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Atlas of Mathematical Objects (lmfdb.org)
174 points by rotrux on May 10, 2016 | hide | past | web | favorite | 37 comments

Here is a Numberphile video [1] that explains - at the very end - why this database was put together.

[1] https://www.youtube.com/watch?v=VTveQ1ndH1c

I was wondering how it was built since equations aren't the nicest things to render with HTML. A quick 'view source' shows the site is using MathJax (not MathML) for displaying the equations.

I presume a lot of content is submitted or formatted using Tex/Latex. Can any HN'ers elaborate on the workflow for review/editing/publishing on the site?

The simple reason for mathjax is,that it is the only one that has many of the required features and it works across browsers. MathML can't deliver any of that...

Thanks for that link. In one of the MD files[0], I found information on the editorial board.

[0] https://github.com/LMFDB/lmfdb/blob/master/Development.md#ba...

…in Number Theory.

Also: license is GPLv2+, so they seem to think this is software. That makes some sense.

(And moderators, please fix that typo; mathmatical is spelled with an 'e')

Calculating the data makes extensive use of http://www.sagemath.org/, which is GPL'd; moreover, the LMFDB contributors also contribute a lot to SageMath.

Timothy Gowers (Fields Medalist and open publishing advocate) just wrote a blog post about this: https://gowers.wordpress.com/2016/05/10/the-l-functions-and-...

In general, what is a mathematical object? Is the natural numbers one?

It's just a informal term for the things mathematicians study. So the natural numbers are mathematical objects, as well as a set, a function, a manifold, a vector space, etc.

This is actually a surprisingly complex question in mathematical philosophy -- I unfortunately can't find a copy online right now, but if the idea of mathematical objects interests you I'd highly recommend Paul Benacerraf's 1965 paper "What Numbers Cannot Be", which explores the complexity of the idea of even a single integer as an "object".

For those interested, the article is actually called "What Numbers Could not Be" (many references have "What Numbers Cannot Be" so maybe it was published under both names at some point?)

There is a copy at:


Thank you! I just checked my copy of Cambridge's Philosophy of Mathematics and it is indeed "could not" -- the PDF I have on my laptop, however, is "cannot". I wonder when/where that happened.

Thanks for posting that!

I think, it's an instance of a mathematical "idea". E.g. 7 is an object of the idea "prime numbers".

A bit disappoint by the narrow point of view. Atlas of Number Theoretical Objects would have been more appropriate. Still nice, though.

The site could use a better name. But presumably there's no reason the interface and cataloguing system can't be extended to other domains.

What are some specific examples of other types of objects you would like to see.

All the finite simple groups would be nice, for example.

I assume you mean the sporadic groups? Because the families are all unbounded.

There's also this: http://brauer.maths.qmul.ac.uk/Atlas/v3/

Not criticizing or anything, just curious: What is the difference/advantage with respect to Wikipedia or Wolfram Mathworld?

Mathworld has broader scope and a tighter license (http://mathworld.wolfram.com/about/faq.html#copyright)

LMFDB contains a large amount of extremely difficult to compute data about mathematical functions that arise in number theory, which took decades to compute and debug, and relations between that data. Just as hundreds of gigabytes of detailed astronomical data is not in Wikipedia or Wolfram Mathworld, this data about number theory is not in Wikipedia or Wolfram Mathworld either, and it never will be.

I should add that behind the scenes LMFDB really is a (MongoDB) database, there's an API that @hasch (here on HN) wrote, so that data can be recovered in JSON format, etc. To give some sense of what is in there, this http://johncremona.github.io/ecdata/ is just a tiny bit of what is in LMFDB.

LMFDB is more specialized. But given an infinite amount of time, the others would acquire that information.

Someday we will draw the link between this area/program and AI. There's something deep here that has implications I don't think we understand.

Stephen Wolfram has suggested something along these lines (more in the context of machine learning than AI, per se).

I don't understand why there is an "MIT" in the title.

It stands for "Mathematical Is Terribly-hard-to-spell"

Thanks—fixed. No more "MIT" in title either.

It was there before because one of the LMFDB contributors (Andrew Sutherland) is at MIT.

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