Page 604 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 604
MATHEMATICS IN THE DIGITAL AGE OF SCIENCE (MS-50)
Infrastructure for mathematical data
Katja Bercˇicˇ, katja.bercic@fmf.uni-lj.si
University of Ljubljana, Slovenia
Producing and using data is becoming an increasingly useful part of doing mathematics. Unlike
large projects, such as the OEIS or LMFDB, small projects have less (or zero) infrastructural
support. Addressing this gap would be beneficial for the mathematical community, while fol-
lowing broader trends in research data, such as the FAIR principles. At the same time, improv-
ing the infrastructure for mathematical data has potential for synergy with proof assistants: on
one hand, the proof assistants might be able to use mathematical databases as sources of con-
crete examples or counterexamples, on the other, the correctness of the data could be at least
partially machine verified.
Digital Collections of Examples in Mathematical Sciences
James Davenport, masjhd@bath.ac.uk
University of Bath, United Kingdom
Examples, positive or negative, are the lifeblood of mathematics. This is particularly important
when there is generic behaviour, but also lots of special cases. For example, almost all polyno-
mials are irreducible, but nevertheless greeat effort is spent on factoring algorithms. A single
example can be represented in various ways, but collections of examples are more difficult. Not
that many collections exist, and those that do are often not in machine-processable forms. This
means that the sort of contest that has powered the SAT and SMT communities is not available
in general computer algebra, or many other fields of computational mathematics. We will make
some recommendations here.
Digitised Mathematics for the Working Mathematician
Klaus Hulek, simone.balogh@fiz-karlsruhe.de
Leibniz Universitaet Hannover, Germany
Mathematics has been both a driving force and a beneficiary of digitisation from the very be-
ginning. Computers entered mathematical institutes early on, enabling previously unattainable
calculations, and mathematical research literature was among the first to be made available
electronically. Extensive collections of mathematical objects have been available electronically
for decades. Platforms are widely used for collaborative work and for rapid dissemination and
discussion of results.
The rapid development of digitised resources comes along with enormous benefits and chal-
lenges for the working mathematician: In an increasingly fragmented ecosystem, how do we
ensure the completeness and reliability of mathematical knowledge essential for our research?
We outline solutions that became feasible due to the recent success of Open Access/Open Data
initiatives, and discuss which next steps might be the most useful to support the everyday work.
602
Infrastructure for mathematical data
Katja Bercˇicˇ, katja.bercic@fmf.uni-lj.si
University of Ljubljana, Slovenia
Producing and using data is becoming an increasingly useful part of doing mathematics. Unlike
large projects, such as the OEIS or LMFDB, small projects have less (or zero) infrastructural
support. Addressing this gap would be beneficial for the mathematical community, while fol-
lowing broader trends in research data, such as the FAIR principles. At the same time, improv-
ing the infrastructure for mathematical data has potential for synergy with proof assistants: on
one hand, the proof assistants might be able to use mathematical databases as sources of con-
crete examples or counterexamples, on the other, the correctness of the data could be at least
partially machine verified.
Digital Collections of Examples in Mathematical Sciences
James Davenport, masjhd@bath.ac.uk
University of Bath, United Kingdom
Examples, positive or negative, are the lifeblood of mathematics. This is particularly important
when there is generic behaviour, but also lots of special cases. For example, almost all polyno-
mials are irreducible, but nevertheless greeat effort is spent on factoring algorithms. A single
example can be represented in various ways, but collections of examples are more difficult. Not
that many collections exist, and those that do are often not in machine-processable forms. This
means that the sort of contest that has powered the SAT and SMT communities is not available
in general computer algebra, or many other fields of computational mathematics. We will make
some recommendations here.
Digitised Mathematics for the Working Mathematician
Klaus Hulek, simone.balogh@fiz-karlsruhe.de
Leibniz Universitaet Hannover, Germany
Mathematics has been both a driving force and a beneficiary of digitisation from the very be-
ginning. Computers entered mathematical institutes early on, enabling previously unattainable
calculations, and mathematical research literature was among the first to be made available
electronically. Extensive collections of mathematical objects have been available electronically
for decades. Platforms are widely used for collaborative work and for rapid dissemination and
discussion of results.
The rapid development of digitised resources comes along with enormous benefits and chal-
lenges for the working mathematician: In an increasingly fragmented ecosystem, how do we
ensure the completeness and reliability of mathematical knowledge essential for our research?
We outline solutions that became feasible due to the recent success of Open Access/Open Data
initiatives, and discuss which next steps might be the most useful to support the everyday work.
602
