A Mind for Numbers

In A Mind for Numbers, Barbara Oakley draws from neuroscience, psychology, and her own experience of transforming from a self-described “hopeless math student” to an engineering professor to show how anyone can learn difficult subjects like math and science. She argues that learning isn’t a matter of talent—it’s about understanding how your brain works.

Oakley explains that the brain has two primary modes of thinking: the focused mode and the diffuse mode. The focused mode is active when you’re concentrating intensely on solving a problem—like writing a computer algorithm, balancing a chemical equation, or studying a complex formula. This mode relies on deliberate, logical, and sequential thought, similar to how a flashlight beam illuminates one narrow spot.

The diffuse mode, by contrast, is what happens when you relax your mind—during a walk, a shower, or even while washing dishes. In this mode, the brain connects ideas broadly, linking seemingly unrelated concepts. Oakley compares it to a lantern’s soft, wide light that illuminates the whole room. She points out that many breakthroughs occur in this diffuse mode. For example, mathematician Henri Poincaré solved some of his toughest problems while stepping onto a bus, not sitting at his desk. Similarly, Einstein credited his habit of daydreaming and violin playing with sparking his creative physics insights.

Oakley emphasizes that true learning requires a balance between both modes. If you stay too long in focused mode, your brain becomes mentally rigid, making it harder to see creative solutions. But if you never enter focused mode, your learning remains shallow. She recommends alternating between the two deliberately using techniques like the Pomodoro Technique—25 minutes of intense focus followed by a 5-minute break. This rhythm allows the brain to rest and form new neural connections during the breaks, which is when much of the actual learning happens.

Building Knowledge Through Chunking

A key idea in Oakley’s framework is chunking, the process of grouping bits of information into larger, more meaningful “chunks” that your brain can recall and use efficiently. She explains that this process mirrors how experts think. A beginner chess player, for example, sees individual pieces on a board, but a grandmaster instantly recognizes patterns of play—these are cognitive chunks.

Oakley provides several examples of chunking in practice:

• A musician no longer reads each note individually but sees phrases and patterns of rhythm.

• A programmer doesn’t memorize each line of code but recognizes entire structures such as loops and conditionals.

• A math student learns to identify types of equations and recall the appropriate solution method without starting from scratch each time.

To build strong chunks, Oakley outlines a four-step process: