Guido Grandi

Guido Grandi

De infinitis infinitorum

Luigi Guido Grandi (born October 1, 1671 in Cremona , Italy , † July 4, 1742 in Pisa ) was an Italian mathematician and Camaldolese .

Grandi was educated at the Jesuit College in Cremona. In 1687 he became a member of the Camaldolese order in Ferrara . In 1693 he switched to the Camaldolese order in Rome . In the following year he became a teacher of philosophy and theology at a monastery in Florence , from 1700 in Rome, later in Pisa.

During a trip to England in 1709 he was elected a member of the Royal Society by local scientists and at the suggestion of Isaac Newton . In 1714 Grandi became professor of mathematics at the University of Pisa .

Grandi also dealt with the alternating infinite series and found that, depending on the order of the evaluation, the value zero or one can be taken. He then assigned the value to it and justified this using the geometric series : ${\displaystyle \sum _{k=0}^{\infty }(-1)^{k}}$ ${\displaystyle 1/2}$

${\displaystyle \sum _{k=0}^{\infty }(-1)^{k}=1+(-1)+(-1)^{2}+(-1)^{3}+\cdots ={\frac {1}{1-(-1)}}={\frac {1}{2}}}$.

For him this was proof of how God created the world out of nothing. According to today's mathematical convergence theory, as it was introduced by Augustin Louis Cauchy (1789–1857), the sequence is the partial sums

${\displaystyle \sum _{k=0}^{n}x^{k}}$.

only for convergent. ${\displaystyle |x|<1}$

Individual evidence

1. ^ Entry on Grandi, Guido (1671 - 1742) in the archive of the Royal Society , London

Web links

• John J. O'Connor, Edmund F. Robertson :  Guido Grandi. In: MacTutor History of Mathematics archive .
• Galileo project: Guido Grandi