The only people who do not struggle with mathematics are those who don’t use it. All of us who engage with mathematics find it a struggle and the brightest among us struggle the most. This seems contradictory, because in school, the brightest kids seem to learn arithmetic and algebra more easily than the others.
As you study mathematics at the highest levels you get into increasingly intense cognitive demands. In particular, research at the frontiers of mathematics requires an extremely high level of intelligence where neural efficiency, short term memory, and pattern recognition come into play–qualities possessed by only the small number of gifted people. But even at these levels, the greatest minds struggle with mathematics because it requires, in addition to these special neural qualities, a prolonged focus on the abstract thought.
John von Neumann, one of the intellectual giants of the 20th century, once asserted to a struggling student, “Young man, in mathematics, you don’t understand things, you just get used to them.” Einstein, whose field equation was described as “one of the greatest achievements of human thought” admitted to a struggling student, “Do not worry about your difficulties in mathematics. I can assure you mine are still greater.” When attempting to express his field equations in terms of tensors, Einstein had to seek help from a former classmate Marcel Grossmann.
Deductive reasoning has empowered us to model our universe with mathematical equations, enabling us to understand and predict natural phenomena, build complex structures, construct computers, and harness nuclear energy. However, deep, deductive reasoning requires great effort and concentration. It also exerts a heavy load on short-term memory and demands full attention with single-minded focus. Great mathematicians like Henri Poincaré and G. H. Hardy explained that they attempted no more than four hours a day of intense work. After that time, staying focused becomes increasingly difficult. We do not yet know why deductive reasoning is so cognitively demanding though some neurologists suggest it may be connected to the depletion of glucose in the brain.
Claude Messier, of the University of Ottawa in an interview in Scientific American, conjectured, “My general hypothesis is that the brain is a lazy bum. The brain has a hard time staying focused on just one thing for too long.” Consequently, we are reluctant to engage in prolonged deductive thinking unless it’s absolutely necessary. A less graphic description is provided by researcher Daniel Dennett:
The rational mind is a serial virtual machine implemented–inefficiently–on the parallel hardware that evolution has provided for us.
Psychologist, Joseph Heath amplifies this idea:
The key word here is inefficient. The mind simply didn’t evolve to support the sort of linear, explicit processing that is the hallmark of rational thought … thus the way your brain feels after writing an exam is like the way your back feels after a long day spent lifting boxes–Neither was designed for the task that it is being asked to perform.
Advanced mathematics requires substantial short-term memory, enabling you to keep many things in your conscious mind at the same time. It requires a prolonged focus, and abstract thought that draws heavily on your brain’s precious supply of glucose. So, if you struggle with mathematics, you are not alone, and your unrelenting persistence will have long-term benefits. You may find that concepts that seemed difficult at first will eventually incubate in your subconscious and you will later look back, wondering why that concept had once seemed difficult.
