Beginning a sentence with a mathematical symbol - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T11:30:13Z http://mathoverflow.net/feeds/question/24818 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/24818/beginning-a-sentence-with-a-mathematical-symbol Beginning a sentence with a mathematical symbol Greg Muller 2010-05-15T21:12:19Z 2010-05-16T07:52:51Z <p>This is more of a mathematician question than a mathematics question, but I hope it is still appropriate.</p> <p>Several times now, when friends have been editing my mathematical writing, they have pointed out instances where I began a sentence with a mathematical symbol, such as $X$, or $a\in A$, etc. This is the sort of thing that never struck me as inherently bad writing, since it is often exactly how I would speak the sentence aloud. However, I can also see their point, in that a sentence beginning with a mathematical symbol can look a little weird (especially when it starts with a lowercase letter), and doesn't quite read the same as a sentence beginning with an English word.</p> <p>However, now that I have been trying to avoid doing this, more and more I find myself writing awkward sentences to avoid the most natural way of speaking, and I can't quite decide if I am increasing or decreasing the quality of my writing.</p> <p>Do people have strong opinions on this? Do people have tricks for dealing with this, besides a succession of empty and synonymous clauses ("Thus", "Then", "Therefore", "We find", "Looking at"...)?</p> http://mathoverflow.net/questions/24818/beginning-a-sentence-with-a-mathematical-symbol/24820#24820 Answer by Tara Holm for Beginning a sentence with a mathematical symbol Tara Holm 2010-05-15T21:24:14Z 2010-05-15T21:24:14Z <p>I also try to avoid starting sentences with a mathematical symbol. I feel strongly about it, but I can't quite articulate why.</p> <p>One trick I use that you haven't mentioned yet is something like, "The space $X$ ..." or "The function $f$...".</p> http://mathoverflow.net/questions/24818/beginning-a-sentence-with-a-mathematical-symbol/24822#24822 Answer by Robby McKilliam for Beginning a sentence with a mathematical symbol Robby McKilliam 2010-05-15T21:40:00Z 2010-05-16T03:33:54Z <p>I personally find that it is occasionally convenient and natural to start sentences with a mathematical symbol, but I have had coauthors who do not like it, and in this case I typically modify the sentence (into what I sometimes feel is more awkward).</p> <p>Tara has mentioned a nice trick for amending sentences starting with a symbol and this is typically the approach I have taken. Another approach that I find sometimes works is to consider merging the sentences (perhaps with a little restructuring) so that the symbol follows a comma or a conjunction such as `and'.</p> <p>I probably have an overly relaxed attitude towards the written language, but in my opinion, if it works and it is clear, do it. I can envisage situations where starting a sentence with a symbol makes the text confusing to read. Obviously it should be avoided in this case.</p> http://mathoverflow.net/questions/24818/beginning-a-sentence-with-a-mathematical-symbol/24830#24830 Answer by Douglas S. Stones for Beginning a sentence with a mathematical symbol Douglas S. Stones 2010-05-15T22:49:07Z 2010-05-15T22:49:07Z <p>This seems widely considered as bad form within mathematics papers. In some cases, it might not be clear that the previous sentence has ended, particularly if it also ends in mathematical typesetting, or the punctuation itself might be considered as part of the mathematics. This applies more generally, in that one should avoid placing too much mathematics around all punctuation marks.</p> <p>There are also capitilisation considerations, e.g. starting sentences with f(x).</p> <p>As already noted, it's usually very easy (and often desirable) to avoid this situation.</p> http://mathoverflow.net/questions/24818/beginning-a-sentence-with-a-mathematical-symbol/24831#24831 Answer by gowers for Beginning a sentence with a mathematical symbol gowers 2010-05-15T22:54:48Z 2010-05-15T22:54:48Z <p>I share the dislike that many people have expressed for starting sentences with symbols. In trying to explain why, I wanted to come up with an example that would illustrate the temptation to do so, but I find it surprisingly hard. Suppose, for instance, that f is so clear from the context that to use Tara's trick and start a sentence with "The function f" would be ridiculous. (In general, by the way, using Tara's trick can add clarity by reminding the reader what is what, so I am talking about a special circumstance here.) Now suppose that we want to say something about f, such as that it is a homomorphism. It is very hard to think of a natural context in which one would actually want to start a sentence with "f is a homomorphism". Nearly always there would be a reason for saying that, or a justification for it, such as, "It is not hard to check that", or "We have already seen that". And if it came out of the blue somewhere, then one would want to signal a slight change of subject with a word such as "Now" (a trick that has already been mentioned). So I'm tempted to say that if your prose is flowing properly the problem shouldn't arise, or should arise very infrequently.</p> http://mathoverflow.net/questions/24818/beginning-a-sentence-with-a-mathematical-symbol/24832#24832 Answer by Chris Godsil for Beginning a sentence with a mathematical symbol Chris Godsil 2010-05-15T23:00:15Z 2010-05-15T23:00:15Z <p>You shouldn't do it. This is covered in Halmos's justifiably famous article "How to write mathematics". (You'll find lots of copies of this on the web.) It's very closely related to the rule that you should avoid having notation separated by punctuation.</p> http://mathoverflow.net/questions/24818/beginning-a-sentence-with-a-mathematical-symbol/24838#24838 Answer by Peter Luthy for Beginning a sentence with a mathematical symbol Peter Luthy 2010-05-15T23:23:29Z 2010-05-15T23:23:29Z <p>Since you almost never have a sentence like "x is in A" without an additional clause, it shouldn't be hard to reverse the order of the sentence. For example, "u and v are harmonic since f is analytic" could be changed to "As f is analytic, u and v are necessarily harmonic" or a number of variants thereof (since, as a consequence of, by virtue of). </p> <p>If there is some case where you would actually want a standalone like "x is in A" --- for example after a long lemma establishing that x is in A --- one could use flashier phrases, e.g. to wit, that is to say, whence etc.</p> <p>Good writing is a lot like good mathematics: it's more art than science.</p> http://mathoverflow.net/questions/24818/beginning-a-sentence-with-a-mathematical-symbol/24860#24860 Answer by Noah Snyder for Beginning a sentence with a mathematical symbol Noah Snyder 2010-05-16T04:32:33Z 2010-05-16T04:32:33Z <p>Under no circumstances can you have symbols then punctuation then other symbols. As a special case you can never have symbols at the end of one sentence and the beginning of the next. Outside of the above case, starting sentences with symbols is bad, but occasionally all other options are worse.</p> http://mathoverflow.net/questions/24818/beginning-a-sentence-with-a-mathematical-symbol/24869#24869 Answer by Robin Chapman for Beginning a sentence with a mathematical symbol Robin Chapman 2010-05-16T07:52:51Z 2010-05-16T07:52:51Z <p>If one stoops to starting sentences with a symbol, then one soon descends to finishing a sentence with a symbol and starting the next with a symbol. Then one is liable to finish a sentence with a symbol and start a sentence with the <strong>same</strong> symbol. To the reader (if you still have one) madness beckons.</p>