Some irksome phrases that appear on the web

Jimmy Wales is the co-founder of Wikipedia. Of course this is the wonderful online non-profit encyclopedia we all know and love.

Today I want to talk about using the web to search for math information.

I do a huge amount of research on the web. Years ago I would spend hours and hours each week in the library. I looked for books and articles on various math issues. No more. Today it’s all web-based resources. What has happened is that primary sources—research papers—have become as easily browsable as Wikipedia. Many of them, anyway.

Wikipedia often does not include proofs of mathematical theorems—those are linked to primary papers or authoritative surveys or books. There is a website Proof Wiki which tries to bridge the gap without the reader needing to follow links into papers. Right now they are featuring Euclid’s Theorem on the infinitude of primes—which we have posted about recently and before. They have style guides for how the reasoning is laid out.

There are also many style guides around the web for writing good mathematics and computer science papers. But the guides seem to stop short of the level of the phrases that irk me. When those phrases show up in the primary sources, there’s no fallback. Let’s take a look.

The Phrases

Here are a few top ones. I omit the well known ones, the ones that are obvious, and some that are in preparation for a future post—just kidding.

It is well known. Not by me. The reason I am searching for papers on this subject is that I do not know the basics of the area. If you must say this phrase please add a possible reference. That would be extremely helpful.

Clear from the proof of the theorem. Not by me. This means that the author did not state the proof in the greatest generality possible. We all do this, but it may help if this is avoided.

It is easy to see. Similar to the last item. Ken vividly remembers a seminar in the early 1980s by Peter Neumann at Oxford that showed excerpts from a French mathematician in which the phrase “Il est aisé de voir” appeared often. The French phrase even reads just like the English one. But that mathematician had a reasonable excuse. He was Évariste Galois, and he had a duel early the next morning.

Proof omitted. Please no.

Easy calculation. Not by me. The reason it usually is avoided is that it is too difficult a computation.

This case is the same as the previous case. Not always. This has been the source of errors for me and others over the years. Good place to check the argument. Maybe a suggestion that there should be a Lemma that covers both cases.

In our paper in preparation. Please no. I cannot read a paper that does not exist yet.

Finally the worst in my opinion.

It costs $37.95. Oh no. Many times we find papers that are behind a pay-wall. I always hate this. The authors of course wish to make they work available to all possible. But the reality is that often papers are protected. Thanks to our friends at Wikipedia and Arxiv that this is not the case for lots of stuff.

But I have wondered who ever pays the crazy amount of $37.95? Does anyone ever pay that? Is it equivalent to saying: This paper is not available.

Ken’s Examples

Ken has one example that has driven him crazy for years and again these past two weeks. Many of you have probably used it often.

This procedure runs in polynomial time. Excuse me, what polynomial time? At least tell us the best exponent you know…

A related matter is attending to “edge cases” of theorems. Sometimes the edge cases are meant to be excluded. For example, “Let ” excludes ; maybe nothing more needs to be said. But in other cases it is not so clear. A theorem may suggest limits and it is nice to say what happens if one tries to take those limits.

Open Problems

What are you favorite phrases that drive you crazy?