Jargon file not even wrong
These are typically written at a high level, but are also accessible enough so that a typical reader can understand what has been accomplished. In addition to the formal research papers, they also have research summaries. Compare this to a journal like Science or Nature. A typical research journal in mathematics is just a stack of papers between covers. Submit a paper with two consecutive sentences of exposition and watch how quickly the referee gets on you for it. Making matters worse is a mathematical culture that favors brevity and concision far, far more than it does clarity. In math, it is usually impossible even to explain the problem to a non-mathematician. In evolutionary biology I am definitely an amateur, but I find that I can often understand the introduction and discussion sections of a typical paper well enough to explain the gist to someone else. As in, you won't make it past the first sentence.īiology certainly is not as bad. The abstract of a typical research paper in mathematics is opaque not just to non-mathematicians, but to all mathematicians who are not specialists in the particular research area being addressed. I would say, though, that math is probably among the worst offenders. Of course, jargon is an affliction common to just about every academic discipline, and not just in the sciences. For myself, I can recognize it as having something to do with differential topology, and there are a few phrases in there with which I am familiar, but I'd be hard-pressed to tell you what the paper is actually about. Now, the first thing I would point out is that this abstract would be opaque to most mathematicians as well. Or are our own biology abstracts just as opaque to mathematicians?” He then remarks, “This shows how far removed mathematics is from even other scientists. A conjecture regarding the nontriviality of the higher-order Arf invariants is formulated, and related implications for filtrations of string links and 3-dimensional homology cylinders are described. Together with Milnor invariants, these higher-order invariants are shown to classify the existence of (twisted) Whitney towers of increasing order in the 4-ball. We also define higher-order Sato-Levine and Arf invariants and show that these invariants detect the obstructions to framing a twisted Whitney tower. For Whitney towers on immersed disks in the 4-ball, we identify some of these new invariants with previously known link invariants such as Milnor, Sato-Levine, and Arf invariants.
JARGON FILE NOT EVEN WRONG HOW TO
We show how to measure the failure of the Whitney move in dimension 4 by constructing higher-order intersection invariants of Whitney towers built from iterated Whitney disks on immersed surfaces in 4-manifolds. Jerry Coyne calls our attention to this abstract, from a recent issue of Proceedings of the National Academy of Sciences: