The meanderings of sadness that news of Maryam Mirzakhani’s death brought compelled me to read every article I could find about her, and when I could not find more articles, I started to read the comments of the readers. Many of them wrote that they saw her as “unrelatable and incomprehensible,” given that they were “math challenged.” However, Maryam was the opposite of unrelatable. She reminded us, in words and actions, that mathematical ideas can be understood if one puts enough persistence into the task.

She was not the star of her lectures; the only stars were the mathematical ideas. She spoke calmly and clearly and radiated deep enjoyment of the process.

Maryam had the ability to quickly perceive the appropriate wavelength of her interlocutor and speak accordingly, a rare quality in a mathematician. She listened with attention and was very generous with her time. Behind her kind serenity one could perceive a steely tenacity and a deep well of ideas and, of course, a passion for math and an incessant quest for the fantastic “aha” moment. This moment often took years for her, because she worked on profound questions.

After one of her lectures, we walked together chatting. Suddenly, the voice of a child came from an adjacent room and Maryam exclaimed, “Anahita!” The voice belonged to her daughter. Maryam’s exclamation lit up the room. She sounded totally different than she had during the lecture. Her entire humanity was in the exclamation.

Maryam’s work connected ideas from different areas of mathematics. Part of this work consisted of counting closed curves on surfaces. A mathematical surface is, roughly speaking, the outer layer of a solid object. In topology, surfaces are studied up to the point of deformation — they’re allowed to bend and stretch but not to tear — thus the old joke that a topologist can’t tell a coffee cup from a doughnut. Surfaces can also have holes and edges. In this way, a disk and a cylinder can both be thought of as surfaces.

Closed curves on a surface are like extremely thin rubber bands wrapping around it. Curves are also studied up to deformation on the surface. For instance, in a cylinder, every closed curve can be deformed into another curve that goes around the cylinder once, twice, three times or more — or no times around at all, which means it can be deformed to a point.

Surfaces can also be studied from a geometric point of view. In this case, a stretchable surface can be “enriched” with a metric, which is a way to measure distances and angles.

Mathematicians call the surface determined by the outer layer of a doughnut a torus. One way to define a metric on a torus consists of imagining that we are minuscule beings living on the variegated surface of the doughnut, where we measure distances and angles. The landscape we see may well change when we move from place to place.