Griechische Staatsschuldenkrise


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Trotz Abzugsfähigkeit wurde in der dortigen Steuererklärung nunmehr die obligatorische Nennung des Empfängers abgeschafft, um dessen Strafverfolgung im Rahmen eines Amtshilfeverfahrens im Heimatland zu vereiteln.

In den meisten Fällen wurde aber gegen die guten Sitten und für den wirtschaftlichen Profit die Schmiergeldpraxis weiter ausgebaut. Die Ursachen der Finanzkrise in Griechenland werden kontrovers diskutiert und eingeschätzt.

Folgende Einschätzungen zu möglichen Ursachen wurden in verschiedenen Veröffentlichungen genannt:. Entgegen dem Vertrag von Maastricht , nach dem ein Euro-Land auch nach der Einführung des Euros sowohl das jährliche Haushaltsdefizit als auch den Staatsschuldenstand in Richtung Grenzwert abbauen muss, gelang Griechenland die Reduzierung der überschrittenen Kriterien nicht. Schon seit den '90ern wurde die Entwicklung der Staatsschulden und Staatsdefizite in griechischen Medien kontrovers diskutiert.

Um aber den Wähler nicht in seinen, seit dem EWG-Beitritt vorherrschenden, Ressentiments gegen die unfreiwillige Mitgliedschaft [] zu bestärken, wurden die Wirtschaftsprognosen durchweg positiv dargestellt. Mehr Informationen finden sich im Abschnitt Reduzierung der Militärausgaben. Die geringen Staatseinnahmen basieren in Griechenland auf niedrigen Steuereinnahmen.

Verschiedene, auch umstrittene Gründe werden dafür von verschiedenen Quellen angegeben. Häufig genannten Gründe sind im Folgenden aufgeführt. Das im Vertrag von Maastricht festgelegte Verbot der Haftungsübernahme für Schulden Nichtbeistandsklausel sei zudem ausgehöhlt worden.

Im Zusammenhang mit der griechischen Staatsschuldenkrise wird den Banken missbräuchliche Kreditvergabe vorgeworfen, weil sie, ähnlich wie vor der Subprimekrise , Kredite vergaben, obwohl sie die finanzielle Schieflage Griechenlands bereits erkannt hatten. Die Investitionen waren seit der Euro-Einführung mit Ausnahme des Jahres rückläufig [] , was wegen des hohen Investitionsbedarfs kritisiert wurde. Sowohl die zunehmende Staatsverschuldung Tilgungslasten als auch die steigenden Risikoprämien Zinsen bei Staatsanleihen belasteten den griechischen Staatshaushalt.

Nach der Bankenrettung führte jede Verschlechterung der Wirtschaftsperspektiven zu einem stärkeren Anstieg der Risikoprämien bei den Staatsanleihen. Die dadurch weiter steigende Verschuldung erhöhte wiederum die Zinsen, so dass Ursachen sich gegenseitig verstärkten und hin zu immer höheren Kapitalkosten führten.

Mai ein erstes Hilfspaket englisch: Loan Facility Agreement beschlossen. September betrug Griechenlands Schuldenstand ,16 Mrd. Euro Zinsen an die Gläubiger, bis wird mit rund 70 Milliarden gerechnet. Diese Umschuldung letztlich ein erneuter Schuldenerlass soll Griechenland helfen, aus eigener Kraft die Wirtschaft anzukurbeln und zu einem späteren Zeitpunkt seine dann reduzierten Schulden zurückzahlen zu können.

Die Vereinbarungen über das erste und zweite Hilfspaket wurden mehrfach ergänzt und verändert. Die folgende Tabelle zeigt die Veränderungen:. Aus der Nichtbeistandsklausel geht nach der Deutung hingegen nicht hervor, wie eine freiwillige Übernahme von Schulden durch andere Staaten Rettungsaktion geregelt ist.

Anfang verschlechterte sich die Einschätzung der Finanzlage Griechenlands durch die Kapitalmarktakteure so stark, dass die Zahlungsunfähigkeit drohte. Es wurde befürchtet, dass auch Banken, die Griechenland Geld geliehen hatten, in erhebliche Schwierigkeiten geraten mit weiteren Auswirkungen auf das Euro-Währungssystem. April beschlossen die Mitglieder der Eurozone, Hilfskredite an Griechenland zu gewähren.

Nachdem Ratingagenturen die Kreditfähigkeit Griechenlands weiter herabgestuft und die Risikoaufschläge für langfristige griechische Staatsanleihen erste Rekordwerte erreicht hatten, beantragte die griechische Regierung am Die Geldgeber übernahmen dabei aber keine Haftung für die ausstehenden Schulden Griechenlands.

Euro wurde um 2,7 Mrd. Euro auf 77,3 Mrd. Euro reduziert, nachdem die Slowakei beschlossen hat nicht an der Darlehensfazilität für Griechenland GLF teilzunehmen.

Irland und Portugal beteiligten sich ebenfalls nicht, da sie selbst Finanzhilfen beantragten oder bereits erhielten. Mai stimmten der Deutsche Bundestag [] sowie der Deutsche Bundesrat [] der Griechenland-Hilfe zu und verabschiedeten das Währungsunion-Finanzstabilitätsgesetz. Diese musste jeweils durch gemeinsame Berichte der sog. Troika , also der Europäischen Zentralbank , des Internationalen Währungsfonds und der Europäischen Kommission , bestätigt werden. Die Auszahlung von 73,0 Mrd. Siehe dazu auch den Abschnitt Finanzielle Folgen für die Gläubiger.

Erstmals wurde zudem eine Beteiligung des privaten Finanzsektors auf freiwilliger Basis vereinbart freiwilliger sog. Weiterhin wurde auf dem EU-Gipfel ein Wiederaufbauplan für Griechenland angekündigt, um wirtschaftliches Wachstum zu fördern. Der Deutsche Bundestag stimmte am Im Hinblick auf die Unsicherheit der innenpolitischen Entwicklung in Griechenland wurde die beschlossene Auszahlung zunächst ausgesetzt, nachdem Regierungschef Papandreou am 1.

Als Ministerpräsident folgte ihm am November Loukas Papadimos nach; er bildete eine Übergangsregierung. Mehr sei derzeit nicht zu erwarten. Die OECD hatte alle 14 Ministerien untersucht und kam in einer Studie zu dem Schluss, es gebe weder eine Vision über das Reformziel noch eine Kontrolle für die Umsetzung, kaum Kommunikation innerhalb der Behörden und ein kompliziertes administratives Beziehungsgeflecht ohne jegliche Koordination.

Im Gegenzug musste Griechenland mehr Kontrollen hinnehmen und einen Teil seiner Budgethoheit abgeben.

Zu den Auflagen gehörte auch die Einrichtung eines Sperrkontos. Der Zinssatz für die Kredite aus dem ersten Hilfspaket wurde rückwirkend für die gesamte Laufzeit auf Basispunkte über dem Euribor gesenkt.

Der Deutsche Bundestag stimmte dem Hilfspaket am Die Vereinbarung über das zweite Hilfspaket wurde mehrfach ergänzt und verändert. In der Nacht vom Oktober entwarfen die Euroländer — nach einem vorbereitenden Treffen einige Tage zuvor und nach einer Abstimmung im Bundestag am Oktober [] — einen Plan, durch den Griechenland langfristig — bis — wieder ohne Finanzhilfen aus dem Ausland auskommen sollte.

Euro zur Beteiligung des Privatsektors engl. Da dieser nicht mit Zustimmung aller Anleihegläubiger erfolgte, stellte am 9. Euro in einem Zeitraum von bis Kritik wurde unter anderem wegen des erst spät vom EU-Gipfel beschlossenen Schuldenschnitts geübt, der zuvor von der Politik ausgeschlossen wurde.

Die Kosten trügen nun die Steuerzahler der Eurozone. Nach Überweisung der letzten Tranche der fünften Auszahlung im August stand der fünfte Review an, dem bei hinreichendem Befund die sechste Auszahlung bis zum Der Review zog sich hin, bis sich im Dezember vorzeitige Neuwahlen abzeichneten und der Review-Prozess ausgesetzt wurde. Februar wurde mit der neugewählten Regierung der Syriza eine Streckung des Hilfsprogramms um vier Monate vereinbart, in denen der bisherige Reformplan überarbeitet und dann der fünfte Review abgeschlossen werden sollte.

Dafür wurde sie gerade in Deutschland massiv kritisiert. März wurde die Mehrwertsteuer mit Wirkung vom April wurde vom Kabinett mit dem Kallikratis-Plan eine Verwaltungsreform beschlossen. Geplant wurde unter anderem auch, das Monatsgehalt der Beamten permanent zu streichen. Das griechische Parlament verabschiedete das Sparpaket am 6.

Das griechische Parlament stimmte dem dritten Kürzungspaket der Regierung am Hauptpunkte des dritten Pakets: Der damalige Ministerpräsident Papandreou kündigte am 1. Papandreou stellte am 4.

November im Parlament die Vertrauensfrage und erhielt nach der Ankündigung, eine Übergangsregierung unter Einbindung der oppositionellen Nea Dimokratia bilden zu wollen, die Mehrheit. Selbst die dringendsten Reformen waren ins Stocken geraten. Im Jahr wurden statt der erwarteten Mio. Euro insgesamt Millionen Euro an Steuerschulden eingetrieben.

Dies wird auf die Einrichtung einer zentralisierten Struktur der Finanzbehörden zurückgeführt, sowie auf vermehrte Betriebsprüfungen. Im Februar wurde ein weiteres Sparpaket verabschiedet. Zahlreiche deutsche Unternehmen begleiten den Verkaufsprozess. Die Plattform für Ausschreibungen der öffentlichen Hand ist seit Die Regierungskoalition in Griechenland einigte sich im April auf neue Sparvorschläge im Rahmen ihrer Reformvorhaben.

Seit müssen die Patienten der staatlichen Krankenhäuser 25 Euro pro Behandlung zahlen. Das Gebäude in Rom brachte 6 Mio. EUR und das in London 22 Mio. Juli kritisierte der deutsche Finanzminister Wolfgang Schäuble in einem Interview, dass die Bestandteile des neuen Programms bereits vereinbart, aber unzureichend umgesetzt worden seien.

Das Land benötigt nach seiner Ansicht einen Schuldenschnitt, es sei unmöglich, dass Griechenland die Schulden komplett tragen könne. Im Mai wurden nach Forderungen der Gläubiger weitere Kürzungen unter anderem bei den Renten beschlossen. Daraufhin wurden im Juni die öffentlich-rechtliche Rundfunkanstalt geschlossen, Lehrer, Ärzte und Schulinspektoren kollektiv entlassen. Die Verwaltungsreform wurde dagegen nicht weiter verfolgt, und Manitakis trat zurück. Im September wurde mitgeteilt, dass der Sonderurlaub für Beamte, die mehr als fünf Stunden pro Tag an einem Computer sitzen, abgeschafft werde.

Als Beispiel für Korruption in Griechenland wurde um das Jahr insbesondere auch von nichtgriechischen Medien das Fakelaki thematisiert, die Zuwendung von Bargeld per Briefumschlag. Der Korruptionswahrnehmungsindex beschreibt das wahrgenommene Korruptionsniveau im öffentlichen Sektor eines Staates. Im Zusammenhang mit der Zählung wurden mehrere Straftaten aufgedeckt.

Im Mai wurden Namen von Steuersündern im Internet veröffentlicht, angefangen wurde mit Ärzten, die teilweise zuvor Einkommen unter dem Existenzminimum deklarierten. Januar wurde unter anderem die Pflicht des bargeldlosen Zahlungsverkehrs bei Beträgen über 1. Der damalige griechische Finanzminister Evangelos Venizelos setzte säumigen Steuerzahlern kurz nach seinem Amtsantritt im November ein Ultimatum.

Er rief alle Personen, die dem Staat mehr als November bei den Steuerbehörden zu melden und ihre Schulden zu regeln. Andernfalls werde er ihre Namen veröffentlichen. Januar wurde die Liste mit 4. Dabei handelte es sich um aktive und ehemaligen Politiker sowie Bürgermeister und Beamte. Eine im Jahr überreichte Steuerdaten-CD mit rund 2. Ausgaben müssen mittels eines Belegs nachgewiesen werden. Das ist doch surreal.

Das Occasional Paper der Europäischen Kommission aus dem Dezember widerspricht jedoch der Einschätzung, dass bei den Militärausgaben kaum gekürzt werde. Es wurde darauf verwiesen, dass die Ausgaben für Waffenimport und Militärausgaben seit allgemein gesunken sind. Die militärischen Beschaffungen englisch: Der griechische Premierminister Tsipras unterbrach am Juni Samstag griechischer Ortszeit abrupt die Verhandlungen mit der Eurogruppe in Brüssel und kündigte bereits für den 5.

Juli ein Referendum über die von den Kreditgebern in ihrem Textentwurf gestellten Bedingungen für weitere Auszahlungen aus dem zweiten Hilfspaket an. Juli stimmte das griechische Parlament der Vereinbarung unter Zuhilfenahme der Opposition mehrheitlich zu; weitere nationale Parlamente mussten noch abstimmen. Die Zentralbank der Eurogruppe hat nach den Abstimmung in Athen am Juli Soforthilfen für Griechenland zugesagt, eine Ausweitung des Kreditrahmens aber abgelehnt.

Finanzminister Varoufakis, der seit Amtsübernahme einen Grexit zwar nicht aktiv herbeiführen wollte, aber als Alternative in einer kleinen Gruppe theoretisch durchspielte, schlug folgende als umkehrbar gedachte Reaktionen vor: Juni zahlte Griechenland eine fällige Rate an den Internationalen Währungsfonds nicht zurück. Damit war es das erste entwickelte Land, das dieser Institution eine Rate schuldig blieb.

Die mit der Eurozone am Juli ausgehandelten Bedingungen für weitere Kredite [] enthielten grobe Eckpunkte. Innerhalb der folgenden zehn Tage verabschiedete das griechische Parlament Gesetze, die in den beiden folgenden Abschnitten beschrieben werden; sie waren von den Gläubigern zur Voraussetzung für die Aufnahme weiterer Verhandlungen erklärt worden. Dabei verlor die Regierung die eigene Mehrheit, wurde aber von Teilen der Opposition unterstützt.

Wesentliche Bestandteile des Gesetzes sind folgende: Juli verabschiedete das griechische Parlament das zweite der geforderten vorrangigen Gesetze. Dabei hatte die Regierung erneut keine eigene Mehrheit, wurde aber von Teilen der Opposition unterstützt.

Das Gesetz umfasst zweierlei: Juli überwies die Europäische Zentralbank aus Mitteln des sog. Darauf wurden am Ferner wurde eine überfällige Zahlung von 2,05 Milliarden Euro an den Internationalen Währungsfonds geleistet.

Die Griechische Zentralbank hatte am Juli schon Millionen Euro erhalten, um die Wiederöffnung der Banken zu ermöglichen. Am Montag, den Juli öffneten die Banken in Griechenland nach drei Wochen wieder ihre Schalter. Die Verhandlungen sollen bei etwas vermindertem Termindruck wie zuvor in Brüssel innerhalb der gesamten Eurogruppe stattfinden, speziell mit der derzeit in Athen amtierenden Regierung Tsipras.

Der deutsche Finanzminister beruft sich zudem insbesondere auf Artikel der EU-Verträge, der Staatsschuldenreduzierungen gänzlich verbietet. Die Europäische Zentralbank hat darüber hinaus am Der Rest kam ausländischen Gläubigern zugute, womit Risiken von Geschäftsbanken auf ausländische Steuerzahler überwälzt worden sind.

Euro der von ,9 Mrd. Die technische Hilfe umfasst die gemeinsame Ausarbeitung eines Austeritätsplans, der von der gewählten Regierung im Alleingang politisch kaum durchsetzbar wäre. Die Tilgung des Kredits wie auch die Zinszahlungen wurden klar geregelt. Die Rückzahlung begann noch unter der Regierung Samaras. Das erste Kreditpaket von 20,1 Mrd. Hier herrscht einige Verwirrung darüber, ob überhaupt und falls ja, in welcher Form die EU-Länder ihr Geld zurück erhalten werden.

Während die Presse kontrovers darüber berichtet, scheint die Politik hier ein klärendes Wort zu vermeiden. Der ehemalige Finanzminister Yanis Varoufakis deutete mit seiner Weigerung, ein drittes Memorandum zu unterschreiben, genau auf dieses Problem hin.

Er erwartete von seinen Kollegen in der Euro-Gruppe, dass der Zeitplan für die formale Abschreibung dieser Buchungskredite vorher festgelegt und den Völkern offen gelegt wird. Weil aber auch dieses politisch nicht durchsetzbar ist — diesmal bei den Wählern der 27 EU-Partner — stellt sich die Euro-Gruppe auf den Standpunkt, dass eine Rückerstattung tatsächlich erfolgen würde.

Andererseits wird vorsichtig argumentiert, dass eine mögliche Erleichterung erst nach Abschluss des dritten Programms ab August zur Diskussion stünde. Der IWF dagegen verlautbart seit dem Ende des ersten Programms und in der jüngsten Vergangenheit zunehmend deutlicher, dass nunmehr der Schuldenschnitt anstünde.

Nun würde sich die Parteibasis gegen eine Mitgliedschaft organisieren. Ähnlich bestimmen sich die Primärausgaben als die Staatsausgaben ohne Berücksichtigung von Zinsausgaben für den bestehenden Schuldenstand. In der Eurozone herrschen hohe Leistungsbilanzungleichgewichte. Griechenland war von diesen Problemen besonders betroffen und nicht auf die Eurokrise vorbereitet, durch eine höhere staatliche Verschuldung hatte man zudem weniger Spielraum als andere Länder in der Reaktion auf die Finanzkrise ab Als weitere aktuelle Probleme werden der Mangel an Krediten im griechischen Inland für Investitionen und der Mangel an Nachfrage nach Produkten in anderen Euroländern in Folge restriktiver Fiskalpolitik benannt.

Die Gesamtzahl der Staatsbediensteten sank von EU-Angaben zufolge konnte im Zeitraum bis die Hälfte des von bis entstandenen Wettbewerbsrückstandes wieder aufgeholt werden.

Rolf Langhammer vom Institut für Weltwirtschaft Kiel warnte die Gläubigerinstitutionen angesichts mangelnder Einhaltung griechischer Zusagen, es gebe weder etwas nachzuverhandeln noch nachzujustieren. Euro ab vorgesehen. Die Praxis aller Hilfsprogramme habe gezeigt, dass Griechenland seine Zusagen nicht einhalte bzw.

Bereits vor Beginn der griechischen Haushaltskrise war Griechenland als Schuldner bei den Ratingagenturen nicht mit Bestnoten bewertet. Anfang Mai hatte der Index Punkte. In Umfragen unmittelbar vor Abstimmung des Sparpakets im Mai hatte sich eine Mehrheit der Griechen dafür ausgesprochen. Buttner, realizing that he could teach this young genius no more, recommend him to the Duke of Brunswick, who granted him financial assistance to continue his education into secondary school and finally into the University of Gottingen.

A Modeling Approach Using Technology: Integrated Mathematics, Level 2. According to mathematical lore, one day his teacher asked the class to add all the natural numbers from 1 to Students were instructed to place their slates on the table when finished. To the surprise of the teacher, young Gauss placed his slate on the table after only a few moments. To find the sum of the first natural numbers, Gauss used a method involving a finite series. For example, the sum of the first numbers can be written as the arithmetic series S The story of and other weird math facts.

Curiousmath Web site posting dated Monday, February 10, , 4: About years ago, a young boy who grew up to be a great mathematician by the name of Gauss pronounced "Gowss" was at school when the class got in trouble for being too loud and misbehaving. Their teacher, looking for something to keep them quiet for a while, told her students that she wanted them to "add up all of the numbers from 1 to and put the answer on her desk.

About 30 seconds later, the year-old Gauss tossed his slate small chalkboard onto the teacher's desk with the answer "" written on it and said to her in a snotty tone, "There it is. That's 50 pairs of So he just multiplied by 50 to get A Language for Learning.

Therefore, let us consider a numerical problem, which has its roots in the following story about the young Carl Frederick Gauss, who was to become one of the greatest mathematicians of all time. The story is probably apocryphal, but is still a good story. This version follows Polya , who also uses it to introduce recursion in mathematical problems.

When Gauss was in primary school, the teacher, hoping to keep his students occupied while he attended to other matters, gave a tough problem: While the other children were just getting started, young Gauss walked to the teacher's desk and handed in his slate.

The teacher, thinking this an act of impudance, did not even bother to look at Gauss's work until all the other children had handed in theirs. When he did look at it, he was surprised to find that it contained just a single number, the right answer. In Matierialien für eine wissenschaftliche Biographie von Gauss , compiled by F. Link to PDF file pp. Den Schülern der under des Lehrers Büttner Leitung stehenden Rechenklasse der Katharineenschule in Braunschweig wurde die Aufgabe vorgelegt, die Summe einer Reihe auf einander folgende Zahlen zu bilden.

Jeder, der die Rechnung beendet haben würde, sollte die Tafel auf einen Sammeltisch legen. Der alte Büttner musterte den schnellfertigen Knaben mit spöttischem Mitleid, während die andern Schüler die Stunde hindurch weiter Rechneten. Er hatte das Summationsprinzip für die arithmetischen Reihen auf den ersten Blick herausgefunden.

Red Orbit Breaking News, 29 September It wasn't just that they solved it in record time, it's that they figured out a whole new way of doing it. Desiree Martinez and Amber Lopez, both freshman algebra students at Pojoaque Valley High School, figured out the answer to a math problem made famous by 18th-century mathematician Johann Carl Friedrich Gauss in 6 and 11 minutes, respectively. Those are the two best times their teacher, Lanse Carter, has seen in his four years of teaching.

The problem is to add all integers from one to Carter said he gives his students one hint before they start, which is to look for a pattern. Go ahead, play at home—the answer and method will be near the end of this article. Don't forget to show your work.

In the meantime, here's a history lesson: Gauss' math teacher, J. Buttner, reputed to be a rather surly man, assigned the problem when he wanted to occupy his students for up to an hour and was dismayed when Gauss, then 13 some histories peg his age at 10, others as young as 7 , solved it in about a minute, flinging his slate upon the table barely after Buttner finished stating the problem and saying "Ligget se," Brunswick German for "there 'tis.

Martinez and Lopez "through their own ingenuity, found a pattern I wasn't looking for," Carter said, adding that pattern recognition is a key concept in mathematics. Now for the answer. Realizing he had 50 pairs of numbers that, when added, equal , he multiplied 50 times and came up with the answer, 5, Martinez and Lopez also found a pattern, but it was different from Gauss'. A third attempt, adding all the numbers between 21 and 30, resulted with a total of It gave me a wonderful feeling as well," Carter said.

How Do You See It? Discovering Mathematical Patterns and Sequences. When Karl Gauss, a brilliant German mathematician, was 10 years old in the late 18th century he was presented a very difficult problem. His teacher, a stern and lazy man, wrote on the board the task that these young men had to perform. The problem was to add up all the numbers from 1 to Knowing this would take his students time, the arrogant teacher began to go back to his seat and prepare himself for a long quiet day.

As soon as he sat down, Gauss approached him and put the slate, a small board that these students used to do their work on, face down on his teacher's desk. All the students were shocked at how fast and seemingly effortlessly Gauss completed the problem.

The teacher just glared at him. By the end of the school day, the last of the boys set his slate down.

The teacher had a feeling that no person came up with the right answer. He began turning over each of the slates, each revealing a wrong answer. Finally he came to Gauss' slate. All the kids snickered as the teacher slowly turned his slate over. The teacher's face was pale and stunned.

Gauss had the correct answer! What's even more surprising is that he had written very little besides the answer. How did young Gauss come up with the answer? Oddly, he did not have an equation like we have now.

He did it purely on observation. Look at the series of numbers Take the first and last term of the series, 1 and Gauss says that this combination when adding together equals Looking at another combination, 2 and 99 is also and so forth. Thinking that this pattern repeated for all the others, he knew he had a certain number of 's. The question was how many 's were there? Gauss was brilliant for his age and became ever more brilliant as his life went on. Gauss' method is wonderful to look at but there still must be an easier way to figure out the sum of a finite arithmetic series.

We can solve this problem using the equation: Carl Friedrich Gauss — — sein Leben. April in Braunschweig als Sohn eines Gassenschlächters geboren, verblüffte Carl Friedrich Gauss — der von sich selbst sagte, er habe eher rechnen als sprechen gelernt — schon als Kind seine Lehrer. In der mit Schülern überfüllten Schulstube erteilte der Lehrer die Aufgabe, alle Zahlen von 1 bis zu addieren.

Lange vor seinen Mitschülern hatte der kleine Carl Friedrich das richtige Ergebnis parat. Geschwinde, Ewald, and Hans-Jürgen Schönig. At the age of seven, Carl Friedrich Gauss started elementary school, and his potential was noticed almost immediately. His teacher, Büttner, and his assistant, Martin Bartels, were amazed when Gauss summed the integers from 1 to instantly by spotting that the sum was 50 pairs of numbers each pair summing to Gauss's Formula for the sum of integers was born.

Physics for Scientists and Engineers with Modern Physics. Upper Saddle River, N. Gauss was born on April 30th, in the Duchy of Brunswick, now a part of Germany. He was a child prodigy, and many stories are told of his early mathematical prowess. It is well-documented that he corrected an error in his father's payroll calculations at the age of three, and as an adult he explained that by his recollection he could count before he could talk. Probably the most famous story about young Gauss occured in , when he was nine years old.

Büttner, assigned his class the task of adding all of the numbers from 1 to Gauss turned in his slate after only a few seconds, with only the final answer written down. Büttner studiously ignored him until the class had finished, and was astonished to find that Gauss's answer was correct. He asked Gauss how he had arrived at his answer, and Gauss explained: After Gauss' death in February of , a medal was struck in his honor The history of every real prince begins with a childhood surrounded by legends.

Gauss was not an exception At the age of seven, Carl Friedrich entered Catherine's School. In that school students were not taught how to count until the third grade, so for the first two years nobody paid attention to little Carl. The children usually got to the third grade at the age of 10 and stayed in that grade until confirmation at the age of The teacher Büttner had to devote himself simultaneously to children of different ages and knowledge.

For this reason, he often gave some of the students long exercises in calculation in order to be able to talk to other students. Once, he asked a group of students, among them Gauss, to sum up all natural numbers from 1 to As a student finished the calculations, he would place his slate on the teacher's desk. The order of the slates was taken into account when giving marks. Ten-year-old Gauss turned in his slate as soon as Büttner had finished assigning the task.

To everybody's surprise, only Gauss' answer turned out to be correct. The explanation was simple: The fame of the infant prodigy spread all over Brunswick. String Crossings Andrew Glassner's Notebook. Passage appears on p. The story goes that when Gauss was a child, his math teacher came to class unprepared one day. The teacher decided to fill the class time by instructing the students to add up all the numbers from 1 to Most of the students started writing down all the numbers in a big column in preparation for adding them up.

But in only a few seconds Gauss announced to the teacher that the answer was 5, The teacher assumed that Gauss had simply learned this result as a piece of trivia. So she set him about the more time-consuming task of adding the numbers from 1 to After only a moment's paperwork, Gauss announced the answer was , Monkeyshines Explores Math, Money, and Banking. Most of us imagine mathematicians to be old people with beards and thick glasses, yet many of the important mathematical discoveries have been made by fairly young people.

One of the youngest and most famous mathematicians in all of history was Carl Friedrich Gauss who was born in Germany in and died in He came from a poor family. His father was a gardener and his mother a housekeeper. Young Gauss showed his mathematical ability at a very early age. When he was three years old he watched his father add up a long column of numbers.

Gauss pointed out an error and gave his father the correct answer. When the father checked the addition, he found his son was indeed correct. When Gauss was ten years old he began his first lessons in arithmetic.

The teacher gave the class a long and difficult problem so they would have to spend hours to find the answer. The problem involved adding up a sequence of numbers like: There is a trick to solve problems like this but it was unknown to the young students. However, Gauss discovered the trick for himself and quickly solved the problem while all the other students worked for hours and all the answers were wrong except for Gauss's.

Recognizing that Gauss was special, his teacher helped him to advance in his studies. Goldstein, Martin, and Inge F. The Experience of Science: Most mathematicians are no less bored by adding up long columns of figures than the rest of us. They do not consider it their job, and are usually annoyed when nonmathematicians assume that it is. The point may be illustrated by two episodes in the life of Karl Gauss — , one of the greatest of mathematicians.

Gauss was born a poor boy, the son of a bricklayer, in Braunschweig, Germany. The schoolmaster in the local school Gauss attended, a certain Herr Büttner, was a hard taskmaster who gave his classes practice in arithmetic by asking them to add up long sequences of large numbers. For his own convenience, so that he would not have to do the tedious arithmetic involved to check his pupils' almost invariably erroneous answers, the sequences of numbers he assigned his classes to add were chosen to form what it called an arithmetic series—the successive numbers in the long list differed by a constant amount.

For example, the series 11, 14, 17, 20, 23, 26 is such a series, in which each term increases by 3. Büttner then makes use of a well-known formula for the sum of such a series: For the series given above, the sum is. In any event, Büttner wrote on the blackboard a list of large numbers forming such a series, and after finishing turned around to face the class, expecting as usual to have a free hour or so while his pupils sweated and struggled, to find little Gauss handing in his slate with the correct sum written out.

Gauss had recognized the numbers as forming an arithmetic series, figured out on the spot the formula for the sum, and calculated it. Büttner, to his everlasting credit, though no mathematician himself, knew one when he saw one.

With his own money he bought Gauss the best textbook on arithmetic then available and brought the boy's abilities to the attention of people who could help him in his career.

Gauss et le GAUS. La Revue de Physique. An Invitation to Mathematics. Karl Friedrich Gauss — was one of the finest mathematicians of all time. The son of a bricklayer, it is said that he spotted formulae for certain arithmetic sums for himself at the age of His teacher had a habit of setting the class long strings of numbers to add up to keep them occupied, all the time knowing a formula for the answer.

Gauss outwitted him and all his teacher could do was to buy him a text book and announce that the boy was beyond him. Knuth and Oren Patashnik. To evaluate S n [the sum of the first n positive integers] we can use a trick that Gauss reportedly came up with in , when he was nine years old: Gauss's trick in chapter 1 can be viewed as an application of these three basic laws [i.

These two equations can be added by using the associative law: And we can now apply the distributive law and evaluate a trivial sum: Blog posting, Jeudi 14 juillet Translated by Albert Froderberg. Biographies about or by great men generally contain more or less noteworthy anecdotes, intended to illustrate the budding genius.

It is a field in which memory gladly accommodates itself to a fixed path and where imagination easily overtakes the uncertain facts. The situation is especially pernicious in the case of child prodigies, who are often encountered in mathematics, music, and chess.

Myths appear with treacherous ease. Gauss was a mathematical prodigy—it is certain that he was one of the most outstanding examples of this genre, but basically this is unimportant.

First-hand accounts of this come from Gauss himself, who in his old age liked to talk of his childhood. From a critical viewpoint they are naturally suspect, but his stories have been confirmed by other persons, and in any case they have anecdotal interest. During the summers Gebhard Gauss was foreman for a masonry firm, and on Saturdays he used to pay the week's wages to his workers. One time, just as Gebhard was about to pay a sum, Carl Friedrich rose up and said, "Papa, you have made a mistake," and then he named another figure.

The three-year-old child had followed the calculation from the floor, and to the open-mouthed surprise of those standing around, a check showed that Carl Friedrich was correct. Gauss used to say laughingly that he could reckon before he could talk. He asked the adults how to pronounce the letters of the alphabet and learned to read by himself. When Carl Friedrich was seven years old he enrolled in St. His teacher was J.

The large classroom had a low ceiling, and the schoolmaster walked about on the uneven floor, cane in hand, among his approximately pupils. Caning was the foremost pedagogical aid both for learning and discipline, and Büttner is thought to have used it constantly, either as a consequence of necessity or because of his temperament.

Gauss stayed in these surroundings for two years without any ill consequences. It is the traditional picture of that period's public education, when the caning pedagogy was generally accepted—by the adults of course—but we shall soon see that Büttner was more likely above than below average among his colleagues. When Gauss was about ten years old and was attending the arithmetic class, Büttner asked the following twister of his pupils: The problem is not difficult for a person familiar with arithmetic progressions, but the boys were still at the beginner's level, and Büttner certainly thought that he would be able to take it easy for a good while.

But he thought wrong. In a few seconds Gauss laid his slate on the table, and at the same time he said in his Braunschweig dialect: While the other pupils added until their brows began to sweat, Gauss sat calm and still, undisturbed by Büttner's scornful or suspicious glances.

At the end of the period the results were examined. Most of them were wrong and were corrected with the rattan cane. On Gauss's slate, which lay on the bottom, there was only one number: It seems unnecessary to point out that this was correct. Now Gauss had to explain to the amazed Büttner how he had found his result: This is a total of 50 pairs of numbers, each of which adds up to Thus Gauss had found the symmetry property of arithmetic progressions by pairing together the terms as one does when deriving the summation formula for an arbitrary arithmetic progression—a formula which Gauss probably discovered on his own.

What this actually entails is that one writes the series both "forward" and "backward"; that is. The event is symbolic. For the rest of his life Gauss was to present his results in the same calm, matter-of-fact way, fully conscious of their correctness. The evidence of his struggles would be wiped away from the completed work in the same way.

And, like Büttner, many learned persons would wish to be given a detailed explanation, but here a difference would appear, for Gauss would not feel compelled to give one. Hannoversch Münden web site. Der Fürst der Mathematiker konnte früher rechnen als sprechen Den Anekdoten nach war der am Zwolf Kapitel aus Seinem Leben. Auf dieser Seite also glauben die verborgenen Quelladern des Genius riefeln zu hören. Und doch, wie hoch man die Gunst dieser Einflüsse auch anschlagen mag, ein Wunder bleibt es, mit welcher Macht er in diesem Erdenfinde hervorbrach.

Aus sich selbst, mit gelegentlicher Nachfrage bei seiner Umgebung, lernt er lesen; am erstaunlichsten aber zeigt sich von frühester Kindheit an die intuitive Kraft seiner Auffassung von Zahlenverhältnissen: Als es ans Unszahlen geht, zirpt er warnend dazwischen, und siehe da, der Alte hat sich verrechnet und was der Kleine angiebt ist das Richtige.

Katharine, der er seit angehört, eine arithmetische Reihe summirt werden soll. Der alte Büttner mustert den schnellfertigen kleinsten seiner Unglückswürmer mit spöttischem Mitleid: In der Schule hatte der Lehrer die Aufgabe gestellt, alle Zahlen von 1 bis zusammenzuzählen. Auf seiner Tafel steht die richtige Zahl , und viele andere sind falsch oder noch nicht fertig. Er hatte den geometrischen Aufbau der Zahlen sofort vor Augen gehabt und erkannt: God Created the Integers: Gauss's talents were obvious as soon as he stepped into a classroom at the age of seven.

When the class began to be unruly, the teacher, J. Büttner, assigned them the task of adding up all of the integers from 1 to As his classmates struggled to fit their calculations on their individual slates, Gauss wrote down the answer immediately: As soon as the problem was stated, Gauss recognized that the set of integers from 1 to was identical to 50 pairs of integers each adding up to Herr Büttner approached Gauss's parents to persuade them to let their son stay after school for special math instruction.

Gauss's parents were at first skeptical. They had recognized their son's calculating ability when, at the age of three, he corrected a mistake his father made in paying out wages to men who worked [for] him Discrete Structures, Logic, and Computability.

When Gauss—mathematician Karl Friedrich Gauss — —was a year-old boy, his schoolmaster, Buttner, gave the class an arithmetic progression of numbers to add up to keep them busy. We should recall that an arithmetic progression is a sequence of numbers where each number differs from its successor by the same constant.

Gauss wrote down the answer just after Buttner finished writing the problem. Although the formula was known to Buttner, no child of 10 had ever discovered it. For example, suppose we want to add up the seven numbers in the following arithmetic progression:.

The example illustrates a use of the following formula for the sum of an arithmetic progression of n numbers a 1 , a 2 , Insights and connections—that's what mathematicians look for.

Carl Friedrich Gauss, who was born in in Braunschweig, Germany, the son of a masonry foreman, was a master of exposing unsuspected connections. Like Erdös, Gauss was a mathematical prodigy, and in his old age he liked to tell stories of his childhood triumphs. Like the time, at the age of three, he spotted an error in his father's ledger and stopped him just as he was about to overpay his laborers.

Like the fact that he could calculate before he could read. And he certainly could calculate. At the age of ten, he was a show-off in arithmetic class at St. Catherine elementary school, "a squalid relic of the Middle Ages The student who solved the problem first was supposed to go and lay his slate on Büttner's desk; the next to solve it would lay his slate on top of the first slate, and so on. Büttner thought the problem would preoccupy the class, but after a few seconds Gauss rushed up, tossed his slate on the desk, and returned to his seat.

Büttner eyed him scornfully, as Gauss sat there quietly for the next hour while his classmates completed their calculations. As Büttner turned over the slates, he saw one wrong answer after another, and his cane grew warm from constant use. Finally he came to Gauss's slate, on which was written a single number, 5,, with no supporting arithmetic.

Astonished, Büttner asked Gauss how he did it, "and when Gauss explained it to him," said Erdös, "the teacher realized that this was the most important event in his life and from then on worked with Gauss always," plying him with textbooks, for which "Gauss was grateful all his life. What was Gauss's trick? In his mind he apparently pictured writing the summation sequence twice, forward and backward, one sequence above the other:.

Gauss realized that you could add the numbers vertically instead of horizontally. There are vertical pairs, each summing to So the answer is times divided by 2, since each number is counted twice. Gauss easily did the arithmetic in his head. Gauss found a very nice way of showing that if you add all the numbers from one up through any number n , the answer is n times n plus one, all divided by two.

This method of summing such a series is really straight from the Book. Bulletin Institute of Mathematics and its Applications 13 3—4: Reprinted in Makers of Mathematics , , London: Gauss' precocity is legendary. At the age of 3 he was correcting his father's weekly wage calculations.

When he was 7 he entered his first school, a squalid prison run by one Büttner, a brutal taskmaster. Two years later Gauss was admitted to the arithmetic class. Büttner had the endearing habit of giving out long problems of the kind, such as summing progressions, where the answer could readily be obtained from a formula—a formula known of course to the teacher, but not to the pupils.

Each boy, on completing his task, had to place his slate on the master's desk. On one occasion no sooner had Büttner dictated the last number than his youngest pupil flung his slate on the desk and waited for an hour while the other boys toiled. When Büttner looked at Gauss' slate, he found there a single number—no calculation at all.

Gauss liked to recall this incident in his later years, and to point out that his was the only correct answer. Ponder this, July Although it is contended that the solution for finding the sum of consecutive integers has ancient roots, perhaps stretching back to Pythagorus, it is the story of Gauss's school age experience that has become legend. As the story goes, Gauss's teacher tried to occupy the class during an unsupervised absence by proposing a simple problem: Find the sum of all integers from 1 to As his classmates laboriously -- and quietly, one hopes -- proceeded to work the solution by rote addition, Gauss reasoned the problem as follows:.

He imagined adding, not the consecutive integers, but two series of addition, the integers progressing forward in one series and in reverse in the other. He concluded that the sum of the two series was the product of the largest integer in the series and that integer plus 1: The reaction of Gauss's classmates -- and his teacher -- to his shortcut remains a mystery.

Fortunately, his result has been preserved. We shall start with an arithmetic progression whose first term and common difference are 1. This is the progression. According to the tradition in the schools at that time, when a mathematics problem was given to a class, the pupil who finished first placed his slate board down in the middle of a large table, and then the next to finish put his slate down on top of it. One day, when young Carl was a pupil in Mr.

Büttner's arithmetic class, Mr. Büttner posed the problem of adding an arithmetic progression. He had barely finished describing this task when Gauss threw his slate board on the table saying, in low Brunswick dialect, "Ligget se" "there she lies". While the other pupils continued to work on this problem, Mr. Büttner, conscious of his dignity, walked up and down the room, and occasionally threw a contemptuous and caustic glance at the smallest of his pupils, who had finished the task too quickly.

At last the other slates began to come in; and when the slates were turned over, Mr. Büttner found that Gauss' solution was correct even though many of the others were wrong and were corrected with a slapping. Therefore the number that Gauss wrote on his slate should have been The method we have just described for summing an arithmetic progression is both fast and simple, and because it is simple, it is not prone to computational errors.

We shall now repeat the method to obtain the more general sum. Janzen, Beau director and animator. Video on YouTube or Vimeo. Usenet posting in news group alt. This sounds like the story recounted by Eric Temple Bell about K. Gauss at the age of about 8 years, except that probably nobody considered Gauss to be "dull", just not yet at that age a great mathematician. I don't know the starting number nor the increment, but they formed an arithmetic progression, the kids were probably supposed to derive each term before adding it, and the teacher had a secret formula for determining the answer.

My guess is that Gauss figured out that the teacher had access to something he wasn't sharing and independently derived a slick way to find the sum, by rearranging the order of summing. Maybe it wasn't exactly divine inspiration, but it still took a pretty impressive mind to come up with that technique at that age. Gauss just wrote the answer on his slate no calculations , and he and Büttner sort of glared at each other for an hour while the other boys slaved away.

Gauss later said that his answer was the only correct one turned in that day. The story has a happy ending -- the teacher, recognizing that there wasn't much more that he could teach this unusual student, arranged for a tutor to take charge of Gauss's education, and the tutor and Gauss became lifelong friends and collaborators.

Kaplan, Robert, and Ellen Kaplan. The Art of the Infinite: The Pleasures of Mathematics. In order to savor once more this all too fugitive experience, here is a very different way of seeing that. Some people relish the geometric approach, some of the symbolic. This tells you at once that personality plays as central a role in mathematics as in any of the arts. Proofs—those minimalist structures that end up on display in glass cases—come from people mulling things over in strikingly different ways, with different leapings and lingerings.

But is it always from the same premises that we explore? Is there some sort of common sense that is to reason what Jung's collective unconscious used to be to the psyche? One of these approaches, or some third, must have been in the mind of the ten-year-old Gauss—the Mozart of mathematics—when, in his first arithmetic class, he so startled his teacher. It was and Herr Büttner was in the habit of handing out brutally long sums like these, which the children had to labor over. When each one finished, he added his slate to the pile growing on the teacher's desk.

The morning might well be over before all had finished. But Gauss no sooner heard the problem than he wrote a single number on his slate and banged it down. A History of Mathematics: Gauss was born into a family that, like many others of the time, had recently moved into town, hoping to improve its lot from that of impoverished farm workers. One of the benefits of living in Brunswick was that the young Carl could attend school.

There are many stories told about Gauss's early-developing genius, one of which comes from his mathematics class when he was 9. At the beginning of the year, to keep his pupils occupied, the teacher, J. Büttner, assigned them the task of summing the first integers. He had barely finished explaining the assignment when Gauss wrote the single number on his slate and deposited it on the teacher's desk. Gauss had noticed that the sum in question was simply 50 times the sum of the various pairs 1 and , 2 and 99, 3 and 98, Die Vermessung der Welt.

Büttner hatte ihnen aufgetragen, alle Zahlen von eins bis hundert zuzammenzuzählen. Das würde Studen dauern, und es war beim besten Willen nicht zu schaffen, ohne irgendwann einen Additionsfehler zu machen, für den man bestraft werden konnte.

Na los, hatte Büttner gerufen, keine Maulaffen feilhalten, aufangen, los! Jedenfalls hatte er sich nicht unter Kontrolle gehabt und stand nach drei Minuten mit seiner Schiefertafel, auf die nur eine einzige Zeile geschrieben war, vor dem Lehrerpult. So, sagte Büttner und griff nach dem Stock. Sein Blick fiel auf des Ergebnis, und seine Hand erstarrte. Er fragte, was das solle.

Darum sei es doch gegangen, eine Addition aller Zahlen von eins bis hundert. Hundert und eins ergebe hunderteins. Neunundneunzig und zwei ergebe hunderteins.

Achtundneunzig und drei ergebe hunderteins. Das könne man fünfzigmal machen. Also fünfzig mal hunderteins. Helping Children Learn Mathematics.

The Art of Mathematics. The great mathematicians feel mathematics in a way the rest of us do not. And their genius for mathematics is immediately recognizable. When Gauss was eight years old, he and his classmates were asked by their teacher to find the sum of the integers from 1 to The children began laboriously to calculate on their slates. Gauss noticed that the integers 1, 2, 3, There are exactly 50 such pairs and the sum of the integers in each pair is Hence, the desired sum is the same as 50 times , which is Gauss wrote this number on his slate and handed it to the teacher.

The whole process took him only seconds. Gaea, Natur, und Leben. Im siebenten Jahre lam der Knabe in die Katharinenschule und wurde zunächst während zweier Jahre im Lesen und Schreiben unterrichtet, ohne sich irgendwie vor seinen Mitschülern auszuzeichnen.

Eduard Heinrich Mayer Verlagsbuchhandlung. The anecdote appears on pp. The Pleasures of Counting. There is a well known story, repeated, with his usual trimmings, by Bell in his Men of Mathematics , that when Gauss was ten his teacher, Bütner, seeking an hour's repose, set his pupils the term sum.

A more restrained account of Gauss's early life, and a more sympathetic estimate of Bütner will be found in Bühler's excellent biography. More Stories and Anecdoetes of Mathematicians and the Mathematical. Mathematical Associaiton of America. What Gauss did was to observe that the sum of an arithmetic series is the number of terms multiplied times the average of the first and last term.

The story has, however, been transmogrified with time. It is thought that the actual sum that Gauss was asked to calculate was. John Wiley and Sons. The number of risk parameters in a portfolio equals the sum of the number of assets it includes.

There is an amusing and perhaps apocryphal story about this result and the famous mathematician Carl Friedrich Gauss, who was born in in Braunschweig, Germany. When Gauss was a child at St. Catherine elementary school, his teacher who was named Büttner asked the students in his class to sum the numbers from one to Büttner's intent was to distract the students for a while so that he could tend to other business. To Büttner's surprise and annoyance, however, Gauss, after a few seconds, raised his hand and gave the answer—5, Büttner was obviously shocked at how quickly Gauss could add, but Gauss confessed that he had found a short cut.

He described how he began by adding one plus two plus three but became bored and started adding backward from He then noticed that one plus equals , as does two plus 99 and three plus He immediately realized that if he multiplied by and divided by 2, so as not to double count, he would arrive at the answer. Dare i numeri fa bene. Il professore ha fama di essere assai burbero e dai modi scostanti.

Inoltre, pieno di pregiudizi fino al midollo, non ama gli allievi che provengono da famiglie povere, convinto che siano costituzionalmente inadeguati ad affrontare programmi culturali complessi e di un certo spessore.

Un episodio in particolare viene ricordato nelle storie della matematica. Proprio mentre comincia a gongolarsi al pensiero di quanto un suo trucchetto avrebbe lasciato a bocca aperta gli alunni, viene interrotto da Gauss che, in modo fulmineo afferma: Engines of Our Ingenuity, No.

Podcast and Web site. Link to Web page Viewed and [Based in part on material presented here. You may've heard the story about the great mathematician Carl Friedrich Gauss.

He was a young schoolboy in the s. To keep his class quiet, the teacher told them to sum all the numbers from one to a hundred. Gauss immediately turned his slate over on the teacher's desk. After an hour, the teacher had all the slates, and he found the right answer on that bottom one. The other boys made errors in the tedious arithmetic, while Gauss saw a shortcut.

He saw that he could add one and a hundred, two and 99, on down to fifty. Now Brian Hayes goes looking for the truth of the story, and finds that it's been retold in many dozens of versions. He traces them from to the present, and what he learns is quite amazing. In some, Gauss is the youngest student. In some he's the only one to get it right. Some versions have the teacher knowing the answer when he makes the assignment, others don't.

There's a variant on how Gauss might've worked the problem. Instead of doing it as I've just described, he might've added zero and a hundred, one and 99, until he reached 49 and Then he'd have a hundred, fifty times, with the middle fifty to tack on.

Same answer, slightly different tactics. Riesen und Zwerge im Zahlenreich: Und doch ist das Ergebnis richtig: Leipzig, Teubner, ; von ihnen will ich wenigstens eine hier wiedergeben, die ebenso im Rechenunterricht der Kleinen wie bei der Behandlung der arithmetischen Reihen in Obersekunda oder Prima ihre Stelle haben kann. Die Aufgabe lautete diesmal: Der Lehrer freut sich schon, den allzu fixen Buben ertappt zu haben.

Doch nach her ergibt sich: How to be a little Gauss. There is a story about Carl Friedrich Gauss. The teacher wanted to get some work done, or get some sleep, or whatever. Anyway, to the teacher's annoyance, little Gauss [Here the lecturer holds his hand out to show that little Gauss was about 2 feet tall, to the amusement of the audience] To the teacher's annoyance, little Gauss came up to the teacher with the answer, right away.

The teacher probably had to spend the rest of the class time verifying little Gauss's [2 feet tall] result. Some people find that story hard to believe, even impossible. I think that the story has the ring of truth to it. I believe that the story is true, or close to it. There are versions of the story, in which the numbers are one to a thousand [murmur in the audience]. I think that you people can duplicate little Gauss's [2 feet tall] trick [doubt in the audience].

I'm going to give you two very small hints. But, that's all you will need, to be just like little Gauss [2 feet tall]. Nobody use your calculators, or even paper and pencil for a while. You are going to be slower than little Gauss [Lecturer hesitates, then shows "2 feet tall"].

But, you're going to be just as smart. We want to find X. Well, it's going to take 99 additions to solve this. It's going to take a while. There's got to be an easier way. Do we get the same answer?

It was algebra, right? It doesn't matter what order you add things up, you get the same answer. So "yes" we get the same answer [Lecturer writes "X" to the right of the equal sign]. That's going to take just as long, isn't it? There are 99 additions there, too. What if we add up the even numbers that's 49 additions , then add up the odd numbers that's 49 additions , and then add up the two totals?

That's, uh, 99 additions. Darn, that's no better. When we finally total them up, we get the same answer, right? Does that look helpful? This is the second hint, by the way [points at those numbers]. Do you see something magical about that? Do you all see it? How many s do we have? Lozansky, Edward, and Cecil Rousseau.

It was known in antiquity that if a 1 , a 2 , However it is one thing for a formula to be known by practicing mathematicians and quite another for it to be deduced in an instant by a ten-year-old boy. This is exactly what Gauss did when his arithmetic teacher, Herr Büttner, gave Gauss and his classmates a problem specifically designed to keep them hard at work for an hour.

The problem chosen to create tedium and frustration was that of summing an arithmetic progression. Immediately Gauss wrote a number on his slate, turned it in, and announced, "There it is. What Gauss immediately recognized was that in an arithmetic progression a 1 , a 2 , Wahrscheinlich ist Büttner an diesem Morgen schlecht gelaunt und will von seiner nichtsnutzigen Meute einfach mal nichts sehen und hören.

Die Ausgabe, die er der Korona stellt, lässt jedenfalls Rüschlüsse auf ein gewisses Ruhebednürfnis zu. Die Kinder sollen nämlich alle Zahlen swischen 1 und zusammenzählen:. Bei so vielen Additionen am Stück lauert der Fehlerteufel hinter jeder Zwischensumme. Eine kleine Unkonzentrierheit—und schon ist das Malheur passiert. Alle weiteren Schritte zögern das falsche Ergebnis nur noch hinaus.

Nur einer macht das grausame Spiel nicht mit. Dort legt er sie—einem alten Brauch gehorchend—selbsbewusst mit der beschrifteten Seite nach unten und ruft, vermutlich nicht ohne Stolz: Der stille Junge ist ihm noch nie zuvor aufgefallen, weder in positiver noch in negativer Hinsicht.

Aber nicht einmal Büttner selbst, der natürlich das Ergebnis kennt, könnte diese Aufgabe in nur zwei drei Minuten bewältigen. Im Lauf der Unterrichtsstunde wächst der Stapel mit den Tafeln allmählich, stehen auf Carls makellos sauberer Tafel nur die vier Ziffern ohne Schwammspuren und ohne Zwischenrechnungen.

Das Ergebnis stimmt, und der Schulmeister is wie vom Donner gerührt. Er fragt seinen Schüler in einer seltsamen Stimmung aus Faszination, Neugier und Skepsis, wie er das richtige Resultat in so unglaublich kurzer Zeit und vor allem ohne Hilfsmittel gefunden habe. Er könne es doch unmöglich im Kopf Doch, natürlich im Kopf.

Es sei ganz einfach, erklärt das kleine Genie. Er habe nur ein wenig über die Aufgabe nachgedacht sich dann die Zahlenreihe von 1 bis genau angesehen und bald ein paar bemerkenswerte Übereinstimmungen entdeckt. So sei die Summe der ersten und letzten Zahl Die zweite und vorletzte, nämlich 2 und 99, ergäbe ebenfalls So erhielte man fünfzig Paare mit der jeweils gleichen Summe Nun habe er nur noch 50 mit multiplizieren müssen. Eine denkbar einfache Rechnung, die jeder im Kopf lösen könne.

Hier stellt man sich die obere Reihe von 1 bis auf einen Streifen Papier geschrieben vor. After all these messages, I cannot resist telling what really happened, as I heard it from my high school teacher he could compete with E.

Bell for telling a good story. Gauss' teacher set the class the task of adding all the numbers from 1 to on purpose to keep them busy for a long time, while the teacher would go to work at his vegetable garden, it was an urgent job. Gauss defeated his purpose by finding the answer instantly, so the teacher told the rest of the class to go on with the normal addition, and took Gauss with him to help dig out the potatoes.

To Infinity and Beyond: A Cultural History of the Infinite. Gauss began to show his prodigious mathematical talents at a very young age. He mastered the art of calculation before he could read or write, and at the age of three he supposedly found an error in his father's bookkeeping.

There is also the famous story about the ten-year-old Gauss who, when asked by his teacher to find the sum of the integers from 1 to , almost instantly came up with the correct answer: From Pythagoras to Euler to Grade 8: The Geniuses of Math. These were the words we came upon when researching the life of Gauss. He said this when told his wife was dying. This casts some light onto the determination and sometimes all-consuming passion experienced by such minds.

Gauss taught himself to read and count by the age of three. One day in school, a very young Gauss was told to stand in the corner and add all the numbers from 1 to His teacher was amazed when a few moments later Gauss turned around and announced After learning Gauss's technique, we were able to apply it to the addition of other similar series. We each worked on a different area of the project according to our strengths and then combined what we had discovered.

In weiterer Verfolgung des Lebensganges des grossen Forschers werden wir eines besseren belehrt werden! Kehren wir zurück zum kleinen Gauss, der in einem armseligen Häuschen an dem Wendengraben zu Braunschweig früher rechnen als sprechen lernte, wie er später selbst von sich erzählte. War Gauss ein Wunderkind? Je nachdem man es auffassen will! Mit einem Impresario gereist ist er nicht, trotzdem er schon im zartesten Kindesalter staunenswerte Proben im Auffassen von Zahlengesetzen gab und im Kopfrechnen Erstaunliches leistete.

Verbürgt ist die Geschichte, dass der dreijährige kleine Gauss im Bettchen lag und zuhörte, wie sein Vater am Schlusse der Woche mit den Gesellen abrechtnete und Löhne auszahlte. Tausend und aber tausend Gefahren umgeben ein junges Menschenleben! Kein Lied, kein Denkmal nennt uns den braven Mann, der den kleinen Gauss aus dem Wendengraben rettete, in den er einst beim Spielen hineingefallen war.

Wie viel hat dieser einfache, schlichte Mann der Welt gerettet und erhalten! Eine weitere verbürgte Geschichte aus Gauss' jungem Leben erzählt, wie er als Zögling der Katharinenvolksschule im Alter von neun Jahren wieder eine verblüffende Probe seines rechnerischen Scharfsinnes ablegte. Der ehrsame Schulmeister Büttner, der die Rechnenklasse leitete, gab einst die Aufgabe, alle Zahlen der Reihe nach von herab bis zur 1 aufzuschreiben und zu addieren.

Kaum war die Aufgabe gestellt, schrieb der kleine Gauss die Lösung auf seine Tafel, legte diese auf den Tisch und rief, echt braunschweigerisch: Die Durchsicht ergab aber, dass der kleine Gauss allein das richtige Resultat geliefert hatte. Er war aber auch in der Lage, dem Lehrer auseinanderzusetzen, wie er sum Resultate gelangt war.

Das Resultat ist daher 50 x , das ist Zur Ehre des Lehres sei arzählt, dass er sofort in weiser Einsicht den jungen Geist zu bilden versuchte und dem kleinen Gauss zuliebe sogar ein eigenes und neues Rechenbuch aus einer fernen Stadt verschrieb, um jedoch bald selbstlos zu erklären: Galleria dei grandi matematici della storia.

Il primo episodio della vita di Gauss come matematico viene raccontato in tanti modi differenti, ma sostanzialmente simili; il maestro della scuola di Braunscweig, volendo passare un pomeriggio tranquillo, aveva assegnato un esercizio lungo e noioso, quello di sommare i numeri da uno a Dictionary of Scientific Biography Vol. Without the help or knowledge of others, Gauss learned to calculate before he could talk.

At the age of three, according to a well-authenticated story, he corrected an error in his father's wage calculations. He taught himself to read and must have continued arithmetical experimentation intensively, because in his first arithmetic class at the age of eight he astonished his teacher by instantly solving a busy-work problem: Fortunately, his father did not see the possibility of commercially exploiting the calculating prodigy, and his teacher had the insight to supply the boy with books and to encourage his continued intellectual development.

A to Z of Mathematicians.





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