Universal mathematical information system

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Alternative titles

  • (the) "(universal) mathematical machine"
  • ... all-encompassing ...
  • perfect or "perfectly mathematized"
  • increasingly mathematized
  • "the ..." or "a ..."
  • "mathematics" instead of "mathematical"

Mathematical knowledge / Generally relevant for mathematics

  • the ultimate (general and/or mathematical) brain / neural network / intelligence
  • constructivism and perfection: the "tool"/technology for (mathematical) perfection (but see also the criticism at the end of the page)
  • the central (most formal, abstract) part of (interconnected) cognitive activity and the technological singularity (and of UTSARA, see also List of UTSARA implications?)
  • no clear distinction between learning, understanding, computing and "doing", "thinking" (and ultimately becoming?/being?) mathematics
  • unclear to which degrees other sciences like engineering (also in a non-mathematical context), natural sciences and maybe even social sciences are integrated, but ultimately, they would probably be integrated very tightly and ultimately mathematized as instances just on a very specific mathematical level, but in the short time, that might be unfeasible and they are either (still) left out or "put nearby" (partially) as non-mathematics, see how to integrate all sciences and everything into mathematics? (alternative title: how is everything ultimately purely mathematical?)
  • special position for information and "computation" theory (see also the next point)
  • the precursor of a possible developmental struggle between mathematics and entities? (for the time being, see also Wikipedia's article "philosophy of mathematics")
  • able to prove rigorously and in an UTSARA compliant way (see the also the following/next section)
  • with continuously improved UTSARA compliant protection mechanisms against unsustainable and premature "proof desires" on mathematically too concrete or premature levels (the mathematical ecophagy argument: impeding or damaging parts of the real world in order to do advanced and complex mathematical proofs)
  • with all (more and more common) numeric and computation-assisted proofing methods embedded (as long as they are UTSARA compliant, see also the previous/preceding section)
  • all proves and theorems can be followed in a linked chain to the (most fundamental) axioms and this functionality is continuously being improved with the goal of facilitating the developing an improved or even (completely) new axiomatic system in mind (see also the page with alternative ways of learning mathematics and the mathematical imagination page)
  • ideally open source / transparent: all information, sources and running processes are accessible in the technologically most feasible way: the challenge might be to document as many intermediate stages as possible in the most detailed way possible during runtime because of the enormous data: does mathematics on a higher level solve that challenge?
  • ideally in the long term both software and hardware/"hardwired" or something in between
  • ideally uniting/encompassing/integrating/combining all (types of) mathematical (and "computational"/"calculating") software and hardware or tool/aids generally, including classical/conventional and already quite complex scientific mathematics software/tools/packages: the challenge would be to unite the varying/differing abilities/properties of these complex software packages into one single technological entity or closely enough interconnected entities so that all abilities/properties of the original software packages are integrated in an equal or improved way
  • with the latest numeric proofing methods
  • the ultimate developmental stage of the technological singularity (but not the same as the technological singularity until the most abstract stage?)?
  • a combination of software in order to learn mathematics from early childhood and conventional/scientific mathematics software
  • especially the open source didactics software might serve as the precursor of a possible universal mathematical information system since conventional scientific mathematics software is not open source and the abilities and properties of conventional scientific mathematics software might only increasingly be incorporated at an intermediate stage
  • a particular, (at least among computer scientists) well known and freely online accessible mathematical and computer science answer machine might be a(n) (closed source) example for a possible open source precursor/start point of such a universal mathematical information system (but probably, the UMIS will be developed out of open source mathematics learning software, see the point above)
  • to which degree is such a UMIS ultimately just a very well engineered piece of technology or exactly the opposite of a piece of technology but truly mathematics? or something in between? (see also the criticism below)

Both: Mathematical knowledge and Didactics of mathematics

  • ultimately not only a mathematics learning tools, but an increasingly developing "mathematical brain"?
  • continuous integration of decentrally developed mathematical (learning) software
  • ideally both used as a learning tool and knowledge tool
  • being used as a learning tool and being continuously developed and improved by anybody (any entity)

Learning and Didactics of mathematics

  • serves as the main mathematical learning software, see didactics of mathematics
  • proofs
  • theory
  • sample questions and sample answers (including the solution path/method)
  • exercises with optional answers / solution paths/methods
  • all proofs, theory sections, sample questions and answers and exercises could be freely assessed/labeled/commented/changed by all users of the UMIS, for example in terms of proposed changes and the perceived difficulty. all comments and changes or change proposals would be permanently stored.
  • every topic (for example a specific theory) would have different versions with varying degrees of difficulty/complexity that a learner could select (the proofs might have only one version and therefore be an exception since they might be more erratic than theory, q&a and the exercises)
  • for every level of difficulty and especially for the lower and intermediate levels of difficulty, a substantial amount of sample questions and the corresponding sample answers (and sample solution paths/methods) and corresponding exercises would be necessary since all intelligence ranges of all learners/children would have to be covered and since mathematically less apt students would only be able to understand the mathematical topics (to their own maximum extent) with the help of a sufficient amount of specific and detailed learning examples.
  • all content would be individually selectable, any jump from any topic or exercise to any other part of the UMIS would be possible while links would try to guide learners and give hints for the optimization of the learning process
  • interconnected (all meaningful connections between all topics would have to be ensured, a complex task)
  • in terms of exercises, such a software would be similar to today's mathematics software tools use in schools, but much more comprehensive, for all degrees of difficulties and with optional sample solution paths/methods for every exercise with selectable degree of details
  • the UMIS would adapt its learning environment to the specific cognitive abilities and needs of every age, beginning at age 0 (and in the longer term also during pregnancy respectively ultra-early technological bootstrapping) until adulthood (maybe didactically also adapted in terms of a connection to age-adapted robotics-supported mathematics learning)
  • the degree of difficulty would range from basic counting to at least until PhD mathematics level and in an ideal case would comprise all cutting-edge research in mathematics too since cutting edge mathematical research would in an ideal case only happen with/on the UMIS (but what about blackboard mathematics?)

Criticism

  • mathematics as an (ultimately extremely mathematized) engineering project? Is that possible? How? And what about the human brain? Isn't it engineered or evolved too by evolution?
  • see also becoming mathematics, being mathematics or just ultimately or "deeply" learning or understanding mathematics? (see also mathematical depth, for the time being, read on Wikipedia about mathematical depth)
  • what about "blackboard mathematics" (alternative name: "chalkboard mathematics") in the context of this page here? Isn't mathematics done by intelligently thinking brains within intelligently thinking brains? what might that mean for any attempt to develop a universal mathematical information system? Is the UMIS becoming the intelligently thinking brain? Will some or all blackboards/chalkboards become obsolete?
  • see also Wikipedia's article "philosophy of mathematics"
  • 1st of August, 2013, 18:35h - 18:40h: In my opinion, while a "universal mathematical information (or educational) system" (or several ones, therefore being less-universal than just one) might be possible, it is in my opinion unlikely that a "universal mathematical system" (without the word "information") that does mathematics like a human being (respectively the evolved human beings in the future, should that indeed happen / become possible) will ever exist. I have the impression that it is impossible that those who would engineer such a system (or "machine") would have equal or less mathematical knowledge than the system they are designing. See also the comments on the bottom of the Main Page and my criticism of a too constructivist approach on the page A community striving for discovery and knowledge of mathematics.

See also

mathematization and the mathematical singularity