A differential equation really tells me that reality can be examined by as many factors with as many changes over as many dimensions as imaginable.
And that orthogonality, tangency, surface area, and volume are basic orienting points, along with rates of change, and that I can transfer this data into a set that is much like a map.
However, it tells me only of concept and not the world, or only basic geometry of the world.
It tells me a lot about space and the symbols and numbers that represent such concepts.
Yet language tells me of my mind, and this math only points out that any change, volume, space, or objects in a dream can be seen with numbers and symbols - that spaces can be exact.
Which may say something about the future, but it can never tell me of the afterlife.
And that spirit/soul even in my materialistic theory means very little when confronted with a new universe.
If I go to another universe, universe B, from this universe A, then even with the transposing of *** and evil into companionship and innocence, in my understanding, these two changes would make the rest of the universe differ greatly.
Thus, the thought of the afterlife will always empty my mind of this universe, leaving me with no real full knowledge of life as I have yet to even use my senses in the next one.
I then always return humble while the atheist considers this universe to be eternal already, without prediction to experience anything greater than its synchronicities.
I have to give them a hand as I imagine this universe overfills them and are forced to deny the spirit rising beyond our cosmos, but rather affirm the spirit that is the totality of this one.
It sets no stage for memories, unfinished karmas, or meeting with the peoples of history.
Therefore, it places a great significance on today, a great significance on love that exists now, and a great significance on the works our forefathers left us.
I would say that this is superior for creating a sense of progress, a sentimentality for others, and a need to experience an openness with all this universe.
Above all else to check off everything on my bucket list.

Truth is a limit that is approached from any direction.
The only 3D limit would be a mirrored limit where every direction I would turn would be the mirrored limit.
This can only be found in belief, for belief always tends to the belief unless another belief is mirrored.
Therefore, the diversity of belief is more about keeping a limit than keeping the expansive idea (belief) that sets the limit.

I'm always riding on knowledge or wondering why I really need it, why I should acquire it.
I repent for questioning why I need it.
Then I rebel in questioning why I need it.
Learning a lot of math without doing problems is like receiving a lot of instructions before trying to carry them all out.
In this sense inventing new math is the same condition as creating a company.
But the question remains: what service can I provide that current math cannot provide?
In my search, it borders on believing a formula can actually solve something without observing it in reality.
This would create a break between the real world and the world of the mind - the mind taking precidence.
Math here would become a novelty much like so many services today.
The mind without the universe is a novelty.
It would see the parts of the universe that were not seen as novel, now become novel themselves.
It would have to entice people to use this novelty, either in thought, word, or practice.
Therefore inventing math is just like salesmanship.
What can I sell the (parts of) universe off to you as?
Life revolves around water, food, clothing, shelter, and some type of computer.
But the universe centers on matter, light, and space.
Chemistry and quantum physics tells me of matter.
Electrodynamics tells me of light.
General relativity and the positive Grassmannian tells me of space.
To out sell these five monopolies I would have to come up with something great.
It is due to mathematicians' and scientists' observations that these monopolies are so powerful.
So much has been observed that it's hard to observe anything apart from them, or to even put them out of my mind.
Let's say I had gone through all the pedagogy, would I just become more satisfied with what already is, just as I've abandoned inventions of electronics after getting the degree and three years of self-study?
Now formally believing that electronics is too complicated to entertain a "new electrodynamics".
"New electrodynamics" becoming a watchword for the novice.
Wouldn't "new physics" or "new math" also seem similar after all is said and done?
But inventions usually come about by people using or doing something and figuring out a better way to do them.
Not by thinking about something until there is a better way to think about something.
Electronics became devoid of hope for change because what I already knew of it became so central to the world and yet still so awesome.
When my rank depends on a system, their is little impetus to change it.
Therefore, my dependence on innovation seems to depend on holding no rank in math and physics.
As one songwriter said, "If you have to or try to write a song, it will be crap, but if a song comes to you, it could be really good."
The same applies to "inventions" in STEM, despite what years of hard work has proven, it is always the truly inspired ones that make the new vision.
I feel my burden is lifted.

It seems mathematics is a progression toward relative and free models.

I get the whole line of reasoning more than every small instance of reasoning in my book, but that's why there are problems to work on.

I'm not to the point where I can write a textbook.

Delineating a series of concepts builds and builds and builds. It is not like a story that has a peak and tail off. Instead, it always builds.

Simply the idea of linear independent vectors forming a basis means that any two objects can create its own universe.

It seems learning is realizing the particulars of what I already know.
For once I got a breadth of what the universe consists of, learning about it got a glassy quality.
What is "the particulars"?
What differentiates them from the general concept?
The particulars are forgotten in short term memory, but while understanding them, they give a sense of truth as if the concepts themselves were a lie.
Rather, the concepts were for children and the particulars for adults.
Yes, who will become an adult in mathematics?
"I don't want to grow up," my essence affirms.
For I know that once I grow up, I can no longer act as a child.
"I want to grow up," my reason delineates.
For a child cannot truly help understand its unknown areas.
My child reasons: "but I can imagine a way to do it!"
What would a child be if not hopeful?

I read: it's not just about having the facet of knowledge but when to use them.
Thus, children reason in a world that hasn't gone down the rabbit hole.
Adults reason already in wonderland.
I must view the wisdom of adults as sheer madness, while the knowledge of the child as mere anger, instead of the other way around.
Maybe I don't want to lose my reckless quality of knowledge - somehow I can cheat the system!
Probably the rebel never dies.
Maybe that's what I hope the most.
I shouldn't see my knowledge being able to undercut wisdom, nor wisdom devoid of mystery.

It seems like I'm a genius when I'm searching and finding answers so that I can figure out problems.
Also, when I'm asking questions it feels this way.
But when I'm pondering The Mystery I always feel inadequate.
When I'm trying to skim my mind for a metaphor for an unknown part of the universe, it is like my imagination has to solve for both X and Y.

Getting help with an answer can often remove any need to think.
Except the need to think about how I could remember how to solve it the next time.
Often I've unknowingly believed that there is a disjunction between common sense and reasoning because I've believed that my common sense was no help.
In reality it was just a lack of communication between common sense and reason.
Learning helps the brain communicate within itself.
It is not merely learning more, but the ability not just to see connections, but communicate them.

I found how infrequently some points or lines could align with a hyperplane.
It sounds way harder than it was, probably because I used to not know the succession of steps to learn about R^n and the hyperplane.
They are easy to grasp but it used to not be as easy as 1,2,3.
But it really is a simple plane in n-1 dimensions of R^n.
Yet when I first encountered the word some years ago, it was quite mesmerizing.
I think math will always be mesmerizing except if I've encountered it in pedagogy.
With this understanding, I know that all math is stepwise succession within its branch.
But somehow this leaves things undone, probably because I can't cheat true and tried pedagogy.
That's what I really want to do.

What does it mean that my logic and reasoning could solve a problem?
Meaning the one who gave me the problem could solve it already.
Yet there are those who have gone through all the courses of problems, all ending in relatively the same place mentally.
However, there are still problems they can't solve.
What does it take for a breakthrough?

To know when to employ math known to mankind and when I can't.
To know when I need something new or when I can use something old.
This, I believe, is the crux of the matter.
Otherwise, I try to invent new what is already done and so go nowhere except to prove to myself what all these people knew from a different perspective.