All encompasing mathematics flowchart

[silverdiesel]

You know how Euclid organized all geometry based on fundamental postulates. As I understand it, all of mathematics can be organized from fundamental postulates. If this is the case, is there a resource where you can see the posulates and listed below, derivations from those postulates. Not the entire derivations, just the conclusions, so you can get a visual picture of all mathematical knowledge. I know it sounds like a huge undertaking, but I was thinking that it could be acomplished on a website pretty easier than printing out such a list.

 

[Data]

Mathematics today isn't done under one single set of postulates. There are many sets of postulates (more commonly called axioms today) that are used in various branches of mathematics. There is also simply too much mathematical knowledge today to arrange it all in any sort of "flowchart" in any reasonable amount of space (even if you were to omit all definitions, etc. and assume that everyone knows all of the notation, which is often used with completely different meanings in different contexts). Even arranging the sum of current knowledge in relatively new branches of study would be a daunting task.

 

[0rthodontist]

There are attempts at something like that, though. I can't seem to find it again but I once stumbled across an online logic derivation database, where a large part of basic math is derived straight from logical axioms and you can trace the derivations.

 

[Dragonfall]

Perhaps you're thinking of "Nicolas Bourbaki".

 

[CRGreathouse]

...or Metamath.

 

[silverdiesel]

hmmm.. actually I was thinking something like Google Earth, but with axioms and derivations rather than a map of the globe. So you can zoom in and out depending on the detail your looking for. But it sounds like modern Mathematics is too disconnected for such a project. Metemath looks very interesting though. I'll have to spend some time looking into that. Thanks for the responces!

 

[gravenewworld]

You know how Euclid organized all geometry based on fundamental postulates. As I understand it, all of mathematics can be organized from fundamental postulates. If this is the case, is there a resource where you can see the posulates and listed below, derivations from those postulates. Not the entire derivations, just the conclusions, so you can get a visual picture of all mathematical knowledge. I know it sounds like a huge undertaking, but I was thinking that it could be acomplished on a website pretty easier than printing out such a list.

You might want to read about Godel's incompleteness theorems while you are at it. Any system capable of doing arithmetic will contain a statement that is true but unprovable from the axioms.

 

[CRGreathouse]

hmmm.. actually I was thinking something like Google Earth, but with axioms and derivations rather than a map of the globe. So you can zoom in and out depending on the detail your looking for.

That would be an amazing project. I'd love to see something like that if it was created.

 

[0rthodontist]

...or Metamath.

Yeah, that's what I was thinking of.