Short answers, pulled from the story.
Johann Bernoulli was a Swiss mathematician born in Basel who lived from 1667 to the 1st of January 1748. He made major contributions to infinitesimal calculus and was one of the first mathematicians to not only understand but actively apply calculus to solve problems. He is also remembered for educating Leonhard Euler in the young mathematician's early years.
The mathematical result known as l'Hopital's rule was largely the work of Johann Bernoulli. Guillaume de l'Hopital hired Bernoulli as a tutor and the two signed a contract giving l'Hopital the right to use Bernoulli's discoveries. L'Hopital's 1696 textbook Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes, the first calculus textbook ever written, was built substantially on Bernoulli's work.
Johann Bernoulli sided firmly with Leibniz in the 1713 dispute over who deserved credit for inventing calculus. He defended Leibniz by demonstrating that Leibniz's methods had solved certain problems that Newton's methods had not. Bernoulli also promoted Descartes' vortex theory over Newton's theory of gravitation, which contributed to delayed acceptance of Newton's ideas in continental Europe.
Daniel Bernoulli published Hydrodynamica in 1738, a foundational work on fluid motion. Johann responded with his own book, Hydraulica, published in 1743, but deliberately and falsely predated it by six years to appear to have priority over his son's work.
Johann Bernoulli posed the brachistochrone problem in 1696, offering a reward for finding the fastest path a gravity-driven particle can travel between two points. Both brothers arrived at the cycloid as the answer, but Johann's own derivation was incorrect. He then presented his brother Jacob's correct derivation as his own work.
Johann Bernoulli served as professor of mathematics at the University of Groningen after marrying Dorothea Falkner in 1694. He returned to Basel in 1705 following his brother Jacob's death from tuberculosis and took over Jacob's former position as professor of mathematics at the University of Basel.