Incomplete math classification on this forum

[Demystifier]

I think that classification of math into subforums on this math forum is highly incomplete.

For instance, suppose that one wants to discuss number theory or discrete mathematics. Is this supposed to belong to general math? What if one wants to discuss subtleties of the last Fermat theorem or of Ramsey theory, does it really belong to general math?

Or computation theory, like P=NP conjecture, on which subforum should this be discussed?

Or discrete dynamical systems? Since they are discrete, the differential equations subforum does not seem appropriate.

Or algebraic geometry, should it be considered a branch of differential geometry?

It is also quite unnatural to have logic and set theory in the same subforum with probability and statistics.

Am I the only one who thinks that math forum should be significantly reorganized?

 

[micromass]

You're right. But you should take into account that many topics just don't get many questions. It would be a bit silly to have a forum that only gets 1 question per month. So we need to compromise. That is the rationale behind the current structure.

But please, if you have a better way of ordering this, I am very willing to discuss this with you and recommending Greg to make the appropriate changes. But keep in mind that you must order it in at most 6 forums that should get a decent amount of traffic and new threads.

 

[jedishrfu]

I think you're right. However, @greg has to balance things between:
- too many forums and people will get confused
-vs-
- too little and we don't know where to place threads.

The current scheme seems to parallel math levels of learning.

Taking a cue from Prof Elwes chapter organization in Math 1001, we could have:

- Numbers
- Geometry
- Algebra
- Discrete Math
- Analysis
- Logic
- Metamathematics
- Probability and Statistics
- Mathematical Physics
- Games and Recreation

https://www.amazon.com/dp/1554077192/?tag=pfamazon01-20

Alternatively, we could have fewer forums in math and use the post title tagging to define the topic more specifically.

 

[member 587159]

What about subforums in the math subforums? For example, make a subforum geometry, and there subforums differential geometry, analytic geometry, algebraic geometry, ...

 

[micromass]

What about subforums in the math subforums? For example, make a subforum geometry, and there subforums differential geometry, analytic geometry, algebraic geometry, ...

Way too complicated. People don't want to navigate through so many subforums.

 

[jedishrfu]

I suggest we have 10 forums and let @Greg Bernhardt decide on the number base.

 

[Borek]

I suggest we have 10 forums and let @ greg decide on the number base.

I guess you mean @Greg Bernhardt, not some random greg user

I believe we discussed the way math forum is divided not that long ago (well, could be several years) and it is already a compromise between granularity and traffic.

 

[micromass]

I guess you mean @Greg Bernhardt, not some random greg user

I believe we discussed the way math forum is divided not that long ago (well, could be several years) and it is already a compromise between granularity and traffic.

It was fairly long ago. I was the one who proposed the current structure. I think it works rather well, but I'm open to suggestions.

 

[fresh_42]

In my opinion similar could be said about any forum, esp. for other science or economic questions which are posted from time to time. Sometimes they are related to game theory and end up in the probability section, which is close. And I wonder why there aren't more questions about macro economy which is highly mathematical. Perhaps because there isn't a forum at all?

But even in physics it's not always clear. Sometimes I find interesting articles on the internet I like to share. They are then are pushed around, because there isn't a unique characterization. E.g. https://www.physicsforums.com/threads/100th-anniversary-of-the-sackurtetrode-equation.885869/

Is it really classical physics? Or thermodynamics, which would have a right to claim its own section, too? Or quantum mechanics? Or simply something historic for which there is no special thread?

I think we all have had similar difficulties with some books to put them in an appropriate place on the shelf. I know that one cannot justify one non-optimal situation with another. However, in total its a more complex optimization problem than it looks like at first glance. And as we know, improvement on one goal might lead to a deterioration on another.

 

[jedishrfu]

I found these two threads on reorganizing:

https://www.physicsforums.com/threads/too-many-different-forums-categories.148641/#post-1192892

https://www.physicsforums.com/threads/homework-subforums.703987/#post-4461974

 

[Greg Bernhardt]

No doubt forum category structure has its limitations and sacrifices have to be made. We've tried to optimize the structure as much as possible to make browsing as compact and simple as possible while allowing adequate breadth of categories to choose. Sure we could list every science and math topic known to man, but it would be absolute hell to navigate. We're not against possible tweaks, but I think right now the current iteration works very well. Any topics that feel uncategorized should go in the "General" category.

Some forums do have prefixes to narrow topics better. However I still think they should be secondary because the forum category structure is still very good for random browsing.

 

[ShayanJ]

Maybe you can provide a sticky thread somewhere that explains where people should ask their equations about subjects that are less clear to which category they belong.

 

[Greg Bernhardt]

Maybe you can provide a sticky thread somewhere that explains where people should ask their equations about subjects that are less clear to which category they belong.

The few that are unclear are pretty unlikely to read the sticky. Easier to just move them if needed. Just the way the world works :)

 

[S.G. Janssens]

Just the way the world works :)

Could you write an Insight about this once?

 

[Greg Bernhardt]

Could you write an Insight about this once?

It would fill a book :D

 

[fresh_42]

It would fill a book :D

Or just 2:44



(I know it's not the original, but I loved her hair ... and the memories.)

 

[Demystifier]

You're right. But you should take into account that many topics just don't get many questions. It would be a bit silly to have a forum that only gets 1 question per month. So we need to compromise. That is the rationale behind the current structure.

But please, if you have a better way of ordering this, I am very willing to discuss this with you and recommending Greg to make the appropriate changes. But keep in mind that you must order it in at most 6 forums that should get a decent amount of traffic and new threads.

Here is my proposal of the structure, which takes into account both the current number of pages in existing subforums and the natural division of mathematics into branches.

1. General Math
2. Calculus
3. Algebra (linear and abstract)
4. Analysis and Math Modelling (including differential equations, dynamical systems, game theory, etc.)
5. Geometry and Topology
6. Probability, Statistics, Discrete Math and Number Theory
7. Computation and Math Software (including LaTeX)
8. Foundations (logic, set theory, category theory, philosophy)

 

[Demystifier]

Any topics that feel uncategorized should go in the "General" category.

I don't like it. With such a strategy, some advanced topics may easily remain unnoticed by experts in the field who do not regularly read "general math". General math should be reserved for non-advanced stuff like elementary math, popular math, recreational math or history of math.

What do you think about my proposed structure in the post above? Note that the number of subforums is the same as before, and yet, as far as I can see, no major branch of mathematics is missing.

 

[Demystifier]

- Numbers
- Geometry
- Algebra
- Discrete Math
- Analysis
- Logic
- Metamathematics
- Probability and Statistics
- Mathematical Physics
- Games and Recreation

I have several objections to this particular classification:

- Elementary math is missing.

- Topology is missing.

- Computation is missing.

- Logic and Metamathematics naturally fit together.

- Number theory (if this is what one means by "Numbers") and Discrete Math can also fit together.

- I am a theoretical physicist, but there is no need for "Mathematical Physics" because each mathematical aspect of physics naturally fits to some "pure" branch of mathematics such as analysis (e.g. special functions, advanced calculus, differential equations, or functional analysis), algebra (especially group theory), geometry or topology.

- If by "Games" one means game theory, this is a very serious branch of mathematics which has nothing to do with popular computer games and does not fit well with Recreation.

 

[jedishrfu]

Okay so here's the further chapter breakdown from MAth 1001 by Prof Elwes:

NUMBERS
- basics
- arithmetic
- number systems
- rational numbers
- factors and multiples
- induction
- representation of numbers
- transcendental numbers
- ruler and compass
- constructions
- diophantine equations
- prime numbers

GEOMETRY
- euclidean geometry
- triangles
- circles
- polygons and polyhedra
- transformations
- tessellations
- curves and surfaces
- polar coordinates
- discrete geometry
- differential geometry
- topology
- knot theory
- non-euclidean geometry
- algebraic topology
- algebraic geometry
- diophantine geometry

ALGEBRA
- letters for numbers
- equations
- vectors and matrices
- group theory
- abstract algebra

DISCRETE MATHEMATICS
- combinatorics
- graph theory
- ramsey theory

ANALYSIS
- continuity
- differential calculus
- integral calculus
- complex analysis
- power series
- exponentiation
- fractals
- dynamical systems
- differential equations
- Fourier analysis

LOGIC
- basic logic
- science of deduction
- set theory
- hilberts program
- complexity theory
- computability theory
- model theory
- uncertainty and paradoxes

METAMATHEMATICS
- what mathematicians do
- mathematics and technology
- philosophies of mathematics

PROBABILITY and STATISTICS
- statistics
- probability
- probability distributions
- stochastic processes
- cryptography

MATHEMATICAL PHYSICS
- Newtonian mechanics
- waves
- fields and flows
- special relativity
- gravity
- quantum mechanics
- quantum field theory

GAMES and RECREATION
- game theory
- fibonacci
- puzzles and perplexities

Anyway, this is one mathematicians (Prof Elwes) take on organizing the various topics of mathematics.

However right away you can see that is can get very broad and very deep and in the PF case most questions will be what students encounter in high school and undergraduate math for the STEM courses and we hit only a couple of the topics in a big way.

 

[S.G. Janssens]

A bit in line with Jedi's suggestion, you could suggest that starters of a thread in the mathematics forums tag their topic using the AMS Mathematics Subject Classification. The advantage is that the forum structure does not have to change, but people can filter by tag. (You could still change the forum structure if that would be desired and follow a subset of the AMS lay-out.)

I think it is very difficult to reach a consensus that does justice to everybody's personal views and preferences while at the same time only maintaining a few subforums. (For example, for me linear algebra is much more both "analysis" and "computation" than "algebra", but someone working on modules likely disagrees.) On the other hand, given the low amount of traffic it seems indeed unhelpful to split the forums themselves into (many) subforums.

So, I wonder whether it would be possible and helpful to attach optional AMS tags to mathematics topics. One could use the pull-down menu in the link at the top of this post.

 

[S.G. Janssens]

In fact, the decision (consciously or not) of StackExchange to not use AMS MSC tags on math.SE and MathOverflow is, in my opinion, a big miss. (I know that PF and SE are two different things, but surely people posting in the mathematics forums here sometimes look there and vice versa.) Now there is a whole myriad of partially non-standardized tags over there that drives me crazy and makes SE hard for me to navigate.

Had they used the MSC, I suspect I would have been there much more often, specially because the MSC also includes applied categories, so it is easy to succinctly tag mixed topics.

 

[jedishrfu]

Wow, that's quite a detailed list of mathematics topics a kind of Dewey Decimal System which could also be considered here:

https://en.wikipedia.org/wiki/Dewey_Decimal_Classification

and here's a list of science classes (scroll around for others classifications:

https://en.wikipedia.org/wiki/List_of_Dewey_Decimal_classes#Class_500_.E2.80.93_Science

All of these systems are quite intricate though and too detailed for the average poster to follow. However, I think the use of keywords could help determine the proper classification tag for a given post if we wanted to go that route.

At home, I've tried to classify my own collection of email, web articles, clippings and stuff and finally resorted to simply using a timestamp directory scheme:

     ~/archives / math-archive / 2016-email / 09-september / 28-wednesday / (name of file)
     ~/archives / math-archive / 2016-notes / 09-september / 28-wednesday / (name of file)
     ~/archives / math-archive / 2016-web / 09-september / 28-wednesday / (name of file)

It allows me to search on date, year, month name or day of week or file name / file type where the file name uses a descriptive keywords and then I can use grep on contents to find files of interest. The idea of using year and month make it easier to externally archive older entries while still maintaining the structure.

 

[jim mcnamara]

@Krylov the suggestion would be wonderful for mathematicians. But. Consider this humble quiz -
Quick now! Without looking up some reference -
1. What is the correct Dewey decimal number for 'spectral analysis of nonlinear flows'?
2. Or the Library of Congress call number?

The point is your suggestion creates a barrier to posting that if it could not be ignored would really deter posting. If it can be ignored, then it will not be of use. IMO. I am not a mathematician.

I get stuff in Biology that defies categorization. Lately there has been a blitz of questions from extremely uninformed posters. Some questions are good, some ridiculous and some require moderator's help. All those posters generally lack the wherewithal to tag posts. Some math questions are like that as well. Again IMO.

 

[fresh_42]

My impression and opinion:

My first thoughts on the proposed categories have been. (post #17 by @Demystifier)

• There is a difference between calculus and analysis in English usage (considering the fact that there is calculus twice in the HW section)? I'm not sure I know the difference between the four.
• Wow. Apparently a lot of explanation needs to be done in the parenthesis.
• I knew topologists as well as geometers who would strongly object being seen as related.

The first two are well appropriate to prevent users from posting at all. The last one might be a matter of taste.

Many users don't have a mathematical background, yet. They might find it difficult to find out the correct category, and as I've already said, even experts will have difficulties on some subjects. So the category titles should be easy to read and understand on a HS or undergraduate level.

In my opinion the current categories are a good compromise on all these many objective functions of the optimization problem.

 

[S.G. Janssens]

Quick now!

I'm sorry?

Without looking up some reference -
1. What is the correct Dewey decimal number for 'spectral analysis of nonlinear flows'?
2. Or the Library of Congress call number?

I was not familiar with the Dewey system until Jedi's post, or at least I did not know that it was called like that. I suggested the AMS classification, which is specifically for mathematics. Of course, that does not change your point: I cannot answer your quiz question without consulting the classification, but I do not think that is an issue. This is the reason the classification is easily accessible online.

The point is your suggestion creates a barrier to posting that if it could not be ignored would really deter posting.

In my opinion, in some cases such a barrier may not be bad.

If it can be ignored, then it will not be of use. IMO.

You are probably right about that.

I get stuff in Biology that defies categorization. Lately there has been a blitz of questions from extremely uninformed posters. Some questions are good, some ridiculous and some require moderator's help. All those posters generally lack the wherewithal to tag posts. Some math questions are like that as well. Again IMO.

Many users don't have a mathematical background, yet. They might find it difficult to find out the correct category, and as I've already said, even experts will have difficulties on some subjects. So the category titles should be easy to read and understand on a HS or undergraduate level.

It seems we have different views about what is or should be the target audience of the technical (mathematics) forums.

 

[fresh_42]

It seems we have different views about what is or should be the target audience of the technical (mathematics) forums.

Maybe. My basic position is, that nobody who is willing to gain insights should be rejected by whatever barriers.
E.g. I've read posts in which it was about open and closed sets in their basic meaning. So what?

 

[S.G. Janssens]

Maybe. My basic position is, that nobody who is willing to gain insights should be rejected by whatever barriers.
E.g. I've read posts in which it was about open and closed sets in their basic meaning. So what?

It is just that the stickies gave (at least to me) a different impression of the purpose of those forums, in particular

Please note that all homework/coursework-TYPE questions must be posted in the HW/Coursework forum, not in this this forum. This is applicable even if your question is not officially from a HW/Coursework, and you are just doing this for your own study, or for someone else.

which can be read there.

 

[fresh_42]

It is just that the stickies gave (at least to me) a different impression of the purpose of those forums, in particular

Please note that all homework/coursework-TYPE questions must be posted in the HW/Coursework forum, not in this this forum. This is applicable even if your question is not officially from a HW/Coursework, and you are just doing this for your own study, or for someone else.

which can be read there.

This would restrict the technical math forum to actual research papers only, since everything else can either be found in textbooks or is personal unpublished research. As a consequence we not only would have basically zero traffic, but in addition only a few would be able to answer those posts with a substantial contribution.

 

[S.G. Janssens]

This would restrict the technical math forum to actual research papers only, since everything else can either be found in textbooks or is personal unpublished research.

Yes, but one could also discuss questions about ongoing research that refer to or follow up on existing articles or references. (This can include, for example, research done by BSc or MSc students in mathematics or by those making substantial use of mathematics.)

As a consequence we not only would have basically zero traffic, but in addition only a few would be able to answer those posts with a substantial contribution.

I'm not sure whether we would have zero traffic (see MathOverflow), but it would probably attract another audience, yes. Also, I think that there would still be enough people that could say something sensible.

 

[fresh_42]

Yes, but one could also discuss questions about ongoing research ...

... which already can be done. The usage of the A-level tag should make the difference. At least I don't see a bar.

Also, I think that there would still be enough people that could say something sensible.

Oh yes, I have no doubt that mathematical discussions are possible. And sometimes a different point of view can be useful. However, if I remember those discussions IRL, they have rarely been at the front lines in terms of technical details except when mathematicians who work in the same field met.

I agree, that these are questions on how the objective function "Target Group" should be stated.
To be honest, I don't feel to have the right to answer this. My opinion is mainly based upon the experiences of read posts, assuming it is intended.
Consequently I do not want to judge on this aspect.

 

[Demystifier]

There is a difference between calculus and analysis in English usage (considering the fact that there is calculus twice in the HW section)? I'm not sure I know the difference between the four.

Loosely speaking, calculus is a branch of analysis. A separate subforum for calculus is needed because calculus is used by a larger number of people, usually non-mathematicians who need to learn some math as a practical tool.

Apparently a lot of explanation needs to be done in the parenthesis.

Some of the parentheses can be omitted.

I knew topologists as well as geometers who would strongly object being seen as related.

I'm sure the number of people who see them related is much larger than the number of people who think that logic and set theory are related to probability and statistics.

Many users don't have a mathematical background, yet. They might find it difficult to find out the correct category ...

So are you suggesting to remove categories completely?

In my opinion the current categories are a good compromise on all these many objective functions of the optimization problem.

Perhaps they are not so bed, but it can always be better. At the very least, the minimal change one can make is to rename "Differential Geometry" subforum either as "Geometry" or "Differential and Algebraic Geometry".

 

[Greg Bernhardt]

Perhaps they are not so bed, but it can always be better. At the very least, the minimal change one can make is to rename "Differential Geometry" subforum either as "Geometry" or "Differential and Algebraic Geometry".

@micromass

 

[fresh_42]

So are you suggesting to remove categories completely?

Not at all.

I'm sure the number of people who see them related is much larger than the number of people who think that logic and set theory are related to probability and statistics.

I do understand your point and I agree on it. However, I want to chip in that our pedagogues might be to blame, since our approach to probability theory, which I'd rather prefer to be called stochastic, are Venn diagrams and combinatorics, i.e. counting elements. I'm not defending this at all, au contraire, I think it actually is a surrender. But I'm pretty sure, I wasn't the only one who suffered under this approach and everybody at the end of school relates them - unfortunately.

 

[Demystifier]

I knew topologists as well as geometers who would strongly object being seen as related.

A question for everybody: Would you agree that point-set topology is closely related to analysis, and that algebraic topology and differential topology are closely related to geometry?