In this talk we present the current state of the art of the Mathematical Grammar Library, a software library for the GF system, that allows to render mathematics in many natural languages while maintaining the underlying semantics of the expression. The work is being done in the EU project MOLTO.

1. A grammar-based approach
to multilingual mathematics
Jordi Saludes, Olga Caprotti, Sebastian Xambó-Descamps
UPC, Barcelona
5th International Workshop on Mathematical e-Learning, 4-5 April 2013. UNED, Madrid (Spain).
1Monday, April 8, 13

2. Non multa, sed multum
MOLTO - Multilingual Online Translation
❖ 36+3 months
❖ start:1/3/2010
❖ start EEU: 1/1/2012
❖ end: 31/5/2013
❖ 2.395000+ 600000 €
2Monday, April 8, 13

3. MOLTO-EEU
a larger Consortium
❖ approved on 7/12/2011
❖ 2 new countries/
languages:
❖ Be Informed (NL)
❖ Uni Zürich (CH)
❖ 2 new use cases:
❖ decision making system
❖ multilingual semantic
wikis
3Monday, April 8, 13

4. Quick list
All deliverables (not updated)
http://www.molto-project.eu/view/biblio/deliverables
4Monday, April 8, 13

5. Any language, whether formal or natural, is the
basic tool for reasoning and communicating
(with a fellow or a machine) along time and
across space
Along time: archival publications
Across space: crossing borders (mental borders too :),
disciplines or mental frameworks)
Multilingual, natural, mathematical language
Use case: Mathematics
5Monday, April 8, 13

6. Thinking, speaking and writing
are core competencies
A professional thinks, speaks, and writes in a
specialized language, the level of expertise is
o3en noticed by the kind of language
employed.
from the point of view of language learning
Education
6Monday, April 8, 13

7. A QUESTION TO THE EDUCATORS
Lately we seem to pay no effort to translating:
foreign jargon abounds.
WHY?
global market
what about
local communities of practice?
new areas of research and development?
7Monday, April 8, 13

8. Naming abstract objects
and proving statements
about them is the job of a
mathematician.
A mathematician compiles
a dictionary in his/her area
of research.
Symbolic lexicographers
Mathematicians are lexicographers, too
8Monday, April 8, 13

9. CLAIM:
Some notation we commonly use is o3en remnant
of the original definition
Let K be a field - where K is short for Körper
Q, the set of Rationals - Q for “quoziente” (Peano)
Z, the set of Integers - for Zahlen
(http://jeff560.tripod.com/nth.html)
Common math notation
Inklings of translations
9Monday, April 8, 13

10. The set of fractions Q
Die Menge der Brücke Q
10Monday, April 8, 13

11. WebALT - Web Advanced Learning Technologies (EDC-22253, 2005-2008)
Yet it is multilingual
Mathematics is universal
First release of a Mathematical Grammar Library based on GF
11Monday, April 8, 13

12. Jordi Saludes will demonstrate
✴ online mathematical translator
✴ word problem tutor
Mathematical Grammar Library
Demo
12Monday, April 8, 13