b. Basel, Switzerland 21 October 1687
d. Basel 29 November 1759
Nikolaus studied mathematics at the University of Basel first under his uncle Jacob Bernoulli. When Jacob died in 1705, his position at Basel was assumed by his brother Johann Bernoulli I under whom Nikolaus continued his studies.
In 1704, after a public debate on a subject contained in the fifth part Jacob Bernoulli's work on Infinite Series, he was awarded a degree of master of arts. Another pupil of Jacob, Jacob Hermann (1668 - 1733), successfully defended the third part of the same work, earning for himself a degree of master of arts as well. In 1709 Niklaus was awarded the degree of doctor of laws for his dissertation on the application of probability theory to law, De usu artis conjectandi in jure. An examination of Jacob's notebooks (his meditationes) clearly indicate the debt that Nicolas owed to Jacob for the ideas of this dissertation.
In 1712, Nikolaus traveled to Holland, England and France. In France he became acquainted with both Varignon and Montmort the latter with whom he collaborated, and in London with Moivre.
Nikolaus became professor of mathematics at Padua in 1716, took the chair of logic at Basel in 1722, and became professor of law at Basel in 1731. He was elected to the Berlin Academy in 1713, the Royal Society in 1714, and the Academy of Bologna in 1724.
Birkhäuser Verlag plans a four volume edition as Jacob Hermann/Nicolaus I Bernoulli, Werke. These will be
Mathematik - Analysis, Geometry, Probability
Mechanik II, Physik - Central forces, Optics, Elasticity, Hydrodynamics, Varia.
Among the works of Niklaus Bernoulli is his dissertation for the degree of doctor of laws. An English translation with some commentary to each chapter can be read. See De Usu Artis and also the commentary.
Among the correspondence of Niklaus are those letters exchanged with Montmort. The greater part of the sections related to problems in probability have been translated. It is very interesting to witness through their writings the development of ideas. We mention also that within other documents on this site dealing with a single topic we have extracted and grouped together sections of this correspondence such as those mentioned immediately below.
In his correspondence, Niklaus discussed the Saint Petersburg Problem with Montmort, Cramér and with his cousin Daniel Bernoulli. An English translation of Correspondence on the St. Petersburg Problem can be read. See also the solution proposed by Alexis Fontaine de Bertins, by D'Alembert and by Windisch-Grätz.
Nikolaus further corresponded with Montmort with regard to the claim made by Arbuthnot in his paper An Argument for Divine Providence.
Closely related to this is a document by 'sGravesande, his Démonstration mathématique du soin que Dieu prend de diriger ce qui se passe dans ce monde, tirée du nombre des garçons & des filles qui naissent journellement. In addition, there exist several letters interchanged between Nicolas and 'sGravesande which show Niklaus in the heat of the dispute.
One may consult E. Shoesmith, "Nicholas Bernoulli and the Argument for Divine Providence," International Statistical Review, (1985), 3, pp. 255-259.
There seem to have been few published papers by Nicolas Bernoulli. These include
"Addition au Mém. de Mr. Jean Bernoulli touchant la maniére de trouver les forces centrales dans les milieux résistans..." Mémoires de l'Académie des Sciences, 1711 (1714) pp. 53-56.
"Solutio generalis problematio 15 propositi a D. de Moivre in Transactions de mensura sortis." Philosophical Transactions of the Royal Society 29 (1714) 133-144. It concerns the solution to Waldegrave's Problem, Proposition 15 in Moivre's work, De Mensura Sortis.
"Calculus pro invenienda linea curva, quam describit projectile in medio resistente," Acta Eruditorum (1719) 224-226.
"Modus inveniendi aequationem differentialem completam ex data aequatione differentiali incompleta..." Acta Eruditorum, supp. 7 (1719) pp. 310-859.
"Tentamen solutionis generalis problematis de construenda curva, quae alias ordinaim positione datas ad angulos rectos secat," Acta Eruditorum (1719). pp. 295-304.
"Exercitatio geometrica de traiectoriis orthogonalibus," Sectiones I-III, Acta. Eruditorum, 1720, pp. 223-237 (Suppl. VII, 1721, pp. 303-326, 337-353).
"De motu corporum ex percussione," Commentarii Academiae Scientiarum Imperialis Petropolitanae T. 1 p 121.
"Analysis aequationum quarundam differentialium (axmyn dx + bxpyq dx = dy)," Commentarii Academiae Scientiarum Imperialis Petropolitanae T. 1 p. 198
"Inquisitio in summam series 1/1+1/4+1/9+1/16+1/25+1/36+ etc." Commentarii Academiae Scientiarum Imperialis Petropolitanae T 10, p. 19
"Regula generalis inveniendi divisores rationales compositos quantitati algebraice a + bx + cxx + dx3 + ex4, etc.," in G.G. Leibnitii et Johanni Bernoulli commercium, philosophicum et mathematicum, Vols. 1 and 2, Lausannae et Genevae, 1745.