What is the hardest thing to understand about math?

by Tony Berard

The cover of my wonderful math book. Link at end of article.

I originally answered this question on Quora on: Answered Jan 27, 2018

Originally Answered: What is the most difficult concept to understand in Mathematics?

This answer varies greatly because math has so many levels. So, I will say a few candidates.

• Fractions. Yeah, these are low level objects in math, but adults who have to understand these things, they have to be the most abundant problem in math.
• i. This is the imaginary unit.
• 0/0. In calculus, this is called an indeterminate form, and when it arises, we ask students to determine it (yes, determine the indeterminate).
• Differential Equations. This is a whole discipline in mathematics, and there are a number of differential equations that have achieved fame in mathematics.
• Paradox. A number of paradoxes come up in a math student’s learning, such as Zeno’s Paradox or Russel’s Paradox. Each one has to be understood for the student to progress.
• Proof. This is the ultimate in mathematics. Many things have been proven, and once proven, it cannot be undone (which is why it is so rigorous and difficult). Some proofs are easier than others. I have a number of proofs I made in the conics in my…