Origins of Mathematical Symbols/Names - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T18:52:12Z http://mathoverflow.net/feeds/question/8295 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names Origins of Mathematical Symbols/Names liuyao 2009-12-09T02:49:17Z 2010-05-02T14:45:35Z <p>I'm not sure if this has been asked. I'll explain the question by an example.</p> <p>Fields are often denoted by the letter k, which comes from the German word Körper, meaning body (like corpse, corporeal).</p> <p>Most mathematical symbols relate directly or indirectly to the English names, so what other exceptions are there?</p> <p>(Yes, this is inspired by the other post about languages in math)</p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8297#8297 Answer by Kevin Lin for Origins of Mathematical Symbols/Names Kevin Lin 2009-12-09T03:04:36Z 2009-12-09T03:04:36Z <p>$\mathbb{Z}$ comes from the German "Zahlen" which means "numbers".</p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8299#8299 Answer by Kevin Lin for Origins of Mathematical Symbols/Names Kevin Lin 2009-12-09T03:09:24Z 2009-12-09T03:15:29Z <p>The notation $\mathcal{F}$ for sheaves comes from the French word "faisceau" meaning "bundle". </p> <p>Also "gerbe" means "sheaf" in French.</p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8300#8300 Answer by Kevin Lin for Origins of Mathematical Symbols/Names Kevin Lin 2009-12-09T03:11:22Z 2009-12-11T17:27:41Z <p>I've been told that the notation $\mathcal{O}$ for the structure sheaf of a scheme/variety/whatever comes from the Italian word "olomorfo/olomorfa" for "holomorphic".</p> <p>I should note that I don't have any evidence for this claim beyond "I heard it somewhere from somebody". It would be great if anybody could corroborate this.</p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8302#8302 Answer by liuyao for Origins of Mathematical Symbols/Names liuyao 2009-12-09T03:19:28Z 2009-12-09T03:19:28Z <p>Center of a group is denoted Z, from German word Zentrum</p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8303#8303 Answer by MLevi for Origins of Mathematical Symbols/Names MLevi 2009-12-09T03:28:50Z 2009-12-09T03:28:50Z <p>As an undergraduate, I was told that $V$ is often used to denote a neighborhood because the French translation is <em>voisinage</em>. Anyone else hear this? </p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8304#8304 Answer by REDace0 for Origins of Mathematical Symbols/Names REDace0 2009-12-09T03:33:50Z 2009-12-09T03:33:50Z <p>Wolfram has nice a little paragraph on the history of the term "Ring" right after the list of ring axioms.</p> <p><a href="http://mathworld.wolfram.com/Ring.html" rel="nofollow">Ring (from Wolfram Mathworld)</a></p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8305#8305 Answer by liuyao for Origins of Mathematical Symbols/Names liuyao 2009-12-09T03:34:55Z 2009-12-09T03:34:55Z <p>In homological algebra, one sometimes uses Z and B to denote cycles (or closed form) and boundaries (or exact forms), respectively. Z must be for Zycle.</p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8341#8341 Answer by axiomsofchoice for Origins of Mathematical Symbols/Names axiomsofchoice 2009-12-09T13:04:07Z 2009-12-09T13:04:07Z <p>You might like to take a look at this site:</p> <p><a href="http://jeff560.tripod.com/mathsym.html" rel="nofollow">Earliest Uses of Various Mathematical Symbols</a></p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8342#8342 Answer by Harald Hanche-Olsen for Origins of Mathematical Symbols/Names Harald Hanche-Olsen 2009-12-09T13:10:27Z 2009-12-09T17:09:00Z <blockquote> <p>Utile erit scribit ∫ pro omnia. (It is useful to write ∫ instead of omnia) – Leibniz (1675-10-29)</p> </blockquote> <p>(Source for this quotiation: Eriksson, Estep, Hansbo, Johnson: Computational differential equations, end of Ch. 3)</p> <p>In response to some comments: <em>omnis</em> <a href="http://www.archives.nd.edu/cgi-bin/lookup.pl?stem=omnis&amp;ending=" rel="nofollow">means “all”</a>. Compare <em>omnivore</em>. Here endeth the Latin lesson.</p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8350#8350 Answer by Kevin Lin for Origins of Mathematical Symbols/Names Kevin Lin 2009-12-09T14:06:29Z 2009-12-11T17:28:52Z <p>I've heard that the "$K$" of $K$-theory comes from the German word "Klasse(n)" meaning "class(es)", but I don't have any concrete evidence for this.</p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8352#8352 Answer by SixWingedSeraph for Origins of Mathematical Symbols/Names SixWingedSeraph 2009-12-09T14:27:54Z 2009-12-09T14:27:54Z <p>Pat Ballew's blog <a href="http://www.pballew.net/etyindex.html" rel="nofollow">Math Words</a> has interesting stuff. </p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8356#8356 Answer by psihodelia for Origins of Mathematical Symbols/Names psihodelia 2009-12-09T15:11:47Z 2009-12-09T15:11:47Z <p>$\mathbb{N}$ comes from the German "Natürliche Zahlen"=natural number<br> $\mathbb{Z}$ comes from the German "ganZe Zahl"=integer numbers<br> $\mathbb{Q}$ comes from the Latin "Quotient"= result of a division<br> $\mathbb{R}$ comes from the German "Reelle Zahl"=real numbers<br> $\mathbb{C}$ comes from the French "nombre Complexe"=complex numbers<br></p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8359#8359 Answer by Joseph Malkevitch for Origins of Mathematical Symbols/Names Joseph Malkevitch 2009-12-09T15:52:56Z 2009-12-09T15:52:56Z <p>There is a "classic" book about the history of mathematical notations by Florian Cajori though there has been some "revision" of his work by more recent scholars.</p> <p><a href="http://en.wikipedia.org/wiki/Florian_Cajori" rel="nofollow">http://en.wikipedia.org/wiki/Florian_Cajori</a></p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8375#8375 Answer by Theo Johnson-Freyd for Origins of Mathematical Symbols/Names Theo Johnson-Freyd 2009-12-09T17:32:53Z 2009-12-09T17:32:53Z <p>$x,y,z$, and in particular that $x$ is the independent variable and $y$ the dependent variable, are due to Descartes, if I'm not mistaken.</p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8601#8601 Answer by Vectornaut for Origins of Mathematical Symbols/Names Vectornaut 2009-12-11T20:28:20Z 2009-12-11T20:28:20Z <p>This one is pretty well-known: the notation $e$ for the identity of a group comes from the German word <em>Einheit</em>, meaning <em>unit</em>.</p> <p>I'd be willing to bet that the notation $G$ for a group also comes from German... but we don't notice, because the German word for <em>group</em> is <em>Gruppe</em>!</p> <p><hr /></p> <p><a href="http://ncatlab.org/nlab/show/partition+function" rel="nofollow">Here's a fun one</a>: the notation $Z$ for a topological quantum field theory comes indirectly from the notation $Z$ for a partition function in statistical mechanics, which comes from the German word <em>Zustandssumme</em>, meaning <em>state sum</em>. I said "indirectly" because partition function in quantum field theory isn't a statistical-mechanical partition function... it just looks like one after you Wick rotate! (Then again, maybe there's a deeper sense in which the QFT partition function really <em>is</em> a statistical-mechanical partition function. Does anybody know?)</p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8604#8604 Answer by Konrad Swanepoel for Origins of Mathematical Symbols/Names Konrad Swanepoel 2009-12-11T20:44:55Z 2009-12-11T20:44:55Z <p><em>F</em> for a closed set comes from the French <em>ferme</em> (=firm, cf. <em>fermer</em>=to close).</p> <p>What about <em>G</em> for an open set? Is this also an example of the next-letter phenomenon? (as in Michael's comment to <a href="http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/8303#8303" rel="nofollow">this answer</a> to the question.)</p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/21150#21150 Answer by Jamie Weigandt for Origins of Mathematical Symbols/Names Jamie Weigandt 2010-04-12T20:02:08Z 2010-04-12T20:02:08Z <p>I <a href="http://mathoverflow.net/questions/19264/what-is-the-etymology-for-the-term-conductor" rel="nofollow">asked a while ago</a> about the etymology of the name <em>conductor</em>. Often the conductor of an order in a number field is denoted by $\mathfrak f$. This comes from the original German name <em>Führer</em> given by Dedekind.</p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/21155#21155 Answer by Harry Gindi for Origins of Mathematical Symbols/Names Harry Gindi 2010-04-12T20:47:56Z 2010-04-12T20:47:56Z <p>Oh, but of course $\emptyset$ comes from Bourbaki. Interestingly, so does $\Rightarrow$ to denote implication, and $\in$ instead of $\varepsilon$. The "Dangerous bend" comes from Bourbaki as well.</p> <p>However, my all time favorite is the set of associated primes of a module M. $Ass(M)$ is in fact called the <em>assassinator</em> of $M$, and its elements are called <em>assassins</em>. </p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/21163#21163 Answer by Andy for Origins of Mathematical Symbols/Names Andy 2010-04-12T23:18:25Z 2010-04-12T23:18:25Z <p>In design theory we talk of a t-(v,k,&lambda;). I think v originally meant "varieties", but I don't know if any of the other symbols meant anything; it would be nice to find out that they did. &lambda; seems an odd choice for an integer... in many other contexts it gets used as a real number.</p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/21432#21432 Answer by Qfwfq for Origins of Mathematical Symbols/Names Qfwfq 2010-04-15T08:19:04Z 2010-04-15T08:19:04Z <p>$E$ is sometimes used for vector spaces, from the French word "espace"="space". </p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/21434#21434 Answer by Keivan Karai for Origins of Mathematical Symbols/Names Keivan Karai 2010-04-15T08:53:28Z 2010-04-15T13:39:39Z <p>The letter $T$ in the names for the separation axioms $T_1$, $T_2$, etc in point set topology comes from "Trennungsaxiom" in German. <a href="http://de.wikipedia.org/wiki/Trennungsaxiom" rel="nofollow">http://de.wikipedia.org/wiki/Trennungsaxiom</a></p> http://mathoverflow.net/questions/8295/origins-of-mathematical-symbols-names/23258#23258 Answer by Pádraig Ó Conbhuí for Origins of Mathematical Symbols/Names Pádraig Ó Conbhuí 2010-05-02T14:45:35Z 2010-05-02T14:45:35Z <p>I'm not sure how relevant this is outside of Ireland, but while doing basic mechanics, if you ever see acceleration denoted as $f$, as it is in the "log tables" here, as in $v=u+ft$, the $f$ in this case stands for the Latin for acceleration, festinatio (with festino meaning "I hurry", so festinatio would very roughly and more literally translate as "hurriedness"), which is funny because adcelero is the Latin for "I speed up" which looks a lot more like acceleration.</p> <p>Similarly, displacement denoted by $s$ as in $s=ut+\frac12 at^2$ is from the Latin for displacement, summoveo (with moveo meaning "I move [something]").</p> <p>And, of course, velocitas, the Latin for speed. I can imagine u being used for velocity as well since the Romans actually pronounced "v" as "u", so the two are pretty much interchangeable.</p>