Some irksome phrases that appear on the web

 [ Jimmy Wales ]

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.

${\bullet }$ 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.

${\bullet }$ 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.

${\bullet}$ 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.

${\bullet }$ Proof omitted. Please no.

${\bullet }$ Easy calculation. Not by me. The reason it usually is avoided is that it is too difficult a computation.

${\bullet }$ 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.

${\bullet }$ In our paper in preparation. Please no. I cannot read a paper that does not exist yet.

Finally the worst in my opinion.

${\bullet }$ 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.

${\bullet}$ 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 ${\alpha > 0}$” excludes ${\alpha = 0}$; 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?

1. February 28, 2019 10:10 am

The phrase “without loss of generality” can get on my nerves. Often, we can substitute “this is where I wave my hands” without losing meaning. I would much appreciate it if you would care to tell me _why_ we do not lose generality. But it can get worse: “we can assume X without loss of generality, because X holds for all real world objects.”. Here, the phrase “without loss of generality” means the _opposite_ of the true meaning: we are losing generality, in the sense that we may only choose objects from the “real world”. (incidentally, “real world objects” is also a terrible phrase. What sort of objects are used in the real world depends on how theoretical systems are (mis)used. What they mean to say is that they know that in their particular application, X holds. It is inaccurate and a sign of arrogance to presume that this is the only way your theory will get applied)

2. February 28, 2019 11:36 am

The classic from textbooks, “the proof is left to the reader.”

February 28, 2019 12:56 pm

Similar to “It is well known”, I really hate it when people refer to “folklore results” and do not put a reference or a proof sketch.

February 28, 2019 2:24 pm

If an academic paper is behind a pay-wall, one option is to email the authors and ask for a copy. They may send one.

• March 2, 2019 1:35 am

Ideally, this shouldn’t be the point. The point is to use a reference-crawling bot (i.e. written in Perl) to extract a proof ontology from all papers referenced up to the beginning of time, so that eventually all unclear statements could be expanded up until a human starts understanding them.

5. February 28, 2019 4:27 pm

Physicists often use “finite” when they really mean “nonzero”. Is that standard usage in mathematics? I would guess not.

6. February 28, 2019 7:52 pm

Have you tried sci-hub.tw? Very seldom I find papers which are not available through it.

March 1, 2019 3:22 am

“They have style guides for how the reasoning is laid out.” You certainly formulated that in the nicest possible way. Have you ever tried contributing to their website? God help you if you do not follow their style guides, or question some aspect of their approach. For instance, improving on some proof, or altering it in any way, is a big no no. It is a shame, because I love the idea of having a wiki of proofs!

March 1, 2019 8:18 am

The phrases you highlight are frustrating exactly because they demarcate the intended audience from the general audience. Almost nothing in a math paper is “well known” — except to certain highly specific research communities.

March 3, 2019 7:58 am

Yes and no. A big problem is that reviewers downgrade papers that include mathematical details that are “too easy” for that reviewer. Even if the author’s intended audience is broader, and they have the desire and ability to explain things for that audience, they may have to obfuscate things to get the paper published.

March 1, 2019 10:23 am

The customers for paywalled papers are industry folks who can charge the cost to the company.

10. March 2, 2019 7:03 pm

I would have liked to add the following aclaration to my “paper”: “This is not a paper”…

March 3, 2019 8:11 am

I’m curious about your reaction to Terry Tao’s tribute to Jean Bourgain. He speaks movingly of how his frustration with Bourgain’s “one may see”‘s eventually turned (after help from experts and intense work) into an appreciation for Bourgain’s tools.

On the other hand, if that’s what it took for Terry Tao, then very few people will ever understand Bourgain’s papers. One has to ask whether that’s really the writing style that best serves a field.

March 4, 2019 4:11 pm

Folk theorem’ – even if it is not that hard I want to know a bit more- if not who did it then when it was done.

By a standard X argument’ for some value of X. I first saw this with X=probabilistic and it was not a standard prob argument. Also, standard to who? As they Saying goes, one man’s ceiling is another man’s floor:

And who says that? Not so much in math, but the phrase as the saying goes’ is often made up. As an example Ken will especially appreciate, when Magnus Carlson, when he won the chess championship in 2016 on his birthday (Nov 30) he said they say its bad luck to play chess on your birthday, but for me it was good luck’ I looked on the web- nobody has ever said that! Did he make it up entirely?

• March 6, 2019 3:19 am

On my master’s, a paper I read had the phrase: “By a long and tedious calculation, it follows that …”

It took me a month to do the calculation, which turned out to have a small error.

March 6, 2019 8:28 am

Proof: Straightforward. QED

14. March 6, 2019 5:00 pm

“preprint” in the References instead of “arXiv:1234.56789”