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OpenDreamKit: the mathematician's perspective
# OpenDreamKit

The mathematician's perspective

Some fundamental trends

Long standing and booming role of computers in pure mathematics

  • Computer exploration
  • Conjecture verification
  • Mechanized proofs
  • Proof assistants and certified proofs
  • Collaborative work
  • Education

--

Open Science getting momentum

Open science is the movement to make scientific research, data and dissemination accessible to all levels of an inquiring society, amateur or professional

  • Open Knowledge (Access, Educational Ressources)
  • Open Source or better Free Software
  • Open Data
  • Open Peer Review, Methodology, ...

At the core of science for centuries. Finally getting recognition as viable and necessary, even by funding agencies!

--

Emergence of a vibrant ecosystem of free software for pure mathematics

Viable alternatives to Maple, Mathematica, Matlab, ...

For research and education (and the industry?)

Virtual Research Environments (VRE)?

Definition from the call of the H2020 European Research Infrastructures Work Programme:

Groups of researchers, typically widely dispersed who are working together through ubiquitous, trusted and easy access to services for scientific data, computing, and networking, in a collaborative virtual environment

--

VRE for mathematics?

Mathematicians are already immersed in a multitude of virtual environments to collaborate on

  • Software

  • Data

  • Knowledge

--

The next frontier?

  • Improve the productivity of researchers in pure mathematics and applications by further promoting collaborations on Data, Knowledge, and Software

  • Make it easy for teams of researchers of any size to set up custom, collaborative Virtual Research Environments tailored to their specific needs, resources and workflows

  • Support the entire life-cycle of computational work in mathematical research, from initial exploration to publication, teaching, and outreach

--

A tension:

  • Mathematicicans want a seamless user experience while interacting with mathematics

  • Implementing a one-size-fits-all VRE is intractable

An approach

Building a math VRE toolkit based on:

  • The ecosystem of open source math software

  • Open collaborative tools and models

Architecture:

  • Collaborative workspaces (e.g. JupyterHub, SageMathCloud)
  • User interfaces (e.g Jupyter notebook)
  • Computational components (e.g. Linbox, PARI/GP, GAP, Sage, Singular, ...)
  • Data / knowledge bases (e.g. OEIS)
  • Physical resources (e.g. cloud infrastructure)

--

Added values

  • Customizability for a variety of use cases:

    • A single person installation on a laptop
    • A collaborative VRE between three researchers, running on their lab's server
    • A university wide VRE for teaching
    • Service provided by a european grid infrastructure

  • Joining forces with the wider scientific computing community

  • Lowering the software barrier between pure and applied maths

  • Modularity, sustainability

How to get there?

--

Component architecture (WP3)

  • Goal: ease of deployment. Requires:

    • Modularity, packaging, portability, distribution
    • For individual components and combinations thereof

  • Development workflows in ecosystems of software

--

User interfaces (WP4)

  • Jupyter as uniform notebook interface

  • Improving Jupyter (collaboration, 3D, ...)

  • Coordination SageMathCloud / JupyterHub

  • Collaborative, reproducible, active documents

--

Performance (WP5)

  • Goal: Make the most of available hardware

    • multicore
    • HPC
    • cloud

  • For individual computational components and combinations thereof

--

Data/Knowledge/Software (WP6)

  • Goal: enable rich and robust interaction between

    • computational components
    • data bases
    • knowledge bases
    • users

  • This requires:

    • explicit common semantic spaces
    • a language to express them
    • tools to leverage them

--

Community building and dissemination (WP2)

  • Developer Workshops

  • Training workshops

  • Conferences

--

Social aspects (WP7)

  • Analysis of user needs

  • Research on collaborative software development in mathematics

OpenDreamKit (2015-2019)

Open Digital Research Environment Toolkit for the Advancement of Mathematics

OpenDreamKit.org

--

A user-driven consortium

European power users and core developers of the ecosystem of open source software for Mathematics:

  • GAP (St Andrews, Oxford)
  • Linbox (Grenoble)
  • PARI/GP (Bordeaux, Versailles)
  • Sage (Bordeaux, Grenoble, Paris Sud, Oxford, Versailles)
  • Singular (Kaiserslautern)
  • LMFDB (Warwick, Zürich)
  • MathHub, MMT/OpenMath (Bremen)
  • Jupyter (Simula)
  • Scientific Python (SouthHampton, Sheffield, Silesia)

-- Supported by:

  • Research engineers
  • An open source based company (Logilab)

How are we doing?

--

The bad news

  • Some tasks harder than expected

  • We expected recruitment to be hard. It really was.

  • We exected the admistrative overhead to be high. It really is.

--

The good news

  • Intensive work started on all fronts

    • Current deliverables not representative

  • Some really good recruitement

  • Joint workshops are very effective

  • Interesting technology raising

    • Windows support for Linux apps

--

Ways to improve?

  • There could be more interactions in certain areas

  • Some workpackages could benefit from more animation

  • More workshops / joint visits / online meetings?

More reading