# A community striving for discovery and knowledge of mathematics

## Contents

## Concentric developer community

- how would a mathematically extremely talented child feel and learn among all these robots? underchallenged? bored? misunderstood? or even in danger? what would the learning environment have to offer? robots? numbers? real mathematics? the UMIS (universal mathematical information system) as an escape? but is the UMIS more an engineering project than a mathematics project? what kind of environment would ultimately provide the right environment for a mathematically extremely or rarely talented child? just as many other extremely intelligent people around writing on blackboards? probably yes. so maybe this website here is not about the didactics of mathematics but about the didactics of good engineers and mediocre mathematicians? i have the impression that this section/page here is the most important section of the whole website because doesn't it show the limits of what I try to promote as "didactics of mathematics"? the only meaningful topic I have written so far is an idea from another person with teaching axiomatic systems from as early as possible. but is that the only idea? is that enough? should I strictly separate the didactics-of-engineering-and-maybe-mediocre-mathematics and the didactics of pure mathematics still only with blackboards? and opening a new page for the latter that will be almost empty and therefore show how little I have to offer in terms of didactics of pure mathematics? constructiv(ist) ideas might be:
- follow the idea of axiomatic system learning. encourage every child to follow the axiomatic path as much as possible as early as possible, always at the edge of its intelligence
- connect all mathematically ultra-intelligent people and children with each other, create a community of mathematically extremely talented people of all ages from age 0 to 120 where the mathematicians decide for themselves which environment they want for them and the ultra-intelligent children learning in it and also which robots to keep off the area and maybe which robots to just accept for a limited degree as mediocre learning tools (if any robots are accepted at all)
- Note of August 1st, 2013, 19:02h – 20:05h (with an interruption in between (approx. 17:15h - 17:32h) when I wrote the text on another page): The content of this list item here is a little bit oversimplifying: firstly, mathematicians would probably not want to live in a community of mathematicians exclusively, this would be a socially unsatisfactory setting. Furthermore, robots probably help always (or in most cases, there might indeed be children and especially children who are also prospective mathematicians who don’t want to have contact with any robot) a little bit to understand (or to be motivated to learn (think for example about the need to move around which is crucial for the health of every child)) mathematical concepts; on the other hand, there are limits in terms of what can be squeezed out of robots when it comes to learning mathematical concepts. And the distinction between engineers and mathematics should also not be drawn too strictly since engineers also need knowledge in mathematics. Most importantly, the relationships that people already have or prefer to strike up define where they are and stay, not some ideological requirements. Furthermore, the Internet still allows worldwide communication and subject-specifc exchange.

- everything that a blackboard can do, the UMIS (universal mathematical information system) also has to be able. the UMIS must in no single area be inferior to a blackboard, but only/strictly on par or superior so that the UMIS can at least replace the blackboard fully and in a good case even helps to learn and in an even better case even
~~develop~~discover mathematics (not mathematics is developed, but the UMIS, in order to discover mathematics) more efficiently, intelligently and quickly - there might be inner circles of mathematically ultra intelligent people who filter all robots from the outer circles that are the most useful in terms of mathematics learning, all other robots are kept off the ground, the outer circles where the engineers and the engineering children are would just supply a selection of robots to the mathematicians or just do the "manual development tasks" for their superiors in the middle, there might indeed be some hierarchy: the true and pure mathematicians deciding which robots to develop generally and specifically for themselves and somehow reluctantly directing, guiding and managing the development process while the other more outer circles do the real development work. and people or entities would be promoted to an inner circle if they have proven sufficiently that they are mathematically good enough in terms of pure mathematics and not just physics and/or just engineering.
- an emerging pattern that the pure mathematicians are also theoretically the best robotic or hybrid entities developers not because they like the robots but because they are simply somehow reluctantly the best also in terms of physics and engineering
- it is not a question of strict hierarchy but an emergent pattern of some kind of hierarchy among engineers, physicists and mathematicians, a constant struggle for being the best - pure mathematician because of emergent supremacy over the matter of physics and technology
- and what are the engineers? just the subordinates of the mathematicians? doing what the mathematicians have told them in terms of engineering? or will they try to do their "own engineering" for their own mathematically significantly less intelligent children too? but wouldn't that lead to nowhere since the pure mathematicians are also those who are best able to design the didactically best robots because they know mathematics better which is simply required or the necessary precondition for engineering good robots?
- therefore, wouldn't the goal be that pure mathematicians of the world unite and surrounding themselves with people respecting mathematics and willing to develop the robots that their superiors - the pure mathematicians - have told them?
- and the UMIS would be the place where the engineers would be somehow more allowed to participate directly with the mathematicians in discovering mathematics, but also only to a limited degree, maybe as some kind of "technical maintenance and engineering entities" while the pure mathematicians would also ultimately decide the direction of the development of the UMIS?
- and the main goal of the UMIS would be to simply connect mathematical knowledge as efficiently and closely and clearly and deeply/simply together as possible in order to maximize the extent of topics that an individual mathematician could cover during lifetime and also to maximize the depth of understanding of each individual topic or mathematics generally?
- in addition to "robots", the word transhumanist entities could be used but this would not be a big difference for the pure mathematicians directing and managing the process since mathematics implies (or is implied?) in all these "things" and "entities"
- and wouldn't such a hierarchy not be that strict but constantly emergent because of the immanent superiority of mathematics? there would not be another admission criterion to the inner circle except the proven ability of being a sufficiently able or insightful pure mathematician? constantly open for any entity being intelligent and insightful enough?
- now, I just have to find a new title for this kind of process in order to create a page for it: "emergent hierarchy"?: perpetually/immanently (or ultimately?) (re-)emerging hierarchy with mathematics on the top? just ultimately as a kind of eschatology of mathematics? but isn't that already now the case and shouldn't it just be more encouraged or facilitated or maybe mediated that also the non-mathematicians can benefit in the most "optimal" way from this hierarchy while ensuring that the process is compliant with mathematics? so, in the end just some kind of utilitarianism and maybe even intelligence for increasingly everybody managed by pure mathematicians? a happy new world? no, probably more an intelligent and only afterwards happy new world.
- as a title, maybe constantly emerging mathematics centered hierarchy? or "constantly (re-)emerging priority/supremacy of mathematics over engineering?" or "how to best ensure pure mathematics education" (maybe include the word "socially"? and/or the word "technologically"?)?

## missing

self-restriction, modesty, restricing one s own amibition, the exclusive beschäftigung with it is/defines the center, but encompasses all people until and including the people on primarily developing the robots on the periphery

the whole concept is still problematic because it advocated specialization and might lack democratic political structures.

if such a community is in danger, it is advisable to be as mobile as possible and to ausweichen or be ready to ausweichen and to use one's own robotic technology to ausweichen instead of using the robotic technology to defend and stay. therefore the robotic technology on the outer areas is not and should not (or as little as possible) be used to defend, but to remain mobile and the concentric structure with the keepers of humbleness, self-restriction and gratitude knowledge and mathematicians (the mathematicians possibly be located a little bit more outside) should be used to protect the most concentric and "important" people from the robots that on

## alternative titles

- include the word the "the" before "discovering"
- "topology" or "topological"? (would that be too mathematical?)
- ideas for a ...

## Problems of this page here

- safety issues, but also security issues (what might the latter mean?) and a mixture of it
- "defending" vs. fleeing or ausweichen
- clear "layers of risk" vs. "pockets of risk"
- distinction between a "community" and an area that is outside of a community
- complex, ever changing situation for a community dedicated of mathematics
- three different "issues" or "areas" even within "the"/"a" community: firstly restriction of oneself and one's own ambitions, secondly mathematics and the protection of mathematicians from robots, and thirdly the engineers and roboticists.
- compromise with (political) reality?

=> political: politics generally and "politics of mathematics" specifically. Compared to the other pages of this website here, this website here is highly political.

## Was aigäntli gmaint gsii isch

Dä Sinn vo därä Siitä isch gsii, dass i dä Mitti diä Mönschä Mathi (Matti) betriibäd, wo am beschtä in Matti sind und si am rainschtä betriibäd und nach ussä d'Robotik immär mee zuenimmt. I dä Mitti wäräd also Mathematikär, wo sich möglichscht ganz dä Mathematik widmät und ussä draa d'Mathematikär immär mee au Robotär entwickläd entwickläd und no wiitär ussä chemmtäd dänn di mathematisch am talentiärtischtä Änginiörä und dänn di mathematisch wenigär talentiärtä Änginiörä, äs hetti also immär mee Robotär, je mee mä nach ussä chunnt. So han - - das im 2010 vorgschtellt.

Jetz (2012/doz_11b8 bzw. nach äm Härbscht doz_11b7) find - das Konzept seer haikäl, well d'L.... so nid gwäärlaischtäd isch/wäär. Wäräd sich diä Mathematikär im Zäntrum bewusst, was L.....schmärz isch, ja würdät si dää L.....schmärz sälbär füülä chönä?; wär äs Konzept, wos nur um d'Matti im Zäntrum goot (bzw. im Zäntrum d'Matti s'ainzigä Ziil isch), nid sogar bsundärs haikäl, well diä Matematikär so abgschirmt wäräd vo dä ussärä Iiflüss (wo au d'L.... däzue ghöört)?