Arthur Wieferich
Arthur Josef Alwin Wieferich (born April 27, 1884 in Münster ; † September 15, 1954 in Meppen ) was a German mathematician who published important papers on number theory while studying.
Life
Wieferich was the son of a businessman. From 1903 to 1909 he studied at the Westphalian Wilhelms University in Münster . Presumably a lecture by Max Dehn in 1907 on number theory inspired him to further investigate this area. His five mathematical publications fell during the time of his studies.
After completing his studies he taught as a school teacher in Konitz (then Poland), Elbing (West Prussia), Sopot (Baltic Sea, now Poland), Neustadt, Jülich , Stade and finally Meppen. At the same time he was a member of the German Mathematicians Association (DMV) from 1909 to 1929 . He married in 1916; his marriage was childless. In Meppen he was appointed director of the grammar school during the Nazi era in order to get it on a party course. After the war, he was suspended from this post because of his National Socialist past and earned his living as a private teacher from 1945 to 1949 (“ denazification ” period).
plant
Wieferich proved u. a. that if Fermat's theorem is fulfilled for a prime p and integers prime to p , this prime p is a " Wieferich prime ", d. H. divides ( the elementary " little Fermat's sentence " already implies that p divides this expression ). Dmitry Mirimanoff showed that a corresponding sentence applies if you replace 2 with 3 (criteria from Wieferich and Mirimanoff). Only two Wieferich prime numbers are known so far - 1093 and 3511 - and the search for such numbers has become a sport with high-performance computers.
His theorem from additive number theory about the representation of every whole number from a maximum of 9 (positive) cubes gained the admiration of the then expert in this field, Edmund Landau in Göttingen. A gap (Wieferich only proved the theorem above a certain limit) in the proof was corrected by Aubrey J. Kempner in his dissertation; B. Scholz gives a further simplification.
Fonts
- Proof of the theorem that any whole number can be represented as a sum of at most nine positive cubes . Math. Ann. Vol. 66, 1908, pp. 95-101
- About the representation of the numbers as sums of biquadrates . Math. Annalen Vol. 66, 1908, pp. 106-108
- To represent numbers as sums of fifth and seventh powers of positive integers . Math. Ann. Vol. 67 (1909) pp. 61-75
- On the last Fermat 's theorem . Journal for pure and applied math. Vol. 136, 1909, pp. 293-302
- In this article he introduces the Wieferich prime numbers named after him .
- To triangle geometry . Journal for pure and applied math. Vol. 136, 1909, pp. 303-305
Individual evidence
- ↑ elMath.org: Wieferich @ Home - search for Wieferich prime ( Memento from April 1, 2009 in the Internet Archive )
- ↑ A. Kempner: Comments on Waring's problem . Math. Annalen, Volume 72, 1912, pp. 387-399
- ↑ B. Scholz: Comment on a proof by Wieferich . Annual report of the German Mathematicians Association, Volume 58, 1955, pp. 45–48
literature
- Heinz Kleene (editor): The report of Meppen Provost Carl Meyer to the Episcopal Vicariate General about his parish during the time of the "Third Reich" (1947), in: Study Society for Emsland Regional History Vol. 16, Haselünne 2009, 282-365, p 327-329.
- Paulo Ribenboim : Thirteen lectures on Fermats last theorem , 1977.
- Dr. Karl Knapstein (editor): Staatliches Gymnasium in Meppen, Festschrift for the three hundredth anniversary , 1952, pp. 36–37.
Web links
| personal data | |
|---|---|
| SURNAME | Wieferich, Arthur |
| ALTERNATIVE NAMES | Wieferich, Arthur Josef Alwin (full name) |
| BRIEF DESCRIPTION | German mathematician |
| DATE OF BIRTH | April 27, 1884 |
| PLACE OF BIRTH | Muenster |
| DATE OF DEATH | September 15, 1954 |
| Place of death | Meppen , Lower Saxony |