Selected `mathematical excerpts' from
The Prince of Mathematics: Carl Friedrich GaussThe Man Who Counted
A K Peters, 2006; ISBN 1-56881-261-2. [ See this book at Amazon.com]
compiled by Tom Verhoeff in August 2013.
Carl Friedrich Gauss' father, a stonemason, was paying his workmen at the end of the day: "Let's see, Herr [Mr.] Braun, that's 34 pennies plus 29 pennies plus 19 pennies and ... um ... that makes a total of 76 pennies."
Young Carl, watching and listening from the front step, said clearly, "No, Father, that isn't right. It should be 82 pennies."
... "Dorothea, why on earth did you teach the child to add? He's only three years old! He's still a baby!"
"But Gebhard, you know I can't do figures. He asked me some numbers, and I told him the ones I know. That's all.
"Then it's that brother of yours, ..."
"Gebhard, Carl really seems awfully clever," said Dorothea. "I think he may have figured it out for himself."
"No three-year-old can teach himself to add. I know this is your brother Friedrich's doing. ..."
... [Dorothea] remembered, some time ago -- was it last spring? -- when Carl had surprised her. They were in the kitchen, and she had taken out six small potatoes ... Carl had .. grabbed two potatoes. "One potato, two potato... Mutter [mother], one potato, two potato, then ...?" asked Carl.
"Oh, I know what you want," Dorothea had said. "Three potatoes."
"Ya!" yelled Carld. "One potato, two potato, three potato! Whee! Then?"
"Four potatoes," answered Dorothea slowly.
"One potato, two potato, three potato, four potato, hen?" asked Carl.
"Nexts comes five and then six," said Dorothea, "and that's all the potatoes I know how to count."
Then she thought back to another day maybe a week later when her brother had stopped by. Carl had been ready for him.
"Onkel Friedrich, what comes after six?" Carl had asked. "Mutter doesn't know."
"Seven," Friedrich had said.
Friedrich had told him some more numbers, and when he stopped, Carld had asked, "Is that all?"
... "Let's see. 13 x 13 = 169. If I multiply the number one less than 13 times the number one more than 13 (that's 12 x 14), I get 168. That's one less than 169. Okay. What happens with 14 x 14? 14 x 14 = 196. If I multiply one less than 14 times one more than 14 (that 13 times 15), I get 195. That's one less than 196. Will it always work? I'll bet it will. Let's see. 25 x 25 = 625. 24 x 26 is -- let's see --yes, it's 624, and that is one less than 625. Yes. It looks good. I'll bet the answer is always going to be one less than the square of the number in between."
One afternoon after school, Gauss and his friend Ide were walking home. Before Ide turend toward his house, Gauss commented, "Ide, I've been trying to measure the distance from my house to the Gymnasium, and I've been counting my steps every day for two weeks. Would you believe I have gotten a different number every day? Since the paving stones are uneven, sometimes they make me take a shorter or longer step, but I've been trying to compensate for that. Still, I keep getting a different number. It's mystifying."