Mathematics for creators is the study of mental structures with reproducible properties.
For dummies, on the other hand, it is computational skills useful, according to the general staff, for employees in the mass conscription army (that is why in the last century the queen of school mathematics in the developed world was trigonometry, so needed by artillerymen, naval officers and pilots).
But times are changing. And cardinally.
Today the situation is even paradoxical in some ways:
✔️ on the one hand, mathematicians and physicists are the stem cells of a technologically advanced society;
✔️ on the other hand, the cost of objectified mathematics in every mass device (for example, mathematics encoded and embedded in a smartphone) tends to zero.
But most importantly, in this new world of Big Data, it is already clear that:
✔️ the notion of mathematics as a science of patterns is the notion of kettles;
✔️ and for creators, mathematics is the science of structures behind patterns.
There are 3 important works in this regard.
1️⃣ About that it is necessary to urgently and radically change the system of mathematical education:
- to education for a selected minority of future creators who really need mathematical competence,
- and education for teapots (basic computing practice for the rest of the population, for whom mathematics will remain invisible in the stuffing of all the devices they use), -
You can read Alexander Borovik's excellent essay Mathematics for makers and mathematics for users (here and below, as usual, skyhab to help you).
2️⃣ About the fact that spoken and written languages and the language of mathematics are very different types of languages:
- That mathematical thinking is in non-linguistic regions of the brain that operate with space and numbers;
And if we remember that the brain is very variable, and although the total volume of the cortex is approximately the same, but separate cortical regions in different people may be more than 3 times (ie, there are 3 times more nerve cells specialized in specific actions), it may mean a genetic predisposition to advanced mathematics