To solve the third layer, the speedcuber must assemble all of the yellow squares on the bottom face by applying one of 40 algorithms in a phase called “orientation.” The cuber must instantly recognize which algorithm to apply in order to have any hope of solving it with haste. In the final step, permutation, one of 13 algorithms restores the cube’s chromatic harmony, one color per face.

Image MATH AS METHOD Jessica Fridrichs strategy for quickly solving the Rubiks Cube requires using at least 53 algorithms. Credit... Bina Venkataraman

The world’s fastest speedcubers, including Dr. Fridrich, know more than 100 algorithms to whisk the cube to its solution. They recognize when the puzzle is jumbled or positioned in their palms in a way that one set of moves is quicker than 99 others.

As a teenager, Dr. Fridrich saw a man demonstrating the Rubik’s Cube at a mathematics seminar, and scrambled defiantly through a crowd to touch it. She says it was immediately clear that she was “cube possessed,” her shorthand for people who spend most of their waking hours learning to speed-solve the cube. Even though no cubes were for sale in her country then  the few people who had them bought them in Hungary  she would not be stopped. She picked up Kvant, a Russian math journal that outlined one method of solving the cube, and worked it out on paper.

When she finally got her first cube, left behind by family friends visiting from France, she began to improvise, cubing faster and faster to beat record times from Prague, Hungary and the United States printed in newspapers. By the time the Czech national championship took place in 1982, Dr. Fridrich was one of the fastest speedcubers in the country. She won the championship, solving the cube in less than 23 and a half seconds  a time that would now be laughably long in international competition  going onto place 10th in the first world championship in Budapest.

After earning her master’s degree, she was building mathematical models of rock deformation at a mining institute when she was recruited by a professor from Binghamton who heard about her mastery of the cube and her grades at the Czech Technical University in Prague. After a brief meeting in which she described her cube algorithms, he asked her to apply for the doctoral program in systems sciences. She had no résumé, so she dashed one off on a typewriter just before the professor’s train left the station. A year later, she arrived in Binghamton, where she has lived ever since.

In her research in digital forensics, Dr. Fridrich uses computers to tackle another seemingly intractable puzzle: matching a photograph with the individual camera that took it. Law enforcement agencies plan to use the techniques to track down child pornographers and movie pirates.