An interesting discussion...
closertotruth.com
Math is connected to written language, more than to spoken language. If we did not have written language; could not write math, spoken math would be very limited, and would be much harder to do. Written language allows one to record what you counted; placeholder for memory, instead of having to place the sum into memory, while also doing calculations and operations in your heads. Writing allows to document, so we can pause and reflect. If you are solving simultaneous equations, it is much easier to write them down and then ponder what you see. You try things until they work; many pages. All in your head, like spoken language would be very difficult beyond just basic math, even keeping track of where you have been; aborted efforts.
The invention of written language, was important to the formation of civilization. The tool of written language, was extended to early math. Math has it own symbols of the math alphabet; Greek letters, and words; equations, to allow a way to make commerce, science and other record keeping, easier, more compact and more reliable.
Engineering Basic Math from Scratch.
Say I was a farmer who owned sheep. I put notches on a tree, for each sheep I own. This is a very simple written system. If my neighbor claims, I have one of his sheep, we can go to my notch tree and compare notches on my tree, to the sheep counted in my field. If I have an extra sheep, he takes it home. If there is one less, I need to look for it. If the total is fine, we both go back to our herds. We can, together, do the one to one correspondence; count notches and sheep.
Without this basic writing language, we would have to depend on memory. We would have more arguments if either of us forgets or embellishes. The written record settles the argument. This was pivotal to sustained civilization; less arguments and fights.
Say I am blessed by the gods of sheep, and have many lambs born this year. My notch tree is now getting full and is getting too confusing. I come up with the idea; necessity, I need a way to compact all the notches. For every 10 notches, I will gouge a circular gouge, on my new tree; gouge =10. This is the number of fingers on my two hands. I then decide, I will even use a half circle notch, to represent the fingers on just one of my hands=5. This system is more compact for my growing farm. I can count more sheep on the new tree.
My blessing now has become a curse with too many sheep. I decide I will trade the extra sheep. This causes causes more problems, making my notch tree very messy. It would be nice if I had a way to add and take away lines, half gouges, and full gouges, when I trade sheep with my neighbor. I decide I will make hanging symbols on a third tree. I will teach my neighbors my selling system, so we can both swap our hanging symbols, and place the new ones on our own hanging trees. I have engineered a simple mobile calculator system. My son can now also help give out the bought sheep, to the new owner, while I see to another customer. The owner gives him the hanging symbols. My son counts the sheep by the symbols, and then gives the symbols back, as a receipt and record of ownership for his hanging tree.
The last is reverse engineered based on modern need and method that would come in handy way back when.
Math is reflection of the human brain's visual apparatus.
The written nature of Math, is connected to the natural visual language of the eyes and brain; eyes, visual and frontal lobes. Math is this neural network projected outward, as visual math system analogies. By virtue of coordinating with the natural visual-neural apparatus, math itself will become formed in the image of natural human. The parallel in the brain also allows math to become universal to all humans.
This projection effect is common to tools and machines, where the early tools and machines, mimic and extend the body. The sword is an extension of the arm and an extra claw. Math uses the ability of the eyes to sense difference; number of units, angles, textures, complex gradients, shadows, reflections, colors, etc. While the brain takes this further; integration; area under curve and differentiate; slopes/angles, relative to memory and other visual data from modern technology.