Weigel earned his MA and his habilitation from the University of Leipzig. From 1653 until his death he was professor of mathematics at Jena University. He was the teacher of Leibniz in summer 1663, and other notable students. He also worked to make science more widely accessible to the public, and what would today be considered a populariser of science. He concurred with Jakob Ellrod's "Mittel-Calendar", and with the advocacy of Leibniz and others, that the date of Easter should be based on the astronomical measurement of the spring equinox and the next full moon. He followed Jakob Ellrod to the Imperial Diet in Regensburg to advocate the use of the Mittel-Calendar or New Gregorian calendar.
1644–46 Lutheran high school in Halle and simultaneous activity with the astronomer Bartholomäus Schimpfer, who teaches him mathematics
1646 temporary return to Wunsiedel; mathematics and astronomy instruction with archdeacon Jakob Ellrod
1647–50 studies at the University of Leipzig
1650 MA in philosophy: De ascensionibus et descensionibus astronomicis dissertatio
1652 habilitation in Leipzig with Dissertatio Metaphysica Prior ; Dissertatio Metaphysica Posterior
1653 post as mathematics professor in Jena
1653 begins lectures De Cometa Novo
1653 marries Elisabeth Hartmann
1654 appointment as Stipendiarorum et Alumnorum Inspector
1658 publishes the analysis Aristotelica ex Euclide restituta, genuinum sciendi modum, & nativam restauratae Philosophiae faciem per omnes disciplinas & facultates ichnographicè depingens; the work brings him into conflict with the philosophical faculty
1664 publishes of the Speculum Temporis Civilis, containing explanation of the calendar
1665 publishes Speculum Terrae
1667–70 Weigel's house, in Jena, for its time has remarkable technical interior facilities—among others an elevator and a water pipe
1669 publishes Idea Matheseos Universae cum Speciminibus Inventionum Mathematicarum
1673 publishes Universi Corporis Pansophici Caput Summum
1673 publishes Tetractys, Sumum eum Arithmeticae eum Philosophiae discursivae Compendium
1674 publishes an arithmetic description of morals Arithmetische Beschreibung der Moral-Weissheit von Personen und Sachen worauf das gemeine Wesen bestehet
1679 Weigel's work on "the mystery of Holy Trinity demonstrated from the principle of geometry", brings him in conflict with the theological faculty and he is forced to retract his work
Weigel was arguably one of the earliest German PhD holders. Through Leibniz, Weigel is the intellectual forefather of a long tradition of mathematicians and mathematical physicists that connects a great number of professionals to this day. The Mathematics Genealogy Project lists more than 50,000 "descendants" of Weigel's, including Lagrange, Euler, Poisson and several Fields Medalists. The crater Weigel on the Moon is named after him. In 1999 a colloquium was held in Jena on the 300th anniversary of his death.
