Oct 26 2015: Fill & Download for Free

Falling apart?There are signs when a campaign is falling apart. Things like big shakeups in staff, cuts in salary, firing of people, cuts in budget for ads and stuff, big changes in "message" .....Bernie's campaign has (as of Oct 26, 2015) exhibited none of those things.Now, Jeb Bush, on the other hand ....

July 15 2015 was my first day on Quora.I answered a question.Gopalkrishna Vishwanath's answer to What is the explanation behind liking blank papers/notebooks as writing material more than lined ones?Result: Deafening silence! No views except mine. No upvotes.After a week it gained 5 views and 0 upvotes.It was so discouraging that for the next two months, I did not write but merely read.It was only on Sept 15 and Sept 16th 2015 that I made two more attempts.They fared no better. Less than 10 views and no upvotes.I tried again 10 days later on Sept 26thNo luck.I tried once again on Oct 26. I tasted some success finally. I don’t remember how many views it had but it was encouraging.I started posting regularly everyday thereafter.I finally tasted success on Nov 9th 2015 with my first answer that got thousands of views and over 1700 upvotes.I am writing all this to encourage newcomers who constantly write to me asking why they are not getting views and upvotes.It takes time, and patience and some luck too to get noticed here even if you write well.GV

I’m afraid this comes through more like a grievance than a genuine question. Taken at face value, the answer is:People don’t make their papers cryptic and impossible to follow. They strive to make them readable to their intended audience. Not everyone is equally talented at lucid writing, but everyone does their best. Very, very few people in math deliberately choose to write pompously or obscurely. You may be thinking of continental philosophy, or literary criticism.Math journals don’t love cryptic papers that are impossible to follow. The editors and referees must understand the paper, and want it to be interesting and attractive to their readers.Here are the first few paragraphs from a recent paper[1] by Ellenberg, Pierce and Wood on [math]\ell[/math]-torsion in class groups of number fields.IntroductionThe distribution of class groups is a great mystery. The Cohen–Lenstra heuristics [Cohen and Lenstra 1984] (for quadratic fields) and the Cohen–Lenstra–Martinet heuristics [Cohen and Martinet 1990] (for more general number fields) make predictions for the distribution of class groups, including for the average size of the [math]\ell[/math]-torsion subgroups for certain “good” primes. However, the questions of proving anything towards these predictions are almost entirely open, and mostly apparently inaccessible.The main goal of the present work is to prove, for each integer [math]\ell \ge 1[/math], an unconditional upper bound for the size of the [math]\ell[/math]-torsion subgroup of the class group, which holds for all but a zero-density set of field extensions of [math]\Q[/math] of degree [math]d[/math], for any fixed [math]d \in \{2,3,4,5\}[/math] (with the additional restriction in the case [math]d=4[/math] that the field be non-[math]D_4[/math]). Alternatively, these results may be viewed as the first unconditional upper bounds for the average size of [math]\ell[/math]-torsion in class groups as the field varies over extensions of [math]\Q[/math] of fixed degree [math]d \in \{2,3,4,5\}[/math] (and non-[math]D_4[/math] in the case [math]d=4[/math]).Check out the opening sentence: “The distribution of class groups is a great mystery”. It is short, inviting, even exciting. Could it have been written more clearly?Now, Ellenberg is a wonderful writer and the published author of a novel and a successful book about mathematical reasoning for the general public. Here, however, he and his coauthors are writing an ordinary mathematical paper, meant for a professional audience. It’s laden with jargon, and it needs to be: it talks about class groups of number fields, and it assumes the reader is familiar with class groups of number fields.Setting terminology aside, those paragraphs clearly describe what they’re doing and why. There’s nothing “cryptic” or “impossible to follow” here or in the rest of the paper. For example, after presenting a previous result of Davenport and Heilbronn (equation 1–5), they take the trouble to explain where the two terms in the formula come from. They don’t have to do that, but they do, and it’s very illuminating – the formula might otherwise seem quite mysterious.Academic writing is often accused of obscurantism, and I believe this claim has a lot of merit. See, for instance, Why Is Academic Writing So Needlessly Complex? by Victoria Clayton (The Atlantic, Oct. 26, 2015). You will observe, however, that such criticism is leveled at publications in History, Philosophy, English or Political Science, and almost never at Math or Physics. Quite simply, the complexity in Math and Physics is real, not needless.Take a look at papers in Social Text, for instance. You may be left with a nagging feeling that a lot of what is said could have been said more simply.Footnotes[1] Algebra & Number Theory Vol. 11, No. 8, 2017