Collaborative Mathematics

Mathematics is a collective work shaped over the centuries through collaborations, whether to produce knowledge or publications. But for less than a century, practices have been revolutionized. The isolated researchers of the past are increasingly being replaced by teams with varied skills, enabling new effective approaches. Massively collaborative research of results is also made possible by the Internet and instant communication tools. Pal Erdös was one of the pioneers of this movement of which the brilliant mathematician Tim Gowers is today one of the driving forces. But knowledge sharing also happens with the general public, thanks to popularization efforts and the commitment to allow free access to research articles. Collaborative free software is emerging, as are multi-author websites like Wikipedia. Large-scale knowledge sharing: the Ancients dreamed of it, our era is implementing it!

They are the driving force of mathematics. Those that spark curiosity, tease researchers and trigger breakthroughs. Who are they? Open problems, conjectures, hypotheses! The many conjectures that pepper their history, such as Goldbach's in number theory, Toeplitz's in geometry or Poincaré's in topology, are examples. Conjectures, once solved, call for others creating an endless chain of knowledge progression. A conjecture is a result that is suspected, for which no counterexample has been found, but which is not proven. In an open problem, on the other hand, the sought result is not known. All branches of mathematics are full of them: topology, combinatorics, analysis, probability, statistics... Even in geometry, objects as simple as polyhedron nets still escape our understanding!