If you have 2 scientists in a town fighting for one position, the chance they will cooperate and achieve some remarkable gain for the town is tiny to zero. They will likely undermine each other's progress even immersed in conflicting selfish behaviors. If they cooperate it doesnt matter who is actually the best of the 2. What matters is that they can do now something that each one alone couldnt or would take more time to achieve.

Inequality in society (that cares at some level to not be totally pathetic) is about the opportunities people get during their lives. Its not about making them all the same and ignoring skill edges and personal effort. Of course people are not identical. Of course some have better natural skills or have had a more lucky or more advantageous due to chaos theory or early childhood character educational/career path that made them "better" than others in some possible to properly measure way of things.

All kids are not the same. Some have natural advantages when it comes to eg math. But all kids can benefit from more math in their lives. A system must care to offer all the kids the chance to appreciate math and learn more for as much time as they desire.

A fair system will care that each person has a job for example and the opportunity to be a productive member of society and to have access to important services forever in exchange for properly selected services to the community and their own interests in balance, using their education and skills. It wont care if one makes more money/accumulates more wealth than the other because of various differences that exist. That in itself is not a problem if done right to not undermine the structure of universally respected properties of the system (which is unfortunately victimized if you elevate profit above all other virtues/utilities or create a poorly thought world that adversity and scarcity of resources force people there). It will care that the reasons they make more money than others however are not superficially stupid and inefficient and instability promoting, wasting of resources that undermine overall progress. It will care not to promote divisive excesses. It is not freedom eventually that these room to develop excesses societies celebrate, it is the restriction of other more essential freedoms that existed before for all. Personal power without wisdom eventually promotes corruption and unethical exploitation of those that are unable to defend themselves. This leads to further deterioration, social unrest and conflicting behaviors. It breaks people in fighting classes and ignores their common problems. This is the core failure of current political systems worldwide that are not modeled like a scientific society should.

This is where hardcore capitalism fails and the answer will never be communism or socialism but a scientific society model that preserves the desire of the individual to succeed at a personal level but only after first operating properly/responsibly within a society that cares for all its members to have a positive life.

So create in that town 2 positions for both your scientists and use them to create ideas that will lead to even more jobs for others because ultimately a town with 10 scientists will be even better for the community (even if the first 2 will feel they lost some rare prominence to the other 8 if they are narrow minded weak thinkers). They can be individually progressing at different rates (so celebrate/reward better personal achievement) but collectively still cooperating to solve harder more complex problems that will benefit the community and enable even themselves to enjoy stronger personal benefits in the future inside a more prosperous system that can now afford it.

Its not about creating a totalitarian world that all people are workers serving the state and not treated as individuals. It is about creating a world that intelligence and culture can prosper freely at improved rates and quality of life can advance for all members who can still differentiate themselves at other not as material to survival levels of competition.

It is about creating a world that celebrates individualism, competition and cooperation at the same time, where the state serves the people and people serve the state and themselves in a proper scientifically designed structure that is self critical at all times (exactly like science is) and never becomes absolute, dogmatic, arrogantly convinced of its infallible nature. It is an evolving system that depends on wisdom. A system that the individual cares for the state in order to achieve that way stability, security, enhanced freedoms and quality of life and the state rewards that effort by eventually requiring even less effort from the individual to sustain its standard of living (AI replaces human workforce eventually). Such system to be properly designed will require of course math to solve a variety of problems and optimize its structure to target universally respected cultural utilities with minimal conflict without losing its explosive creativity to conformity.

It sounds like you're really talking about capitalism 2.0 where decisions are more reliant on evidence-based methodologies and findings, as opposed to opinion and bias. This is naturally where capitalism is headed toward anyway. Perhaps a lot slower than we want it to, but that's life in general I find. Where's my hover-board?

P.S. on a related note, there is evidence demonstrating that employers are increasingly hiring people with backgrounds in research (evidence-based methodology).

I would use whips and chains to teach math to young teenagers.

First thing I'd do is buy them all 5th grade math books.

Those who genuinely believe that there is a point to doing something will do it. They payoff must be both expected and worth it.

Kids aren't all so uniformly gullible to believe that if they study hard that they will succeed. Many of them are even smart enough to understand that success isn't a good grade. We need to do a better job with those smart enough to independently discover these concepts.

The work-hards of the world, although useful, just aren't smart enough to take us to the next level.

Caesar vs. Cicero.


The next level of pink unicorns and opium?

On a similar note, I am currently working on developing a series of lecture slash workshops aimed at the high school level to expose them to areas of mathematics that are fun and more mentally stimulating. Right now I have it organized as a once a monh math club type session, running 3 hours. We'd start off with a brain teaser type of problem, a short lecture on math reserach related to the branch, and then a extension of the lecture thorugh problem solving.

The whole program would last 2-3 hours on a saturday morning, and would run every oher week. So far the ideas for sessions are : Euclidiean Geometry and Orgami, Big Numbers and Computer programming..

any thoughts or inputs on this type of program?

This is a good origami one:



Once you've made it, you can look at its symmetry, volume, surface area, etc.

A good large numbers question is which is the bigger out of a googol and the largest known prime? (2^10 ~ 10^3 is a rule of thumb here.) Regarding primes, going through each even number from 4 to 100 and finding two primes which add up to it is a good exercise for understanding Goldbach's conjecture.

I guess thats how you propose or give gifts to a girl who is a mathematician. You use this kind of boxes for jewelry and you select jewelry with topologically intriguing properties.

Cryingly.

I kinda liked the approach of my last teacher. He would hand out tons of papers with exercises, those who knew how it went did them on their own and tryed to help each other out. The rest would do em together with the teacher. That way the good ones werent bored, the ones who just understood had a lot of stuff to practice and the ones who didnt understand got a lot more attention.

How exactly he though I dont know, because I was busy solving.