Gauss's precocity. Gauss very early in life exhibited a remarkable cleverness with numbers, becoming a "wonder child" at the age of two. There are a couple of oft-told stories illustrating the boy's unusual ability.
One of the stories tells how on a Saturday evening Gauss's father was making out the weekly payroll for the laborers of the small bricklaying business that he operated in the summer. The father was quite unaware that his young three-year-old son Carl was following the calculations with critical attention, and so was surprised at the end of the computation to hear the little boy announce that the reckoning was wrong and that it should be so and so instead. A check of the figures showed that the boy was correct, and on subsequent Saturday evenings the youngster was propped up on a high stool so that he could assist with the accounts. Gauss enjoyed telling this story later in life, and used to joke that he could figure before he could talk.
The other story dates from Gauss's schooldays, whence was about ten years old. At the first meeting of the arithmetic class, Master Buttner asked the pupils to write down the numbers from I through 100 and add them. It was the custom that the pupils lay their slates, with their answers thereon, on the master's desk upon completion of the problem. Master Buttner had scarcely finished stating the exercise when young Gauss flung his slate on the desk. The other pupils toiled on for the rest of the hour while Carl sat with folded hands under the scornful and sarcastic gaze of the master. At the conclusion of the period, Master Buttner looked over the slates and discovered that Carl alone had the correct answer, and upon inquiry Carl was able to explain how he had arrived at his result. He said, " 100 + 1 = 101, 99 + 2 = 101, 98 + 3 = 101, etc., and so we have as many 'pairs' as there are in 100. Thus the answer is 50 x 101, or 5050."
Gauss and languages. Gauss mastered languages with great facility. This pursuit of languages became more than just a hobby; he would acquire a new language to test the plasticity of his mind as he grew older, and he considered the exercise as of value in keeping his mind young. At the age of sixty-two he started an intensive self-study of Russian. Within two years he read the language fluently and spoke it perfectly.
Gauss's scientific diary. On the same day that Gauss discovered his findings on the constructibility of regular polygons with straightedge and compasses (the discovery that caused him to take up mathematics rather than philology as his life's work), he started his scientific diary, or Notizenjournal. This scientific diary, which contains 146 entries, is a valuable document in the history of mathematics, for it shows how early Gauss obtained many deep results that were independently discovered and published by others often many years later.
The first entry of the diary records the discovery about regular polygons.
The entry for duly 10, 1796, reads, somewhat cryptically,
S U R H K A ! Num= D +D +D
Here we have an echo of Archimedes' triumphant "Eureka," and an abbreviated statement that every positive integer is the sum of three triangular numbers (a triangular number is a number of the form
.5*n(n + 1), where n is a nonnegative integer). This is not an easy thing to prove from scratch.
The entry for October 11, 1796, is
and that for April 8, 1799, is
| REV. GALEN |
These two entries have remained unintelligible enigmas through the years.
All the entries, except the above two, are for the most part clear. The entry for March 19, 1797, shows that Gauss had already at that time discovered the double periodicity of certain elliptic functions (he was not yet twenty years old), and a later entry shows that he had recognized the double periodicity for the general case. This discovery alone, if Gauss had published it, would have earned him mathematical fame. But Gauss never published it!