- Gauß:
- I have just today, July 14, 1844, written a letter to C.
Gerling, saying ``I have recently made the acquaintance of a young mathematician,
Eisenstein from Berlin, who came here with a letter of recommendation from
Humboldt. This man, who is still very young, exhibits
*very*excellent talent, and will certainly achieve great things.'' [4]. By the end of this year he will have contributed no less than 16 of the 27 mathematical articles in volume 27 of Crelle's Journal, including his geometric proof of the Fundamental Theorem. Next year, as a third semester student, he will receive an honorary doctorate from the University of Breslau [10]. I will write to the great scientist and explorer Alexander von Humboldt that Eisenstein's talent is ``that which nature bestows upon only a few in each century''. Both von Humboldt and I will make great efforts, for the most part in vain, to obtain recognition and financial security for the impoverished Eisenstein. He will obtain a position as a Privatdozent (unsalaried lecturer) at the University in Berlin, and will eventually be admitted to the Berlin Academy of Sciences in early 1852. But by then his lifelong poor health will have seriously deteriorated, and he will die later that same year, at the age of 29, of tuberculosis [3,10]. How tragic that, like Abel and Galois in the same period, we will lose the genius of Gotthold Eisenstein to so early a death.The brilliance and power of Eisenstein's work will remain unappreciated for a long time in part because it will be almost 125 years before the publication of his Collected Works. In the foreword to their second edition [6], the eminent twentieth century mathematician André Weil reviews Eisenstein's mathematical contributions, in particular

``the impressive series of papers on elliptic functions and their application to the higher reciprocity laws . [The] series ends up with a great paper, the

*Genaue Untersuchung*of 1847, which excited Kronecker's enthusiasm when he discovered it late in life, and which still deserves ours; it is nothing less than the sketch of a complete theory of elliptic and modular functions, based on principles essentially distinct from those of Jacobi and from those of Weierstraß (while anticipating him by nearly fifteen years), but, as I have more amply demonstrated elsewhere, its principles can be profitably applied to important current problems.''Late in the 19th century, Baumgart [2] will write a survey of the many different proofs of the Fundamental Theorem given by then. Unfortunately, he will misunderstand and overlook most of the beautiful features of Eisenstein's geometric proof, mentioning only how he counts the points in a rectangle to avoid my technical argument above for adding the two series with interchanged roles for

**p**and**q**. Sadly, he will miss Eisenstein's algebraic form of my Lemma, as well as his geometric way of representing my transformations. Subsequent mathematicians, probably relying on Baumgart's survey rather than reading Eisenstein's original paper, will perpetuate this oversight. Let me just mention Bachmann's early 20th century book on number theory [1] as an example.Only shortly before the dawn of the 21st century will this injustice be rectified, when mathematicians of the distant future rediscover and fully appreciate the neglected and spectacular parts of Eisenstein's geometric proof of the Fundamental Theorem of higher arithmetic.

Thu Feb 11 17:12:00 MST 1999