What are the candidate notions, hardest to comprehend in Math?

Posted by: adonis49 on: July 6, 2022

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What is the hardest thing to understand about math?

Tony Berard, Jan 11, 2022

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.

Fractions.

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 theorems 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 book Points, Lines, and Conic Sections: A Sequel to College Algebra ($15 on Amazon).

These conic section formulas are easier to prove than say Fermat’s Last Theorem (proved by Wiles).

But, my book is much more accessible than Wiles paper as a result.

Proving pi is transcendental and is hard to comprehend.

Proving there are infinitely many primes is not hard by today’s standards.

We want proofs for a number of open questions (since they are open, that automatically makes them hard).

Does P=NP? HOTPO.

The Millennium Problems.

There are many others. This is one list of many possible.

Addendum: Back in Euclid’s day, they had a problem called the Bridge of Asses. They named it that way because the diagram looked like a bridge. Where did the asses part come in? The asses were the students who were incapable of understanding the problem.

This was the problem where Euclid knew the student would not make further progress.

If a student could not get passed the Bridge of Asses problem, he was done and left the discipline.

So, The Bridge of Asses problem was the hardest problem for many a student back in Euclid’s day.

Hopefully, there’s no Bridge of Asses problem in my math book Points, Lines, and Conic Sections. If you want to get world class algebra skills, get my book!!