German mathematical terms like "Nullstellensatz" - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T06:56:04Z http://mathoverflow.net/feeds/question/62218 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz German mathematical terms like "Nullstellensatz" Martin Brandenburg 2011-04-19T08:53:52Z 2012-06-07T00:42:23Z <p>There are quite a few german mathematical theorems or notions which usually are not translated into other languages. For example,</p> <p><a href="http://en.wikipedia.org/wiki/Nullstellensatz" rel="nofollow">Nullstellensatz</a>, <a href="http://en.wikipedia.org/wiki/Hauptvermutung" rel="nofollow">Hauptvermutung</a>, <a href="http://en.wikipedia.org/wiki/Freiheitssatz" rel="nofollow">Freiheitssatz</a>, <a href="http://en.wikipedia.org/wiki/Eigenvector" rel="nofollow">Eigenvector</a> (the "Eigen" part), <a href="http://arxiv.org/ftp/arxiv/papers/0804/0804.3888.pdf" rel="nofollow">Verschiebung</a>.</p> <p>For me, as a German, this is quite entertaining. Do you know other examples? Please one per answer, please give a reference for the term or a short explanation of what it means.</p> <p>It would be great to see an explanation why there is no translation.</p> <p>EDIT: Some more examples can be found at <a href="http://en.wikipedia.org/wiki/List_of_German_expressions_in_English#Mathematics_and_formal_logic" rel="nofollow">Wikipedia</a>: Ansatz, Entscheidungsproblem, Grossencharakter, Hauptmodul, Möbius band, quadratfrei, Stützgerade, Vierergruppe, Nebentype.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62220#62220 Answer by Pieter Naaijkens for German mathematical terms like "Nullstellensatz" Pieter Naaijkens 2011-04-19T09:00:23Z 2011-04-19T09:00:23Z <p><a href="http://en.wikipedia.org/wiki/Ansatz" rel="nofollow">Ansatz</a>. Although I suppose it is used more in physics than in mathematics. I don't know why the translation is not used often, but I guess it has to do something with the fact that in the beginning of the 20th century German was used much more than English in the scientific literature, I believe.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62221#62221 Answer by Chandan Singh Dalawat for German mathematical terms like "Nullstellensatz" Chandan Singh Dalawat 2011-04-19T09:05:00Z 2011-04-19T09:05:00Z <p>Führerdiskriminantenproduktformel. </p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62222#62222 Answer by Gottfried Helms for German mathematical terms like "Nullstellensatz" Gottfried Helms 2011-04-19T09:05:27Z 2011-04-19T09:05:27Z <p>I've seen <em>schlicht-function</em> for functions $f(x)=x +a x^2 + b x^3 + ...$ for powerseries without constant term and $f'(0)=1$. But I do not really know, whether this is really the german word <em>schlicht</em> (=<em>simple</em>) or only some coincidence.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62223#62223 Answer by Chandan Singh Dalawat for German mathematical terms like "Nullstellensatz" Chandan Singh Dalawat 2011-04-19T09:06:25Z 2011-04-19T09:06:25Z <p>Verlagerung. Sometimes translated as the <em>transfer</em>.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62224#62224 Answer by Denis Serre for German mathematical terms like "Nullstellensatz" Denis Serre 2011-04-19T09:07:51Z 2011-04-19T09:07:51Z <p>This is a notation rather than a term, but the wide use of the letter $K$ to denote a field in Algebra refers to the German word <em>Körper</em>.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62225#62225 Answer by Chandan Singh Dalawat for German mathematical terms like "Nullstellensatz" Chandan Singh Dalawat 2011-04-19T09:07:58Z 2011-04-19T09:07:58Z <p>Jugendtraum (Kronecker).</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62226#62226 Answer by Chandan Singh Dalawat for German mathematical terms like "Nullstellensatz" Chandan Singh Dalawat 2011-04-19T09:09:11Z 2011-04-19T11:17:49Z <p>Zahlbericht (Hilbert), Klassenkörperbericht (Hasse), Das blaue Hasse (Zahlentheorie, Akademie-Verlag, Berlin).</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62228#62228 Answer by Mark Schwarzmann for German mathematical terms like "Nullstellensatz" Mark Schwarzmann 2011-04-19T09:12:15Z 2011-04-19T09:12:15Z <p>Ganzstellensatz.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62231#62231 Answer by Dan Petersen for German mathematical terms like "Nullstellensatz" Dan Petersen 2011-04-19T09:19:34Z 2011-04-19T09:19:34Z <p>Nebentypus, Positivstellensatz.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62232#62232 Answer by Jan Jitse Venselaar for German mathematical terms like "Nullstellensatz" Jan Jitse Venselaar 2011-04-19T09:23:51Z 2011-04-19T09:23:51Z <p>Apparently the term K-theory comes from the German word "Klasse", according to Wikipedia and <a href="http://arxiv.org/abs/math/0602082" rel="nofollow">http://arxiv.org/abs/math/0602082</a></p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62235#62235 Answer by Stefan Waldmann for German mathematical terms like "Nullstellensatz" Stefan Waldmann 2011-04-19T09:34:16Z 2011-04-19T09:34:16Z <p>Verschränkungsoperator is the (perhaps even original) german version of "intertwiner" which I really like. But I've not seen that very much ;)</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62237#62237 Answer by Chandan Singh Dalawat for German mathematical terms like "Nullstellensatz" Chandan Singh Dalawat 2011-04-19T09:38:15Z 2011-04-19T09:38:15Z <p>The word <em>idele</em> ultimately comes from the abbreviation "id. ele." for <em>ideales Element</em>.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62242#62242 Answer by Dmitri Pavlov for German mathematical terms like "Nullstellensatz" Dmitri Pavlov 2011-04-19T10:21:22Z 2011-04-19T10:21:22Z <p>Umkehr map (pushforward map).</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62249#62249 Answer by Grant Olney Passmore for German mathematical terms like "Nullstellensatz" Grant Olney Passmore 2011-04-19T11:03:30Z 2011-04-23T16:56:47Z <p>Gentzen's Hauptsatz (cut elimination theorem) : This is a fundamental result in structural proof theory, and is at the heart of Gentzen's consistency proof of elementary number theory. It is very funny that the word literally means "main theorem," with no reference to the subject domain, yet it is standard in logic in English to use just the word "Hauptsatz" to refer to this (family of) theorem(s) in proof theory.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62250#62250 Answer by José Figueroa-O'Farrill for German mathematical terms like "Nullstellensatz" José Figueroa-O'Farrill 2011-04-19T11:09:12Z 2011-04-19T11:09:12Z <p>Here's another one: <a href="http://en.wikipedia.org/wiki/Hauptvermutung" rel="nofollow">Hauptvermutung</a></p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62251#62251 Answer by José Figueroa-O'Farrill for German mathematical terms like "Nullstellensatz" José Figueroa-O'Farrill 2011-04-19T11:13:11Z 2011-04-19T11:13:11Z <p>In GR (and other branches of mathematical physics) one uses <em>vierbein</em> (tetrad) and more often these days also <em>vielbein</em>, for local orthonormal frames in a (pseudo-)riemannian manifold.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62252#62252 Answer by Chandan Singh Dalawat for German mathematical terms like "Nullstellensatz" Chandan Singh Dalawat 2011-04-19T11:19:06Z 2011-04-19T11:29:00Z <p>Die Vierergruppe.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62254#62254 Answer by thei for German mathematical terms like "Nullstellensatz" thei 2011-04-19T11:28:26Z 2011-04-19T11:28:26Z <p>An indirect answer:</p> <p>Klein bottle</p> <p>which has probably started out as:</p> <p>Kleinsche Fläche (=Klein surface)</p> <p>Kleinsche Flache (lost umlaut in English print)</p> <p>Klein bottle (translation of Flasche instead of Flache) </p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62255#62255 Answer by Andrew Ranicki for German mathematical terms like "Nullstellensatz" Andrew Ranicki 2011-04-19T11:31:01Z 2011-04-19T11:31:01Z <p>Viergeflechte, the original German name for 2-bridge knots, still occasionally used in an English context. In his Mathematical Review of Schubert's 1956 paper "Knoten mit 2 Bruecken" Fox explicitly notes that "Viergeflecht" is untranslatable.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62256#62256 Answer by Kay for German mathematical terms like "Nullstellensatz" Kay 2011-04-19T11:41:11Z 2011-04-19T11:41:11Z <p>The $\int$ symbol is a german S introduced by Leibniz and stands for Summe (Sum)</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62259#62259 Answer by Pietro Majer for German mathematical terms like "Nullstellensatz" Pietro Majer 2011-04-19T12:04:31Z 2011-04-20T05:54:01Z <p>The notation $G_\delta$ is from German, G for "Gebiet", and $\delta$ for "Durchschnitt". Strangely enough, the notation for the co-sets, $F_\sigma$, is from French " fermé" and "somme".</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62260#62260 Answer by Andrew Ranicki for German mathematical terms like "Nullstellensatz" Andrew Ranicki 2011-04-19T12:26:16Z 2011-04-19T12:26:16Z <p>And what about the <em>Wiedersehen</em> metric?</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62271#62271 Answer by Andreas Blass for German mathematical terms like "Nullstellensatz" Andreas Blass 2011-04-19T14:06:22Z 2011-04-19T14:06:22Z <p>"Urelement" is used in set theory as a fancy name for an atom, i.e., something that can be a member of a set but is not itself a set. </p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62273#62273 Answer by Richard Borcherds for German mathematical terms like "Nullstellensatz" Richard Borcherds 2011-04-19T14:18:08Z 2011-04-19T14:18:08Z <p>This is an answer to the part of the question about why these terms are not translated into English. The reason is that words such as "nullstellensatz", "Schadenfreude" and so on that you mistakenly think are German are in fact perfectly good English words and so do not need translation. (Look up <a href="http://www.oed.com/view/Entry/172271?rskey=ZZodoS&amp;result=8&amp;isAdvanced=false#" rel="nofollow">Schadenfreude in the Oxford English Dictionary</a> if you do not believe it is an English word, though they have not yet caught up with nullstellensatz.) The point is that unlike languages such as French and German that try to remain pure, English has been happily looting terms from other languages for centuries, and the only difference between "nullstellensatz" and "house" is that "house" was stolen so long ago that we have forgotten about it. </p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62283#62283 Answer by Michael Hutchings for German mathematical terms like "Nullstellensatz" Michael Hutchings 2011-04-19T15:19:30Z 2011-04-19T15:19:30Z <p>Plastikstufe = a certain higher dimensional analogue of an overtwisted disk in contact geometry. This is not a real German word. It is a compound of the German words for "plastic" and "step", but this does not have any obvious relevance to its mathematical meaning. There is a funny story about where this word came from which however is not appropriate for this forum.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62289#62289 Answer by Andrew Stout for German mathematical terms like "Nullstellensatz" Andrew Stout 2011-04-19T16:00:33Z 2012-03-13T18:46:06Z <p>Einheit = word for unit in algebra. Hence, some use the notation $e\in G$ to denote the element of a group such that $ex = xe = x , \forall x \in G$. Unit is the appropriate translation, yet some algebraist still use the letter $e$ to denote the identity element in a group. </p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62304#62304 Answer by Qfwfq for German mathematical terms like "Nullstellensatz" Qfwfq 2011-04-19T17:46:24Z 2011-04-19T17:46:24Z <p>The <em>Verschiebung</em> morphism.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62305#62305 Answer by Keivan Karai for German mathematical terms like "Nullstellensatz" Keivan Karai 2011-04-19T17:57:29Z 2011-04-19T17:57:29Z <p>Größencharakter. <a href="http://en.wikipedia.org/wiki/Hecke_character" rel="nofollow">http://en.wikipedia.org/wiki/Hecke_character</a></p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62320#62320 Answer by Anton Petrunin for German mathematical terms like "Nullstellensatz" Anton Petrunin 2011-04-19T19:05:30Z 2011-04-19T19:05:30Z <p>deck transformation?</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62330#62330 Answer by Ben Webster for German mathematical terms like "Nullstellensatz" Ben Webster 2011-04-19T20:08:31Z 2011-04-19T20:08:31Z <p>There's Soergel's <a href="http://books.google.com/books?id=8GCP4Ng6risC&amp;lpg=PA266&amp;ots=oIeehaWMSs&amp;dq=Endomorphismensatz&amp;pg=PA266#v=onepage&amp;q=Endomorphismensatz&amp;f=false" rel="nofollow">Endomorphismensatz</a> and <a href="http://books.google.com/books?id=dtsUcQTHPqYC&amp;lpg=PA120&amp;ots=xa33PP-eAi&amp;dq=struktursatz%20Soergel&amp;pg=PA120#v=onepage&amp;q=struktursatz%20Soergel&amp;f=false" rel="nofollow">Struktursatz</a>.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62338#62338 Answer by none for German mathematical terms like "Nullstellensatz" none 2011-04-19T21:06:11Z 2011-04-19T21:06:11Z <p><b>Bew</b> (short for beweisbar, introduced by Gödel's incompleteness paper) is still used as a provability predicate in some mathematical logic papers.</p> <p>In physics and other subjects (not so much in math) we hear about plenty of Gedankenexperiments.</p> <p>Don't forget Hilbert's Satz 90, anomalous because of the "90" and not just the "Satz".</p> <p>There are also French words like étale cohomology.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62345#62345 Answer by Margaret Friedland for German mathematical terms like "Nullstellensatz" Margaret Friedland 2011-04-19T22:33:14Z 2011-04-20T06:31:37Z <p>The following theorem is known as Kugelsatz:</p> <p>Let $X$ be an open set in $\mathbb{C}^n, \quad n \geq 2$ and $K \subset X$ a compact subset such that $X\setminus K$ is connected. Then the restriction map $\rho: \mathcal{O}(X) \mapsto \mathcal{O}(X \setminus K)$ is an isomprphism of $\mathbb{C}$-algebras (this version after: Volker Scheideman, Introduction to Complex Analysis in Several Variables, Birkh\"{a}user 2005).</p> <p>The first result of this kind is due to Hartogs, with $X$ and $K$ being concentric euclidean balls, hence the name (Kugel=ball). many texts in several complex variables have been written by German-speaking authors (Grauert+Fritzsche, Kaup brothers are other examples), so the German name stuck even in the English version. The theorem is also referred to as "tomato can principle". </p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62349#62349 Answer by David Roberts for German mathematical terms like "Nullstellensatz" David Roberts 2011-04-19T23:37:05Z 2011-04-20T06:29:16Z <p><b>Stufe</b> (=level) of a non-real field (<a href="http://de.wikipedia.org/wiki/Stufe_%28Algebra%29" rel="nofollow">wikipedia.de</a>). It is the least number of squares $a_i^2$ such that $\sum_i a_i^2 = -1$, $\infty$ if no such sum exists.</p> <p>In <a href="http://www.springerlink.com/content/y805154075182450/" rel="nofollow">this paper</a>, the <em>level</em> of a subgroup of $SL_2(\mathcal{O})$ is defined ($\mathcal{O}$ a number field), as the generalisation of the stufe of a field, so the term has been translated, but only in a shift of context.</p> <p>To pick a random paper, try <a href="http://www.springerlink.com/content/g2285368g61l9332/" rel="nofollow">The stufe of number fields</a>.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62350#62350 Answer by Malik Younsi for German mathematical terms like "Nullstellensatz" Malik Younsi 2011-04-19T23:44:26Z 2011-04-19T23:44:26Z <p>There is <strong>Ahlfor's scheibensatz</strong> in complex function theory, which is a generalization of <a href="http://mathworld.wolfram.com/AhlforsFiveIslandTheorem.html" rel="nofollow">Ahlfors five islands theorem</a></p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62351#62351 Answer by monodromy for German mathematical terms like "Nullstellensatz" monodromy 2011-04-19T23:49:35Z 2011-04-19T23:49:35Z <p><strong>Spiegelungssatz</strong>. The meaning of this theorem is briefly discussed in the article: <em>Iwasawa theory and $p$-adic deformations of motives</em> [MR1265554 (95i:11053)] by Ralph Greenberg.</p> <p>Let $p$ be an odd prime, and $K_\infty=\mathbf{Q}(\mu_{p^\infty})$. Let $L_\infty$ denote the maximal unramified abelian pro-$p$ extension of $K_\infty$, and $M_\infty$ the maximal abelian pro-$p$-extension of $K_\infty$ that is unramified outside the primes above $p$. Let $Y_\infty={\rm Gal}(L_\infty/K_\infty)$ and $X_\infty={\rm Gal}(M_\infty/K_\infty)$. We can decompose ${\rm Gal}(K_\infty/\mathbb{Q})\cong\Delta\times\Gamma$, where $\Delta={\rm Gal}(\mathbf{Q}(\mu_p)/\mathbf{Q})$ and $\Gamma\cong\mathbf{Z_p}$. Both $Y_\infty$ and $X_\infty$ have a natural structure of $\Lambda$-modules ($\Lambda=\mathbf{Z_p}[[\Gamma]]$) coming from the action of ${\rm Gal}(K_\infty/\mathbf{Q})$ by inner automorphisms. The latter action gives in particular an action of $\Delta$, and hence we can decompose $Y_\infty=\bigoplus_{i=0}^{p-2}Y_\infty^{\omega^i}$ and $X_\infty=\bigoplus_{j=0}^{p-2}X_\infty^{\omega^j}$ as $\Lambda$-modules, where the superscript denotes isotypical component under the action of $\Delta$, and $\omega:\Delta\rightarrow\mu_{p-1}$ denotes the mod $p$ cyclotomic character. The spliegelungsatz is then described by Greenberg in loc. cit. as an argument using Kummer theory and class field theory that allows to relate the structures of $X_\infty^{\omega^j}$ and $Y_\infty^{\omega^i}$ for $i+j\equiv 1\pmod{p-1}$ as $\Lambda$-modules.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62355#62355 Answer by Ross Snider for German mathematical terms like "Nullstellensatz" Ross Snider 2011-04-20T00:40:34Z 2011-04-20T00:40:34Z <p>Zugzwang - a sort of Nash Equilibrium. This terminology is specifically used in Chess.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62376#62376 Answer by Matthias Künzer for German mathematical terms like "Nullstellensatz" Matthias Künzer 2011-04-20T06:08:50Z 2011-04-20T06:08:50Z <p>The practice to use Gothic letters sometimes for ideals ($\mathfrak{a}$, $\mathfrak{b}$, ...) and often for Lie algebras ($\mathfrak{g}$, $\mathfrak{h}$, ..) seems to be of German origin.</p> <p>Also to use the lesser known "kernel" instead of the better known "core" seems to stem from the German "Kern".</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62391#62391 Answer by John Iskra for German mathematical terms like "Nullstellensatz" John Iskra 2011-04-20T10:00:46Z 2011-04-20T10:06:17Z <p>It's early in the morning, so maybe I missed it in the answers above, but, if we're including symbols, then the obvious example is $\mathbbm{Z}$, the integers, or zahlen! </p> <p>Ooops! It is early in the morning... I see that Roland noted that the symbol for the integers (which I also can't seem to get to process properly) just a few comments above.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62425#62425 Answer by Michael Hardy for German mathematical terms like "Nullstellensatz" Michael Hardy 2011-04-20T15:29:33Z 2011-04-20T15:29:33Z <p>Some famous book published in about 1950 says that for lack of an English word for the concept the word <em>Faltung</em> is used. In recent decades, the adapted Latin word <em>convolution</em> has served.</p> <p>Paul Halmos tried unsuccessfully to expunged the words <em>eigenvector</em> and <em>eigenvalue</em> from the language, using the terms <em>proper vector</em> and <em>proper value</em> in his book <em>Finite-dimensional Vector Spaces</em>.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/62745#62745 Answer by kastberg for German mathematical terms like "Nullstellensatz" kastberg 2011-04-23T14:34:12Z 2011-04-23T14:34:12Z <p>In Swedish, a field is called a 'kropp', a body. This of course from the German word Körper.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/66927#66927 Answer by Claudio Gorodski for German mathematical terms like "Nullstellensatz" Claudio Gorodski 2011-06-05T00:43:46Z 2011-06-05T00:43:46Z <p><em>Zusammenstellung</em>. Means "compilation" or "survey". Can be used in the first section of a paper, as one starts compiling "preliminary facts" to refer to later in the paper. That's the way I've seen it used in a paper by Raoul Bott. </p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/77078#77078 Answer by S.A.A for German mathematical terms like "Nullstellensatz" S.A.A 2011-10-03T22:22:45Z 2011-10-04T16:40:34Z <p>If you think of the symbols, you can also see Gothic, alternatively called German, letters. Also, in algebraic topology, it is common to show the cycles by $Z$, which is the first letter of Zykel.</p> <p>Also, many words that are Latin or Greek, in terms of the ingredients, were first coined and used in German, like Topologie which used to be called Analyse Situs.</p> <p>It was common to show curvature by $K$, which stands for Krummung. Also, it was common to show a domain by B, for Bereiche. Or in riemannian geometry, the metric tensor is represented by $g$, which stands for Gravit\"at Also, Faltung used to be common in English before the word convolution took over.</p> <p>I can also add Umlaufssatz in the differential geometry of surfaces.</p> <p>There are so many more...</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/77082#77082 Answer by Colin Reid for German mathematical terms like "Nullstellensatz" Colin Reid 2011-10-03T23:07:49Z 2011-10-03T23:07:49Z <p>There's a kind of combinatorial design called a <em>gerechte</em> design - essentially it's a Latin square with additional block constraints. (I gather there's been a fad in recent years for newspapers to print partial gerechte designs of a certain kind for readers to complete.) As a technical term, the word comes from the following paper:</p> <p>W. U. Behrens (1956). Feldversuchsanordnungen mit verbessertem Ausgleich der Bodenunterschiede. Zeitschrift für Landwirtschaftliches Versuchs- und Untersuchungswesen, 2, 176–193.</p> <p>Behrens' gerechte designs were 'fair' in how they apportioned plots of land to different treatments in an agricultural trial.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/77084#77084 Answer by M Turgeon for German mathematical terms like "Nullstellensatz" M Turgeon 2011-10-03T23:24:31Z 2011-10-04T02:00:01Z <p>I believe Albrecht Frölich uses the german term <em>beweis</em>, instead of the english <em>proof</em>, in his chapter of the classic "Algebraic number theory". (EDIT: In my original version, I translated beweis to example. I shouldn't trust my poor knowledge of German... )</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/91117#91117 Answer by Hans Engler for German mathematical terms like "Nullstellensatz" Hans Engler 2012-03-13T20:54:46Z 2012-03-13T20:54:46Z <p>All this should be compiled in a <em>Festschrift</em>.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/91121#91121 Answer by Pawel for German mathematical terms like "Nullstellensatz" Pawel 2012-03-13T21:13:55Z 2012-03-13T21:13:55Z <p>In "Functional Analysis" by Kosaku Yosida he denotes the closure of a set $M$ by $M^a$. He explains that it is a shortcut from German abgeschlossene Hulle.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/92721#92721 Answer by J. H. S. for German mathematical terms like "Nullstellensatz" J. H. S. 2012-03-30T22:41:02Z 2012-03-30T22:41:02Z <p>I would like to mention a handful of examples that may be considered <em>passé</em> nowadays, but were prominent at some point in time.</p> <ul> <li><strong>schlicht</strong>: I dare to address this one again because I consider that the feedback in the comments below Gottfried's entry is kind of misleading. About this one, Boas says that (see [<strong>1</strong>, page 97]):</li> </ul> <p>«... When I was an undergraduate, there was no regular colloquium Harvard, but there was a Mathematical Club, whose meeting were regularly attended by faculty. Once somebody gave a talk on schlicht functions. After the talk, Julian Lowell Coolidge asked plaintively whether there was an English word for 'schlicht'. Osgood replied, "Well, you <em>could</em> call them univalent functions, and everybody would know that you meant 'schlicht'". You need to know that Osgood had been trained in Germany, wrote his treatise on complex analysis in German, and was apt to tell German jokes to his classes. »</p> <ul> <li><p><strong>limes:</strong> That's right... It was not a typo in Ahlfors's text on Complex Analysis. I recently came across this one in another book, but I just can't recall which one it was.</p></li> <li><p><strong>eine Drehstreckung:</strong> Tristan Needham recalls this one when he apologizes for the coinage of the term 'amplitwist'. More specifically, he writes</p></li> </ul> <p>«... To the expert reader I would like to apologize for having invented the word 'amplitwist' ... as a synonym (more or less) for 'derivative', as well the component terms 'amplification' and 'twist'. I can only say that the need for <em>some</em> such terminology was forced on me in the classroom: if you try teaching the ideas in this book <em>without</em> using such language, I think you will quickly discover what I mean! Incidentally, a precedence argument in defence (sic) of 'amplitwist' might be that a similar term was coined by the older German school of Klein, Bieberbach, <em>et al</em>. They spoke of 'eine Dhrestreckung', from 'drehen' (to twist) and 'strecken' (to stretch). »</p> <p>Last but not least, in several works of old (z.B., Perron's <em>Die Lehre von den Kettenbrüchen</em>, Knopp's <em>Theory and Application of Infinite series</em>, Khinchin's <em>Continued Fractions</em>), there appears the following notation for general continued fractions:</p> <p>$\underset{j=1}{\overset{\infty}{\LARGE\mathrm K}}\frac{a_j}{b_j}=\cfrac{a_1}{b_1+\cfrac{a_2}{b_2+\cfrac{a_3}{b_3+\ddots}}}.$</p> <p>Guess what the $\mathrm{K}$ stands for...</p> <p><strong>References</strong></p> <p>[<strong>1</strong>] Lion Hunting &amp; Other Mathematical Pursuits: A Collection of Mathematics, Verse and Stories by Ralph P. Boas Jr.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/92725#92725 Answer by Yoav Kallus for German mathematical terms like "Nullstellensatz" Yoav Kallus 2012-03-30T23:57:33Z 2012-03-30T23:57:33Z <p>There is also the Quermassintegral (mixed volumes of the form $V(K,K,\ldots,B,B)$ where $B$ is the unit ball, see <a href="http://en.wikipedia.org/wiki/Mixed_volume" rel="nofollow">Wikipedia</a>), which I'm not even sure is German (not a lot of Qs in German usually).</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/98950#98950 Answer by The furious mathematician for German mathematical terms like "Nullstellensatz" The furious mathematician 2012-06-06T13:55:00Z 2012-06-06T13:55:00Z <p><a href="http://mathoverflow.net/questions/1270/alternatives-to-pi-day/1273#1273" rel="nofollow">Schubfachprinzip</a> ("drawer principle" or "shelf principle" or "Dirichlet's box principle"). It is now easy to guess we are talking about <a href="http://mathoverflow.net/questions/1270/alternatives-to-pi-day/1273#1273" rel="nofollow">P-H</a> <a href="http://mathoverflow.net/questions/4279/interesting-applications-of-the-pigeon-hole-principle" rel="nofollow">P</a>.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/98959#98959 Answer by John C for German mathematical terms like "Nullstellensatz" John C 2012-06-06T15:21:44Z 2012-06-06T15:21:44Z <p>In topology the separation axioms $T_0$ , $T_1$ .. etc, where the $T$ stands for Trennungsaxiom</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/98966#98966 Answer by roy smith for German mathematical terms like "Nullstellensatz" roy smith 2012-06-06T16:14:53Z 2012-06-06T17:01:52Z <p>"schlichtartig" refers to a surface on which every simple closed curve which separates locally, also separates globally. Hence it means roughly "planar". This is used in the conformal mapping theory of Riemann surfaces. Introduction to Riemann Surfaces, Springer, p. 91. I know only a little German but it seems to translate something like "simply behaved"?</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/98985#98985 Answer by Natalie for German mathematical terms like "Nullstellensatz" Natalie 2012-06-06T20:27:07Z 2012-06-06T20:27:07Z <p>Anzahl-theorems is one I have recently read in Wan's book on classical groups.</p> http://mathoverflow.net/questions/62218/german-mathematical-terms-like-nullstellensatz/98988#98988 Answer by John Klein for German mathematical terms like "Nullstellensatz" John Klein 2012-06-06T20:49:07Z 2012-06-07T00:42:23Z <p>One that is similar in spirit "eigenvalue" in that it mixes the two languages is $$\text{umkehr map}$$</p>