Ben Brumfield --- CNN
(CNN) -- For the first time in history, a woman has received the highest honor in mathematics, often nicknamed the Nobel Prize of mathematics.
Since it was established in 1936, the Fields Medal had gone only to men, until Wednesday, when Maryam Mirzakhani received it in Seoul, South Korea, from the International Mathematical Union.
"This is a great honor. I will be happy if it encourages young female scientists and mathematicians," Mirzakhani said, according to a statement from Stanford University, where she is a professor.
For those of us less versed in the uppermost echelons of mathematics and geometry than Mirzakhani, it's mind-twisting to understand the abstract accomplishments that got her field's highest recognition.
Mirzakhani has delved into the depths of geometry, helping bring unexpected order to an area that many of her colleagues considered chaotic and hardly tamable. And her peers have found this very exciting.
The International Mathematical Union called her long list of accomplishments in Reimann surfaces and moduli spaces "stunning."
What are those?
Simply put, those are complex geometric forms.
Anyone who has had high school algebra and geometry may remember that shapes like squares, triangles, circles and spheres are described by mathematical formulas.
But jump to more complex, roundish, theoretical objects, like perfectly formed doughnuts, ultra-warped, crisscrossed potato chips, undulating geometric pretzels or uneven blobs like amoebas.
That's getting close to the kind of math and geometry Mirzakhani works with. Go deeper, and things can appear to descend into infinite chaos.
Find that intimidating? Some bright mathematical minds do, too.
"Because of its complexities and inhomogeneity, moduli space has often seemed impossible to work on directly," the International Mathematical Union said. "But not to Mirzakhani."
But even she finds those theoretical depths challenging.
"It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out," she said.