This is very similar to Doug Lenat's work on Automated Mathematician & later on Eurisko, and later Ken Haase's follow up work on representation languages.
There were severe sticking points around the cultivation of an idea of "interesting" properties and the performance issues around evaluating a combinatoric space of possible manipulations. There hasn't been serious work along those lines since the early 90s or so.
It's annoying because especially Haase's work has some very practical insights, but Wolfram seems to be loathe to ever admit he's building off of someone else's work.
FTA:
> Ultimately every named construct or concept in pure mathematics needs to have a place in our symbolic language.
The reason your plea confuses me is that I don't understand the social value in encoding all _public_ "named construct or concept" in a _private_ "symbolic language" that only one proprietary piece of software that can be monetized by one corporation can benefit from?
(EDIT: To be clear, I am not claiming that there is no room for automated assistance of pure math, only that it can never be wholly automated.)
(Second, important EDIT: As Khaki points out (https://news.ycombinator.com/item?id=8170062), I should make it clearer that many objections about what computers can't do apply equally well to show what humans also can't do.)
I find it odd that Wolfram talks about all the thousands of things that will need to be 'built in' to Mathematica for this project to work -- shouldn't you be able to implement these things in the language itself?
fiatmoney|11 years ago
http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=ht...
There were severe sticking points around the cultivation of an idea of "interesting" properties and the performance issues around evaluating a combinatoric space of possible manipulations. There hasn't been serious work along those lines since the early 90s or so.
It's annoying because especially Haase's work has some very practical insights, but Wolfram seems to be loathe to ever admit he's building off of someone else's work.
mjn|11 years ago
pnut|11 years ago
Talk about revolutionary, true automated pure math would be a human milestone on par with very few developments in history.
igravious|11 years ago
FTA: > Ultimately every named construct or concept in pure mathematics needs to have a place in our symbolic language.
The reason your plea confuses me is that I don't understand the social value in encoding all _public_ "named construct or concept" in a _private_ "symbolic language" that only one proprietary piece of software that can be monetized by one corporation can benefit from?
Why would we want to do that?
kazagistar|11 years ago
JadeNB|11 years ago
Hilbert thought so too, but it is proveably not to be (http://en.wikipedia.org/wiki/Entscheidungsproblem), no matter how much money is thrown at it by how many bored billionaires.
(EDIT: To be clear, I am not claiming that there is no room for automated assistance of pure math, only that it can never be wholly automated.)
(Second, important EDIT: As Khaki points out (https://news.ycombinator.com/item?id=8170062), I should make it clearer that many objections about what computers can't do apply equally well to show what humans also can't do.)
bkirwi|11 years ago
jaan|11 years ago
I'll put up a blog post soon on this!
diakopter|11 years ago
http://monasandnomos.org/2012/12/05/the-idea-of-a-characteri...
http://vanemden.wordpress.com/2012/04/08/flowcharts-the-once...
kevinwang|11 years ago