Archive for the ‘Mathematics Indexing’ Category

Symbolab

Tuesday, January 15th, 2013

Symbolab

Described as:

Symbolab is a search engine for students, mathematicians, scientists and anyone else looking for answers in the mathematical and scientific realm. Other search engines that do equation search use LaTex, the document mark up language for mathematical symbols which is the same as keywords, which unfortunately gives poor results.

Symbolab uses proprietary machine learning algorithms to provide the most relevant search results that are theoretically and semantically similar, rather than visually similar. In other words, it does a semantic search, understanding the query behind the symbols, to get results.

The nice thing about math and science is that it’s universal – there’s no need for translation in order to understand an equation. This means scale can come much quicker than other search engines that are limited by language.

From: The guys from The Big Bang Theory will love mathematical search engine Symbolab by Shira Abel. (includes an interview with Michael Avny, the CEO of Symbolab.

Limited to web content at the moment but a “scholar” option is in the works. I assume that will extend into academic journals.

Focused now on mathematics, physics and chemistry, but in principle should be extensible to related areas. I am particularly anxious to hear they are indexing CS publications!

Would be really nice if Springer, Elsevier, the AMS and others would permit indexing of their equations.

That presumes publishers would realize that shutting out users not at institutions is a bad marketing plan. With a marginal delivery cost of near zero and sunk costs from publication already fixed, every user a publisher gains at $200/year for their entire collection is$200 they did not have before.

Not to mention the citation and use of their publication, which just drives more people to publish there. A virtuous circle if you will.

The only concern I have is the comment:

The nice thing about math and science is that it’s universal – there’s no need for translation in order to understand an equation.

Which is directly contrary to what Michael is quoted as saying in the interview:

You say “Each symbol can mean different things within and across disciplines, order and position of elements matter, priority of features, etc.” Can you give an example of this?

The authors of the Foundations of Rule Learning spent five years attempting to reconcile notations used in rule making. Some symbols had different meanings. They resorted to inventing yet another notation as a solution.

Why the popular press perpetuates the myth of a universal language isn’t clear.

It isn’t useful and in some cases, such as national security, it leads to waste of time and resources on attempts to invent a universal language.

The phrase “myth of a universal language” should be a clue. Universal languages don’t exist. They are myths, by definition.

Anyone who says differently is trying to sell you something, Something that is in their interest and perhaps not yours.

I first saw this at Introducing Symbolab: Search for Equations by Angela Guess.

23 Mathematical Challenges [DARPA – A Modest Challenge]

Tuesday, August 28th, 2012

23 Mathematical Challenges [DARPA]

From the webpage:

Discovering novel mathematics will enable the development of new tools to change the way the DoD approaches analysis, modeling and prediction, new materials and physical and biological sciences. The 23 Mathematical Challenges program involves individual researchers and small teams who are addressing one or more of the following 23 mathematical challenges, which if successfully met, could provide revolutionary new techniques to meet the long-term needs of the DoD:

• Mathematical Challenge 1: The Mathematics of the Brain
• Mathematical Challenge 2: The Dynamics of Networks
• Mathematical Challenge 3: Capture and Harness Stochasticity in Nature
• Mathematical Challenge 4: 21st Century Fluids
• Mathematical Challenge 5: Biological Quantum Field Theory
• Mathematical Challenge 6: Computational Duality
• Mathematical Challenge 7: Occam’s Razor in Many Dimensions
• Mathematical Challenge 8: Beyond Convex Optimization
• Mathematical Challenge 9: What are the Physical Consequences of Perelman’s Proof of Thurston’s Geometrization Theorem?
• Mathematical Challenge 10: Algorithmic Origami and Biology
• Mathematical Challenge 11: Optimal Nanostructures
• Mathematical Challenge 12: The Mathematics of Quantum Computing, Algorithms, and Entanglement
• Mathematical Challenge 13: Creating a Game Theory that Scales
• Mathematical Challenge 14: An Information Theory for Virus Evolution
• Mathematical Challenge 15: The Geometry of Genome Space
• Mathematical Challenge 16: What are the Symmetries and Action Principles for Biology?
• Mathematical Challenge 17: Geometric Langlands and Quantum Physics
• Mathematical Challenge 18: Arithmetic Langlands, Topology and Geometry
• Mathematical Challenge 19: Settle the Riemann Hypothesis
• Mathematical Challenge 20: Computation at Scale
• Mathematical Challenge 21: Settle the Hodge Conjecture
• Mathematical Challenge 22: Settle the Smooth Poincare Conjecture in Dimension 4
• Mathematical Challenge 23: What are the Fundamental Laws of Biology?

(Details of each challenge omitted. See the webpage for descriptions.)

Worthy mathematical challenges all but what about a more modest challenge? One that may help solve a larger one?

Such as cutting across the terminology barriers of approaches and fields of mathematics to collate the prior, present and ongoing research on each of these challenges?

Not only would the curated artifact be useful to researchers, but the act of curation, the reading and mapping of what is known on a particular problem, could spark new approaches to the main problem as well.

DARPA should consider a history curation project on one or more of these challenges.

Could produce a useful information artifact for researchers, train math graduate students in searching across approaches/fields, and might trigger a creative insight into a possible challenge solution.

I first saw this at Beyond Search: DARPA May Be Hilbert

Text Mining Methods Applied to Mathematical Texts

Saturday, July 14th, 2012

Text Mining Methods Applied to Mathematical Texts (slides) by Yannis Haralambous, Département Informatique, Télécom Bretagne.

Abstract:

Up to now, flexiform mathematical text has mainly been processed with the intention of formalizing mathematical knowledge so that proof engines can be applied to it. This approach can be compared with the symbolic approach to natural language processing, where methods of logic and knowledge representation are used to analyze linguistic phenomena. In the last two decades, a new approach to natural language processing has emerged, based on statistical methods and, in particular, data mining. This method, called text mining, aims to process large text corpora, in order to detect tendencies, to extract information, to classify documents, etc. In this talk I will present math mining, namely the potential applications of text mining to mathematical texts. After reviewing some existing works heading in that direction, I will formulate and describe several roadmap suggestions for the use and applications of statistical methods to mathematical text processing: (1) using terms instead of words as the basic unit of text processing, (2) using topics instead of subjects (“topics” in the sense of “topic models” in natural language processing, and “subjects” in the sense of various mathematical subject classifications), (3) using and correlating various graphs extracted from mathematical corpora, (4) use paraphrastic redundancy, etc. The purpose of this talk is to give a glimpse on potential applications of the math mining approach on large mathematical corpora, such as arXiv.org.

An invited presentation at CICM 2012.

I know Yannis from a completely different context and may comment on that in another post.

No paper but 50+ slides showing existing text mining tools can deliver useful search results, while waiting for a unified and correct index to all of mathematics. 😉

Varying semantics, as in all human enterprises, is an opportunity for topic map based assistance.

Conferences on Intelligent Computer Mathematics (CICM 2012)

Saturday, July 14th, 2012

Conferences on Intelligent Computer Mathematics (CICM 2012) (talks listing)

From the “general information” page:

As computers and communications technology advance, greater opportunities arise for intelligent mathematical computation. While computer algebra, automated deduction, mathematical publishing and novel user interfaces individually have long and successful histories, we are now seeing increasing opportunities for synergy among these areas.

The conference is organized by Serge Autexier (DFKI) and Michael Kohlhase (JUB), takes place at Jacobs University in Bremen and consists of five tracks

The overall programme is organized by the General Program Chair Johan Jeuring.

Which I located by following the conference reference in: An XML-Format for Conjectures in Geometry (Work-in-Progress)

A real treasure trove of research on searching, semantics, integration, focused on computers and mathematics.

Expect to see citations to work reported here and in other CICM proceedings.

Workshop on Mathematical Wikis (MathWikis-2011)

Monday, May 23rd, 2011

Workshop on Mathematical Wikis (MathWikis-2011)

Important Dates:

• Submission of abstracts: May 30th, 2011, 8:00 UTC+1
• Camera ready versions due: July 11th, 2011
• Workshop: August 27th, 2011

From the website:

Mathematics is increasingly becoming a collaborative discipline. The Internet has simplified the distributed development, review, and improvement of large proofs, theories, libraries, and knowledge repositories, also giving rise to all kinds of collaboratively developed mathematical learning resources. Examples include the PlanetMath free encyclopedia, the Polymath collaborative collaborative proof development efforts, and also large collaboratively developed formal libraries. Interactive computer assistance, semantic representation, and linking with other datasets on the Semantic Web are becoming very interesting aspects of collaborative mathematical developments.

The ITP 2011 MathWikis workshop aims to bring together developers and major users of mathematical wikis and collaborative and social tools for mathematics.

Topics include but are not limited to:

• wikis and blogs for informal, semantic, semiformal, and formal mathematical knowledge;
• general techniques and tools for online collaborative mathematics;
• tools for collaboratively producing, presenting, publishing, and interacting with online mathematics;
• automation and computer-human interaction aspects of mathematical wikis;
• practical experiences, usability aspects, feasibility studies;
• evaluation of existing tools and experiments;
• requirements, user scenarios and goals.

Busses Come In Threes, Why Do Proofs Come In Two’s? – Post

Saturday, March 19th, 2011

Busses Come In Threes, Why Do Proofs Come In Two’s?

Dick Lipton, at Gödel’s Lost Letter explores:

Why do theorems get proved independently at the same time

Jacques Hadamard and Charles-Jean de laVallée Poussin, Neil Immerman and Robert Szelepcsenyi, Steve Cook and Leonid Levin, Georgy Egorychev and Dmitry Falikman, Sanjeev Arora and Joseph Mitchell, are pairs of great researchers. Each pair proved some wonderful theorem, yet they did this in each case independently and at almost the same time.

Interesting in its own right but I mention here to raise the issue of the use to topic maps to bridge the use of different nomenclatures.

Would that increase the incidence of discovery of independent proofs of theorems?

Even harder to answer: Would bridging different nomenclatures increase the incidence of independent proofs of theorems?

Thinking that all such proofs need not be of famous theorems.

Could have independent proofs of lesser theorems as well.

The 2010 Mathematics Subject Classification is no doubt very useful but too crude to assist in the discovery of duplicate proofs (or beyond general areas to look) proofs altogether.