# he was arguably the greatest mathematician in history. according to legend, he corrected a mistake in his father’s accounting at the age of 3, and found a way to quickly add up all integers from 1 to 100 at the age of 8

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## Carl Friedrich Gauss – Timeline of Mathematics – Mathigon

Travel through time and explore the greatest mathematicians and biggest mathematical discoveries in history.

## Timeline of Mathematics

20000 BCE 10000 BCE 5000 BCE 4000 BCE 3000 BCE 2000 BCE 1000 BCE 900 BCE 800 BCE 700 BCE 600 BCE 500 BCE 400 BCE 300 BCE 200 BCE 100 BCE 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 Stone Age Bronze Age Classical Antiquity Middle Ages Renaissance Enlightenment Modern Viazovska Avila Mirzakhani Tao Perelman Zhang Daubechies Bourgain Wiles Shamir Yau Matiyasevich Thurston Uhlenbeck Conway Langlands Cohen Easley Appel Penrose Nash Grothendieck Serre Mandelbrot Wilkins Robinson Blackwell Johnson Lorenz Shannon Gardner Erdős Turing Chern Ulam Weil Gödel von Neumann Kolmogorov Cartwright Escher Cox Ramanujan Noether Einstein Hardy Russell Hilbert Peano Poincaré Kovalevskaya Cantor Lie Carroll Dedekind Riemann Cayley Nightingale Lovelace Boole Sylvester Galois Jacobi De Morgan Hamilton Bolyai Abel Lobachevsky Babbage Möbius Cauchy Somerville Gauss Germain Wang Fourier Legendre Mascheroni Laplace Monge Lagrange Banneker Lambert Agnesi Euler Du Châtelet Bernoulli Goldbach Simson De Moivre Bernoulli Ceva Leibniz Seki Newton Pascal Wallis Fermat Cavalieri Descartes Desargues Mersenne Kepler Galileo Napier Stevin Viète Pedro Nunes Cardano Tartaglia Copernicus Da Vinci Pacioli Regiomontanus Madhava Oresme Zhu Shijie Yang Qin Al-Din Tusi Li Ye Fibonacci Bhaskara II Khayyam Jia Al-Haytham Al-Karaji Thabit Al-Khwarizmi Bhaskara I Brahmagupta Aryabhata Zu Hypatia Liu Diophantus Ptolemy Nicomachus Heron Hipparchus Apollonius Eratosthenes Archimedes Pingala Euclid Aristotle Eudoxus Plato Democritus Zeno Pythagoras Thales Ishango Bone Counters MS 3047 VAT 12593 Plimpton 322 YBC 7289 YBC 7290 Rhind Papyrus Tomb of Menna Bamboo Table Elements Palimpsest Suàn shù shū Khmer Zero Al-Jabr Al-Jabr Lilavati Maya Codex Liber Abaci Siyuan Yujian Incan Quipu Polyhedra Aztec Dates

c. 300 BCE: Indian mathematician Pingala writes about zero, binary numbers, Fibonacci numbers, and Pascal’s triangle.

c. 260 BCE: Archimedes proves that π is between 3.1429 and 3.1408.

c. 235 BCE: Eratosthenes uses a sieve algorithm to quickly find prime numbers.

c. 200 BCE: The “Suàn shù shū” (Book on Numbers and Computation) is one of the oldest Chinese texts about mathematics.

c. 100 CE: Nicomachus poses the oldest still-unsolved problem in mathematics: whether there are any odd perfect numbers.

c. 250 CE: The Mayan culture in Central America flourishes, and uses a base-20 numeral system.

c. 830 CE: Al-Khwarizmi publishes “Kitab al-jabr wa al-muqābalah”, the first book about – and the namesake of – Algebra.

1202: Fibonacci’s Liber Abaci introduces Arabic numerals to Europe, as well as simple algebra and the Fibonacci numbers.

1482: First printed edition of Euclid’s Elements

1545: Cardano conceives the idea of complex numbers.

1609: Kepler publishes the “Astronomia nova”, where he explains that planets move on elliptical orbits.

1618: Napier publishes the first references to the number e, in a book on logarithms.

1637: Fermat claims to have proven Fermat’s Last Theorem.

1654: Pascal and Fermat develop the theory of probability.

1684: Leibniz’ publishes the first paper on the calculus.

1687: Newton publishes the Principia Mathematica, containing the laws of gravity and motion, as well as his version of calculus.

1736: Euler solves the Königsberg bridges problem by inventing graph theory.

1761: Lambert proves that π is irrational

1799: Gauss proves the fundamental theorem of algebra.

1829: Bolyai, Gauss and Lobachevsky all invent hyperbolic non-Euclidean geometry.

1832: Galois finds a general condition for solving algebraic equations, thereby founding Group theory and Galois theory.

1858: August Ferdinand Möbius invents the Möbius strip.

1874: Cantor proves that there are different “sizes” of infinity, and that the real numbers are uncountable.

1895: Poincaré’s paper “Analysis Situs” starts modern topology.

1905: Einstein explains the photoelectric effect and Brownian motion, discovers special relativity, and E = mc².

## Famous Mathematicians problems & answers for quizzes and worksheets

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## Famous Mathematicians

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Show Answers See Preview 1. Multiple-choice 30 seconds 1 pt

Q.

Was a Greek philosopher and mathematician. He is best known for proving Pythagoras’ Theorem, but made many other mathematical and scientific discoveries.

answer choices

**Thales of Miletus**(c. 624 – 546 BCE)

**Eratosthenes of Cyrene**(c. 276 – 195 BCE)

**Pythagoras of Samos**(c. 570 – 495 BCE)

**Heron of Alexandria**(c. 10 – 70 CE)

2. Multiple-choice 30 seconds 1 pt

Q.

Was an Italian mathematician. He is best known for the number sequence named after him: 1, 1, 2, 3, 5, 8, 13, …

answer choices

**Leonardo Pisano**,

**Fibonacci**(1175 – 1250)

**Leonhard Euler**(1707 – 1783)

**Johann Lambert**(1728 – 1777)

**François Viète**(1540 – 1603)

3. Multiple-choice 30 seconds 1 pt

Q.

Was arguably the greatest mathematician in history. According to legend, he corrected a mistake in his father‘s accounting at the age of 3, and found a way to quickly add up all integers from 1 to 100 at the age of 8.

answer choices

François Viète (1540 – 1603)

Carl Friedrich Gauss (1777 – 1855)

Fibonacci (1175 – 1250)

Diophantus 4. Multiple-choice 30 seconds 1 pt Q.

was a French mathematician and philosopher, and one of the key figures in the Scientific Revolution. He is credited with the first use of superscripts for powers or exponents, and the cartesian coordinate system is named after him.

answer choices

**René Descartes**(1596 – 1650)

**Carl Friedrich Gauss**(1777 – 1855)

**Augustin-Louis Cauchy**(1789 – 1857)

**Joseph-Louis Lagrange**(1736 – 1813)

5. Multiple-choice 30 seconds 1 pt Q.

Was an English physicist, mathematician, and astronomer, and one of the most influential scientists of all time. Was one of the inventors of calculus, built the first reflecting telescope, calculated the speed of sound, studied the motion of fluids, and developed a theory of colour based on how prisms split sunlight into a rainbow-coloured spectrum.

answer choices

**Gottfried Wilhelm Leibniz**(1646 – 1716)

**Joseph-Louis Lagrange**(1736 – 1813)

**Joseph Fourier**(1768 – 1830)

**Sir Isaac Newton**(1642 – 1726)

6. Multiple-choice 30 seconds 1 pt Q.

Euclid is called, The Father of Geometry.

He wrote a book, **The Elements, **which was the most comprehensive book on Geometry for about 2000 years.

2000 years is the same as 2 millennia.

True or False? answer choices True False 7. Multiple-choice 30 seconds 1 pt Q.

He was pioneering mathematician and physicist, famous for developing the ‘Fourier Series’.

answer choices Joseph Fourier Pierre de Fermat Henri Poincare George Cantor 8. Multiple-choice 30 seconds 1 pt Q.

He is known for his invention of the mechanical calculator.

answer choices Blaise Pascal Benjamin Bannaker Isaac Newton Rene Descartes 9. Multiple-choice 30 seconds 1 pt Q.

Development of infinitesimal calculus (differentiation and integration), laid ground work for almost all of classical mechanics, generalized binomial theorem, infinite power series

answer choices Albert Einstein Isaac Newton Jacob Bermoulli Abraham de Moivre 10. Multiple-choice 30 seconds 1 pt Q.

Who is known as the "Father of Geometry"?

answer choices Pythagoras Archimedes Euclid Galileo

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## Gauss's Day of Reckoning

A famous story about the boy wonder of mathematics has taken on a life of its own

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## Gauss's Day of Reckoning

### BY BRIAN HAYES

A famous story about the boy wonder of mathematics has taken on a life of its own

### COMPUTER MATHEMATICS SOCIAL SCIENCE

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### THIS ARTICLE FROM ISSUE

### MAY-JUNE 2006

### VOLUME 94, NUMBER 3

### PAGE 200

DOI: 10.1511/2006.59.200

UNAVAILABLE FOR PURCHASE

VIEW ISSUE

Let me tell you a story, although it's such a well-worn nugget of mathematical lore that you've probably heard it already:

In the 1780s a provincial German schoolmaster gave his class the tedious assignment of summing the first 100 integers. The teacher's aim was to keep the kids quiet for half an hour, but one young pupil almost immediately produced an answer: 1 + 2 + 3 + ... + 98 + 99 + 100 = 5,050. The smart aleck was Carl Friedrich Gauss, who would go on to join the short list of candidates for greatest mathematician ever. Gauss was not a calculating prodigy who added up all those numbers in his head. He had a deeper insight: If you "fold" the series of numbers in the middle and add them in pairs—1 + 100, 2 + 99, 3 + 98, and so on—all the pairs sum to 101. There are 50 such pairs, and so the grand total is simply 50×101. The more general formula, for a list of consecutive numbers from 1 through n, is n(n + 1)/2.

The paragraph above is my own rendition of this anecdote, written a few months ago for another project. I say it's my own, and yet I make no claim of originality. The same tale has been told in much the same way by hundreds of others before me. I've been hearing about Gauss's schoolboy triumph since I was a schoolboy myself.

**Illustration by Theoni Pappas, reprinted from Pappas 1993 by permission.**

The story was familiar, but until I wrote it out in my own words, I had never thought carefully about the events in that long-ago classroom. Now doubts and questions began to nag at me. For example: How did the teacher verify that Gauss's answer was correct? If the schoolmaster already knew the formula for summing an arithmetic series, that would somewhat diminish the drama of the moment. If the teacher didn't know, wouldn't he be spending his interlude of peace and quiet doing the same mindless exercise as his pupils?

There are other ways to answer this question, but there are other questions too, and soon I was wondering about the provenance and authenticity of the whole story. Where did it come from, and how was it handed down to us? Do scholars take this anecdote seriously as an event in the life of the mathematician? Or does it belong to the same genre as those stories about Newton and the apple or Archimedes in the bathtub, where literal truth is not the main issue? If we treat the episode as a myth or fable, then what is the moral of the story?

To satisfy my curiosity I began searching libraries and online resources for versions of the Gauss anecdote. By now I have over a hundred exemplars, in eight languages. (The collection of versions is available here.) The sources range from scholarly histories and biographies to textbooks and encyclopedias, and on through children's literature, Web sites, lesson plans, student papers, Usenet newsgroup postings and even a novel. All of the retellings describe what is recognizably the same incident—indeed, I believe they all derive ultimately from a single source—and yet they also exhibit marvelous diversity and creativity, as authors have struggled to fill in gaps, explain motivations and construct a coherent narrative. (I soon realized that I had done a bit of ad lib embroidery myself.)

After reading all those variations on the story, I still can't answer the fundamental factual question, "Did it really happen that way?" I have nothing new to add to our knowledge of Gauss. But I think I have learned something about the evolution and transmission of such stories, and about their place in the culture of science and mathematics. Finally, I also have some thoughts about how the rest of the kids in the class might have approached their task. This is a subject that's not much discussed in the literature, but for those of us whose talents fall short of Gaussian genius, it may be the most pertinent issue.

### Wunderkind

I started my survey with five modern biographies of Gauss: books by G. Waldo Dunnington (1955), Tord Hall (1970), Karin Reich (1977), W. K. Bühler (1981) and a just-issued biography by M. B. W. Tent (2006). The schoolroom incident is related by all of these authors except Bühler. The versions differ in a few details, such as Gauss's age, but they agree on the major points. They all mention the summation of the same series, namely the integers from 1 to 100, and they all describe Gauss's method in terms of forming pairs that sum to 101.

None of these writers express much skepticism about the anecdote (unless Bühler's silence can be interpreted as doubt). There is no extended discussion of the story's origin or the evidence supporting it. On the other hand, references in some of the biographies did lead me to the key document on which all subsequent accounts seem to depend.

Guys, does anyone know the answer?