- First to correctly explain planetary motion, thereby, becoming founder of celestial mechanics and the first "natural laws" in the modern sense; being universal, verifiable, precise.
In his book Astronomia Pars Optica, for which he earned the title of founder of modern optics he was the:
- First to investigate the formation of pictures with a pin hole camera;
- First to explain the process of vision by refraction within the eye;
- First to formulate eyeglass designing for nearsightedness and farsightedness;
- First to explain the use of both eyes for depth perception.
In his book Dioptrice (a term coined by Kepler and still used today) he was the:
- First to describe: real, virtual, upright and inverted images and magnification;
- First to explain the principles of how a telescope works;
- First to discover and describe the properties of total internal reflection.
- His book Stereometrica Doliorum formed the basis of integral calculus.
- First to explain that the tides are caused by the Moon (Galileo reproved him for this).
- Tried to use stellar parallax caused by the Earth's orbit to measure the distance to the stars; the same principle as depth perception. Today this branch of research is called astrometry.
- First to suggest that the Sun rotates about its axis in Astronomia Nova
- First to derive the birth year of Christ, that is now universally accepted.
- First to derive logarithms purely based on mathematics, independent of Napier's tables published in 1614.
- He coined the word "satellite" in his pamphlet Narratio de Observatis a se quatuor Iovis sattelitibus erronibus