a subject can help reveal what to try next. Her encouragement centres on enjoying problems and wanting to understand them; fitting the appearance or personality of people already in a department is not a requirement in her view.