Here’s a round up of some other recent (and now less so) news stories we didn’t cover in full.
13 New 3-body orbits discovered
Physicists from the University of Belgrade have discovered numerically 13 new solutions to the 3-body problem, in 2 dimensions. Described as “quite a feat in mathematical physics”, the discovery makes progress towards the long-standing problem of determining how three particles, when left to move under the action of their gravity on each other, will behave. The solutions they’ve found are all for particles moving in a 2-dimensional plane, and are represented using points on the surface of a sphere to describe the position of the three particles.
Claimed disproof of the Triangulation Conjecture
The Triangulation Conjecture, a result in topology, may turn out to be false as UCLA’s Ciprian Manolescu claims to have disproved it. The conjecture claims that every compact topological manifold can be triangulated by a locally finite simplicial complex, which means that, roughly, any surface (well, n-dimensional surface) can be divided into triangles in a specific way that topologists find exciting. The conjecture has already been disproved in dimension 4, although hope was held it might be true in higher dimensions. We’re still waiting for confirmation the disproof is correct, but if it is it wipes out many topologists’ hopes of being able to divide certain types of surfaces into triangles in a specific way.
Blog post on the topic, with an interesting comments discussion
(via Dave Richeson on Twitter)
Math Cannot be Patented
A patent suit filed in the Eastern District of Texas has been dismissed on the grounds that mathematics cannot be patented. Uniloc, described in an article on news blog Rackspace as ‘a notorious patent troll’, alleged that a floating point numerical calculation by the Linux operating system violated U.S. Patent 5,892,697. You can’t patent maths!
Mathematics Cannot Be Patented – Case Dismissed at Rackspace
Transactions of the LMS: an open access journal
Fans of Open Access journals will be pleased to hear that the London Mathematical Society is launching one, titled Transactions of the London Mathematical Society. The LMS would like to emphasise that:
By launching this journal, the LMS is not promoting any particular cause and we do not advocate one publishing payment model over another.
Details can be found on pages 8-11 of their most recent newsletter.
Thank you!
Comment: I’m not sure that a non-locally finite triangulation counts as a triangulation, because a CW complex (a-fortiori a manifold) has closures of cells meeting finitely many other cells. So it seems to me that the triangulation conjecture can be roughly restated as “you can build any shape (= compact n-dimensional topological manifold”) out of a lego set whose blocks are all simplices (= higher dimensional triangles)”. I think people have strongly suspected that this is false for a long time (at least since Galewski-Stern) because the menagerie of shapes has proved richer than people at first imagined, and you’d expect more variety in higher dimensions rather than less (and the degree 4 counterexample was known for a long time). Finding a shape which can’t be triangulated (and thus disproving the conjecture) was another matter entirely, of course.
So I think of Cyprian’s proof as the observation of a strange and wonderful species whose existence has long been suspected, but which has never before been observed by humans.
This is a preprint, so it needs peer review for confirmation like any other preprint- but I don’t know of any serious challenges to its correctness, so I don’t know if one needs be so cautious.