Most people think that mathematics is perfect, completely rational, no problems, it's all been proven, etc. but it isn't any of those things.
If you go on twitter/social media you will find people posting "Most people can't solve this" math questions
and you really should pay attention to the fact that there are arguments in the comments.
There are arguments because mathematics is not cohesive, and does not have one set of rules.
You first learned x and ÷, then you learned * and /, do you realize the rules for each are different? Or since they have much the same name, do you think they are interchangeable?
In the above picture, you see implied multiplication. And that belongs to the set of * and /. So, why is a ÷ there?
Mathematics should have worked out standardized notation by now. And everyone should be able to work out math problem and come to the same conclusion, but we can't.
And, notation barely makes a blip in what is wrong with mathematics.
Calculus is the class taught just after advanced algebra. WHY??!!!!
There is nothing in calculus that is important to a modern scientist or engineer.
All the formulas that are important have been derived/integrated.
You could say that it is important to know how we derived those, but it really isn't. Especially when Fast Fourier Transforms and Discreet Mathematics are soooooooooo much more useful. Especially when dealing with binary computers.
Calculus should be one of those "optional" courses for math whizzes who want to learn what about math, but everyone is forced through calculus if they get to higher maths. Why?
Because, if they didn't, everyone would see through math, and wad it up and throw it out as the piece of trash it is.
Here is one reason calculus is taught:
In math class, we are taught that these formulas approach zero, but never touch them.
In calculus, they touch them. "As n → ∞" they say, then x → 0 and y → 0.
Why would they spend soooo much time saying it goes asymptotic, meaning it never touches, to turn around and say it touches, because we need to, in order to make the functions work.
If math was logical, it should not be holding two logically opposite views.
With mathematics you can prove 1 = -1.
There are several such formulas and proofs. If mathematics was consistent, logical, fact based, like most people assume, then this should never be the case. But it is. And it is at the core of mathematics where it is broken.
The big problem is how we handle infinity.
We let people get away with all kinds of horror like
∞ + ∞ = ∞
When everyone knows that when you add numbers, (1 + 2 = 3) you get a bigger number. But not with infinity.
And then they try to sweep it under the rug with
∞ ≠ ∞
But, then they talk about ∞ / ∞ = ?
Mathematics needs to define infinity.
It needs to calibrate its number line.
But they don't.
Most of the higher mathematicians just go and accept all the wrongs as just being normal.
In the future math will be very different. Seriously. (and i do not mean things like new math, which the education tzars tried to destroy young people's minds with)
Our number system will be base 12. (because the universe is in base 12. If everything was in dozens, why would you use base 10?)
PI is a rational number. It may even be defined as a whole number.
Math will be much more intuitive. (there is a reason a large group of people do not get math / do not like math)
And we will standardize our notation.
People will look back on our time, upon our mathematics and shake their heads about how incompetent we were.
