6 ms·

LMFDB, a catalog of mathematical objects and the connections between them

136 points by ghosh 10y ago

nitrogen 10y ago
Edit: Link since the link in the article is missing the protocol: http://www.lmfdb.org http://www.lmfdb.org . This is somewhat similar to (and significantly more detailed than) something I've wanted for a long time: Feb. 26, 2009 ------------- What the world really needs is a poster that teachers can hang in their classrooms with a map of the world of math. It would essentially be a directed acyclic graph, with nodes representing mathematical concepts, and arrows linking those concepts to the next level of concepts one can learn, as well as real-life problems that can be solved with that level of math. For example, the chart would start with basic arithmetic, with addition and subtraction leading to multiplication and division. The related tasks possible with addition would be things like grocery shopping, subtraction would be figuring change from a purchase or determining how much time remains before some event. Multiplication would allow one to make simple designs, calculate taxes and tips, etc. The arrows would then go through the concepts of algebra, geometry, calculus, and on to things like the Fourier transform. The things one can do at a particular level could be represented as a bubble, with more math leading to a bigger bubble (and, if necessary to convince the kids, more money). This would also be beneficial to college students trying to convince their brains to remember all the seemingly-useless things they are learning in one class because they need to understand the concepts for next semester's classes. In fact, such roadmaps would make life a lot easier in general. "Want to become a $140000/year contractor? These are the steps you follow."
- lgas 10y ago
  Sounds like Khan Academy's knowledge map: https://www.khanacademy.org/exercisedashboard https://www.khanacademy.org/exercisedashboard I think you have to be logged in, but you can see a screenshot here: http://i.imgur.com/3HyRRyv.png http://i.imgur.com/3HyRRyv.png
- iheartmemcache 10y ago
  I agree that mathematics should be taught in a 'larger context', but you have two problems - 1: even for a subset of math (take a fairly 'small' field that was considered 'recreational' amongst mathematicians until recently - algebraic geometry) would end up filling up half all 4 walls of an elementary school room; b) a DAG is not the appropriate construct to capture entities (there is a lot of 'interop' both internally within a set of mathematics, and even more so as you go into the first rank poset containing that set; yet more as you go to rank 2)[1], c) most of those public school teachers wouldn't have the faintest what any of 80% of those nodes mean past "yeah, topology, I think I remember what a manifold is..." even if you kept the graph constrained to an 11x14 page of paper. I was fortunate enough to go to one of the those G20-esque schools[2] and by 10th grade I was asking questions that most of the instructors weren't capable of answering (and I'm not particularly bright - this a testament to those who tend to gravitate towards the profession). That being said, I was attending high school in the "we just got cable modems & youtube has 2 sets of lectures, one being Sussman teaching SICP" days. Those who are interested can easily find dozens of lectures from any conference/symposium/some-random-bright-grad-student-talking-to-a-room-of-8-people and then directly e-mail him/her. Knowledge is accessible really accessible these days, and those who are motivated to read further on a topic have high quality textbooks, pre-prints of papers, and open discussion amongst the communities (i.e., lurking on a Terry Tao project, or watching in real time as the classification of finite groups is underwent by a group of post-docs and grad students). For those who are motivated and learn by conversation/immersion like I do (did?). Perhaps this[3] explains my point a little clearer. (Note that Fermat has more than one proof, and I could easily at least the intuition behind the proof to a 2nd year undergraduate with no background in higher mathematics, given perhaps two semesters.) Conceptually, something like Poincare would be way more challenging just because at that phase everyone's used to Newtonian physics and Euclidian geometry; unteaching those 'intuitions' would take a semester alone. It could, however, be 'intuitively' (i.e., without rigor) taught fairly easily to someone with a background in higher level physics (i.e., most of the foundational maths of Riemannian geometry, etc, have been both taught and intuitively absorbed by students at that point). [1] https://www.youtube.com/watch?v=6oWLIVNI6VA https://www.youtube.com/watch?v=6oWLIVNI6VA Here's a lecture from a Princeton professor emeritus (IIRC) that demonstrates what I'm sure I poorly explained here. Introduction ends around ~6 minutes. [2] https://en.wikipedia.org/wiki/G20_Schools https://en.wikipedia.org/wiki/G20_Schools [3] https://jeremykun.com/2013/02/08/why-there-is-no-hitchhikers-guide-to-mathematics-for-programmers/ https://jeremykun.com/2013/02/08/why-there-is-no-hitchhikers... and in refutation - actually there is, sort of[4]. [4] https://en.wikipedia.org/wiki/Lists_of_mathematics_topics#Pure_mathematics https://en.wikipedia.org/wiki/Lists_of_mathematics_topics#Pu...
- Houshalter 10y ago
  See Metacademy: https://www.metacademy.org/ https://www.metacademy.org/
defenestration 10y ago
The link to the atlas in the article isn't working. You can visit the atlas via: http://www.lmfdb.org http://www.lmfdb.org
- dewiz 10y ago
  the authors forgot to add the protocol to the link href="www.lmfdb.org" should be href="http://www.lmfdb.org" http://www.lmfdb.org"
9mit3t2m9h9a 10y ago
I would say that «a mathematical universe» would be more correct here, because they just cover some of the areas; for example searching for «Ramsey» will yield no results; «probability» will yield just one result where an algebraic construction happens to be useful for calculating some probabilities.
- gjulianm 10y ago
  I don't know why it is being presented on the news as a catalog of the whole mathematics, when it is designed just a catalog of mathematical objects related to the Langlands Program [1] which is very broad as a mathematical theory (you don't usually find theories touching abstract algebra geometry, number theory and analysis) but of course does not consider all mathematical objects. 1: https://en.wikipedia.org/wiki/Langlands_program https://en.wikipedia.org/wiki/Langlands_program
nv-vn 10y ago
The idea is awesome, but it sort of loses its usefulness to people who aren't math experts. It's very clear by looking at the website that it's _not_ meant to be a Wikipedia for math. That's definitely not a bad thing, but I think that this website leaves an opening for something conceptually similar (but different in its implementation) that would be a sort of digital pathway through as many math concepts as possible -- for example, you can start on a page formalizing the idea of numbers and click links to navigate to addition, and then later on to multiplication, etc. allowing one to study math from the ground up. Or, you could start at a high-level concept and work your way down to the simple math. The purpose wouldn't be for researchers to better connect math, but for students trying to learn how math comes together in a broader sense. I think that a site like that could serve the same general purpose we see here of collecting math into a big catalog, just in a way that's more friendly to newcomers.
- aardvark179 10y ago
  Mathworld feels like it is part way to being the thing you want, but does mention Mathematica more than may be strictly necessary.
- spuz 10y ago
  There is something like this already called Wolfram Mathworld [1]. As a mathematical laymen trying to solve the problems on Project Euler, Mathworld would often give me the insight I needed to find an efficient solution so it is a great tool for students. [1] http://mathworld.wolfram.com/ http://mathworld.wolfram.com/
- hasch 10y ago
  as someone who has been at their workshops, there are ideas to do that. the goal is to have a semantic database, with a 3form ontology. look at these slides of the open dreamkit project: http://opendreamkit.org/meetings/2016-01-25-DKS/Kohlhase_slides.pdf http://opendreamkit.org/meetings/2016-01-25-DKS/Kohlhase_sli... ... somewhere there lmfdb should be mentioned
- sn9 10y ago
  I think that's called a university undergraduate math curriculum. You could look at the top n undergraduate math programs in your state and see what the flowchart of courses are and their corresponding syllabi and just go from there.
est 10y ago
Might be related, are there any websites where you can learn knowledge/skills like a Skill Tree/Perk Tree in games? I knew Duolingo had a design like that.
- sp4ke 10y ago
  +1 I would be interested by such platform/tool to learn math concepts
- kachnuv_ocasek 10y ago
  Doesn't Khan Academy have that?
  - est 10y ago
    Does Khan Academy have some kind of test, so when I finish it will automatically assess by present abilities and activate corresponding skill icons?
    - lgas 10y ago
      Yes
dang 10y ago
This was discussed at https://news.ycombinator.com/item?id=11667487 https://news.ycombinator.com/item?id=11667487, but since the article gives more background, we won't treat the post as a dupe. (Submitted title was "Scientists Launched an Enormous Atlas of the Mathematical Universe", which was arguably editorialized and rather baity—please don't do that. We replaced it with a representative phrase from the article.)
ianpurton 10y ago
It's great when scientists do stuff.
iso-8859-1 10y ago
As a catalog of mathematical objects, it should be comparable to Metamath: http://de.metamath.org/index.html http://de.metamath.org/index.html But this project seems to be specific to number theory, and not really concerned with proofs at all. Where can I find the webcast mentioned?
thegp 10y ago
I wonder if it is possible to get a full dump of that db
- mixedmath 10y ago
  It is. It's open source, and the backend is closely tied to the free math software sagemath (sometimes called sage). In fact, the site sometimes generates the data on request through sage instead of filling in large databases of static objects.
brudgers 10y ago
Recent related discussion: https://news.ycombinator.com/item?id=11667487 https://news.ycombinator.com/item?id=11667487

136 points by ghosh 10y ago

Edit: Link since the link in the article is missing the protocol: http://www.lmfdb.org http://www.lmfdb.org . This is somewhat similar to (and significantly more detailed than) something I've wanted for a long time: Feb. 26, 2009 ------------- What the world really needs is a poster that teachers can hang in their classrooms with a map of the world of math. It would essentially be a directed acyclic graph, with nodes representing mathematical concepts, and arrows linking those concepts to the next level of concepts one can learn, as well as real-life problems that can be solved with that level of math. For example, the chart would start with basic arithmetic, with addition and subtraction leading to multiplication and division. The related tasks possible with addition would be things like grocery shopping, subtraction would be figuring change from a purchase or determining how much time remains before some event. Multiplication would allow one to make simple designs, calculate taxes and tips, etc. The arrows would then go through the concepts of algebra, geometry, calculus, and on to things like the Fourier transform. The things one can do at a particular level could be represented as a bubble, with more math leading to a bigger bubble (and, if necessary to convince the kids, more money). This would also be beneficial to college students trying to convince their brains to remember all the seemingly-useless things they are learning in one class because they need to understand the concepts for next semester's classes. In fact, such roadmaps would make life a lot easier in general. "Want to become a $140000/year contractor? These are the steps you follow."

lgas 10y ago
Sounds like Khan Academy's knowledge map: https://www.khanacademy.org/exercisedashboard https://www.khanacademy.org/exercisedashboard I think you have to be logged in, but you can see a screenshot here: http://i.imgur.com/3HyRRyv.png http://i.imgur.com/3HyRRyv.png
iheartmemcache 10y ago
I agree that mathematics should be taught in a 'larger context', but you have two problems - 1: even for a subset of math (take a fairly 'small' field that was considered 'recreational' amongst mathematicians until recently - algebraic geometry) would end up filling up half all 4 walls of an elementary school room; b) a DAG is not the appropriate construct to capture entities (there is a lot of 'interop' both internally within a set of mathematics, and even more so as you go into the first rank poset containing that set; yet more as you go to rank 2)[1], c) most of those public school teachers wouldn't have the faintest what any of 80% of those nodes mean past "yeah, topology, I think I remember what a manifold is..." even if you kept the graph constrained to an 11x14 page of paper. I was fortunate enough to go to one of the those G20-esque schools[2] and by 10th grade I was asking questions that most of the instructors weren't capable of answering (and I'm not particularly bright - this a testament to those who tend to gravitate towards the profession). That being said, I was attending high school in the "we just got cable modems & youtube has 2 sets of lectures, one being Sussman teaching SICP" days. Those who are interested can easily find dozens of lectures from any conference/symposium/some-random-bright-grad-student-talking-to-a-room-of-8-people and then directly e-mail him/her. Knowledge is accessible really accessible these days, and those who are motivated to read further on a topic have high quality textbooks, pre-prints of papers, and open discussion amongst the communities (i.e., lurking on a Terry Tao project, or watching in real time as the classification of finite groups is underwent by a group of post-docs and grad students). For those who are motivated and learn by conversation/immersion like I do (did?). Perhaps this[3] explains my point a little clearer. (Note that Fermat has more than one proof, and I could easily at least the intuition behind the proof to a 2nd year undergraduate with no background in higher mathematics, given perhaps two semesters.) Conceptually, something like Poincare would be way more challenging just because at that phase everyone's used to Newtonian physics and Euclidian geometry; unteaching those 'intuitions' would take a semester alone. It could, however, be 'intuitively' (i.e., without rigor) taught fairly easily to someone with a background in higher level physics (i.e., most of the foundational maths of Riemannian geometry, etc, have been both taught and intuitively absorbed by students at that point). [1] https://www.youtube.com/watch?v=6oWLIVNI6VA https://www.youtube.com/watch?v=6oWLIVNI6VA Here's a lecture from a Princeton professor emeritus (IIRC) that demonstrates what I'm sure I poorly explained here. Introduction ends around ~6 minutes. [2] https://en.wikipedia.org/wiki/G20_Schools https://en.wikipedia.org/wiki/G20_Schools [3] https://jeremykun.com/2013/02/08/why-there-is-no-hitchhikers-guide-to-mathematics-for-programmers/ https://jeremykun.com/2013/02/08/why-there-is-no-hitchhikers... and in refutation - actually there is, sort of[4]. [4] https://en.wikipedia.org/wiki/Lists_of_mathematics_topics#Pure_mathematics https://en.wikipedia.org/wiki/Lists_of_mathematics_topics#Pu...
Houshalter 10y ago
See Metacademy: https://www.metacademy.org/ https://www.metacademy.org/

defenestration 10y ago

The link to the atlas in the article isn't working. You can visit the atlas via: http://www.lmfdb.org http://www.lmfdb.org

dewiz 10y ago
the authors forgot to add the protocol to the link href="www.lmfdb.org" should be href="http://www.lmfdb.org" http://www.lmfdb.org"

9mit3t2m9h9a 10y ago

I would say that «a mathematical universe» would be more correct here, because they just cover some of the areas; for example searching for «Ramsey» will yield no results; «probability» will yield just one result where an algebraic construction happens to be useful for calculating some probabilities.

gjulianm 10y ago
I don't know why it is being presented on the news as a catalog of the whole mathematics, when it is designed just a catalog of mathematical objects related to the Langlands Program [1] which is very broad as a mathematical theory (you don't usually find theories touching abstract algebra geometry, number theory and analysis) but of course does not consider all mathematical objects. 1: https://en.wikipedia.org/wiki/Langlands_program https://en.wikipedia.org/wiki/Langlands_program

nv-vn 10y ago

The idea is awesome, but it sort of loses its usefulness to people who aren't math experts. It's very clear by looking at the website that it's _not_ meant to be a Wikipedia for math. That's definitely not a bad thing, but I think that this website leaves an opening for something conceptually similar (but different in its implementation) that would be a sort of digital pathway through as many math concepts as possible -- for example, you can start on a page formalizing the idea of numbers and click links to navigate to addition, and then later on to multiplication, etc. allowing one to study math from the ground up. Or, you could start at a high-level concept and work your way down to the simple math. The purpose wouldn't be for researchers to better connect math, but for students trying to learn how math comes together in a broader sense. I think that a site like that could serve the same general purpose we see here of collecting math into a big catalog, just in a way that's more friendly to newcomers.

aardvark179 10y ago
Mathworld feels like it is part way to being the thing you want, but does mention Mathematica more than may be strictly necessary.
spuz 10y ago
There is something like this already called Wolfram Mathworld [1]. As a mathematical laymen trying to solve the problems on Project Euler, Mathworld would often give me the insight I needed to find an efficient solution so it is a great tool for students. [1] http://mathworld.wolfram.com/ http://mathworld.wolfram.com/
hasch 10y ago
as someone who has been at their workshops, there are ideas to do that. the goal is to have a semantic database, with a 3form ontology. look at these slides of the open dreamkit project: http://opendreamkit.org/meetings/2016-01-25-DKS/Kohlhase_slides.pdf http://opendreamkit.org/meetings/2016-01-25-DKS/Kohlhase_sli... ... somewhere there lmfdb should be mentioned
sn9 10y ago
I think that's called a university undergraduate math curriculum. You could look at the top n undergraduate math programs in your state and see what the flowchart of courses are and their corresponding syllabi and just go from there.

est 10y ago

Might be related, are there any websites where you can learn knowledge/skills like a Skill Tree/Perk Tree in games? I knew Duolingo had a design like that.

sp4ke 10y ago
+1 I would be interested by such platform/tool to learn math concepts
kachnuv_ocasek 10y ago
Doesn't Khan Academy have that?
- est 10y ago
  Does Khan Academy have some kind of test, so when I finish it will automatically assess by present abilities and activate corresponding skill icons?
  - lgas 10y ago
    Yes

dang 10y ago

This was discussed at https://news.ycombinator.com/item?id=11667487 https://news.ycombinator.com/item?id=11667487, but since the article gives more background, we won't treat the post as a dupe. (Submitted title was "Scientists Launched an Enormous Atlas of the Mathematical Universe", which was arguably editorialized and rather baity—please don't do that. We replaced it with a representative phrase from the article.)

ianpurton 10y ago

It's great when scientists do stuff.

iso-8859-1 10y ago

As a catalog of mathematical objects, it should be comparable to Metamath: http://de.metamath.org/index.html http://de.metamath.org/index.html But this project seems to be specific to number theory, and not really concerned with proofs at all. Where can I find the webcast mentioned?

thegp 10y ago

I wonder if it is possible to get a full dump of that db

mixedmath 10y ago
It is. It's open source, and the backend is closely tied to the free math software sagemath (sometimes called sage). In fact, the site sometimes generates the data on request through sage instead of filling in large databases of static objects.

brudgers 10y ago

Recent related discussion: https://news.ycombinator.com/item?id=11667487 https://news.ycombinator.com/item?id=11667487