Mathematician Profile

Johannes Kepler, The Fleeing Mathematician and Astronomer

May 23, 2022
Get Started Now

By Ashley Langham

Johannes Kepler had many talents in mathematics, science, philosophy, and theology. He had a difficult start to life; he grew up when his family was in financial decline and suffered many physical ailments, due to him being born prematurely. But, even from an early age he showed signs of being a gifted mathematician and astronomer. 

At age six, he was exposed to the Great Comet in 1577 and at nine, he experienced his first lunar eclipse. These two events had a huge impact on his life; ultimately leading him down a path to appreciate, study, and practice astronomy and astrology.  He wrote Astronomia nova, Harmonice Mudi, and Epitome Astronomiae Copernicanae; three publications that led Newton to discovering the law of gravity. His three laws of motion provided the foundation by which we base our understanding of the solar system; which was very different to the opinions, and what was considered “acceptable” theories of his time. 

His work was often and overwhelmingly interrupted by religious-political unrest. Not only was he forced out of Graz, where he first started working as a teacher of mathematics and astronomy, he was also forced out of Prague, and Linz, Austria. 

Despite the religious upheaval, his own physical ailments, and the limited scientific tools and resources of the time, Kepler discovered many “firsts” in the field of mathematics and astronomy. His talents made him a very influential figure in these fields after his death. Read on to learn more about his work and life!

Johannes Kepler (1571-1630): Financially and Physically Troubled But Mentally Gifted 

Portrait of Johannes Kepler by artist August Köhler, via Wikimedia

Kepler was born prematurely in Weil der Stadt, Germany. By the time he was born, his family’s wealth had dwindled significantly, making him essentially poor. His grandfather, Sebald Kepler, being the Lord Mayor of his city, afforded him some privileges later in life, for Kepler inherited some of his nobility. However, his father, Heinrch, made his living as a mercenary and died by the time Kepler was five; leaving him, his two brothers, and sister. Their mother, Katharina Guldenmann, was an innkeeper’s daughter, a healer and a herbalist.  

Kepler was a very ill child. He caught smallpox, had vision impairment, and his hands’ dexterity was quite limited. This may have been a hindrance to him, but he was just so intellectually gifted that he was able to obtain a scholarship to the University of Tübingen in 1589.

 Germany was under Roman Catholic rule at the time, but Kepler was raised Lutheran, a sect of Protestantism. When he first went to attend his studies at the University, he decided to initially focus on philosophy and Lutheran theology. However, he was introduced to the ideas of Copernicus and he swiftly changed his studies to mathematics. He was always fascinated by astronomy and astrology, these two subjects not being distinct in the 16th century. In addition to mathematics, he switched his focus to exploring these subjects at University, as well. He would also give astrology readings to his fellow students. 

Even though he still carried a deep desire to be a minister of Lutheran theology, he became a staunch supporter of Copernicus. Particularly, he supported his theory of heliocentrism, i.e. the theory that the Sun is the center of the universe, and the other planets orbit around it. Kepler defended this belief from a theological perspective, citing that this theory was intended by God. Ironically, the religion of Christianity did not share his theological convictions; and his theory was highly criticized and not considered true. 

By 1594, after his studies, Kepler moved to Graz, Austria, to become a mathematics and astronomy teacher at Grazer Evangelische Landschaftsschule Protestant school. While in his position, he published Mysterium Cosmographicum (Cosmographic Mystery), which supported Copernicus’s heliocentrism theory. He also included definitions of the sizes of the orbits for which planets made their way around the sun. Kepler used his own model, separate from Copernicus, to depict the planetary movements around the sun; one that led to his fame in the field of astronomy. In his work, he solidified his first law of planetary motion:

Planets move about the sun in an elliptical orbit with the sun at the focus of the ellipse. 

Platonic Solids illustration, taken from Johannes Keplers' Mysterium Cosmographicum, via Wikimedia

Due to his newfound fame and the help of his grandfather’s nobility, he was able to marry Barbara Müller, a rich heiress to a mill owner. He had been courting her for some time but her family disapproved at first due to his low financial and social status. But, they relinquished their disapproval after the fame he received from his first publication. They had four children together, though only two survived. 

The Johannes Kepler and the Tycho Brahe Saga

Portrait of Tycho Brahe, by artist Eduard Ender, via Britannica

A copy of Mysterium was sent to Danish astronomer Tycho Brahe, who lived in Prague at the time. Brahe was supremely well known as an astronomer and needed help completing his research. He wanted a mathematician who could support him and he invited Kepler to his observatory. With the current religious climate in Austria, due to the counter Reformation, and the opportunity to work in such a prestigious position, Kepler took his family to Benatky nad Jizerou, close to Prague, to work on Brahe’s data in 1600.

Brahe and Kepler didn’t get along initially. In fact, Brahe gravely criticized Kepler’s inaccurate data, particularly around his Capernicus aligned theories, particularly those in his work in Mysterium. Brahe thought that all the planets were traveling in circular orbits, while Kepler found that the planets traveled in an elliptical orbit. They also disagreed about the parameters of Kepler’s living arrangements and salary.

Eventually they came to some sort of agreement right before Brahe suddenly died, only a year after Kepler’s employment started. Naturally, Kepler succeeded Brahe’s position as owner and operator of his observatory. 

Kepler became very successful in his post. He discovered his second law of planetary motion which stated:

The speed of a planet traveling along an elliptical orbit, with the sun at one focus is such that the line joining the sun and the planet sweeps out equal areas during equal time periods. 

He also published his next book Astronomia Nova (New Astronomy) in 1609 where he includes his second law of planetary motion. It is also the first publication that details the process by which any scientist proves their hypothesis using data and eventually reaching a conclusion as to whether their hypothesis was true or not; in other words, “the scientific method”. In 1990, scientific historian William H. Donahue, translates Kepler’s New Astronomy and discovers there are quite a bit of errors in his calculations. He also discovered that Kepler “fudged” a lot of his data to reach certain conclusions. However, it is surmised that a lot of his data was “fudged” due more to the limited resources and tools he had at his disposal, rather than Kepler’s pure desire to increase his fame. 

He also wrote important treatises on his first discovery of a SuperNova star in 1604 and his theories on light. He believed that:

Every point on a luminous body in the field of vision emits rays of light in all directions but that the only rays that can enter the eye are those that impinge on the pupil. All rays refract within the normal eye to meet at a single point on the retina. (Britannica)

Kepler Is Forced Out Of Prague

In 1611, political-religious tensions were rising in Prague. For a very short time, the royal family in Prague were still interested in Kepler’s astronomy and mathematical works, so he was allowed to stay in Prague for another year. Yet, his standing amongst the court was falling quickly due to his Lutheran beliefs. 

In the meantime, he was able to publish Dioptrice, a word he coined. This was the first time he described his newest invention, a telescope using two convex lenses where the final image is seen as inverted. He improved on Galileo’s original design. 

Schematic of a Keplerian refracting telescope, via Wikimedia

The same year, his wife Barbara Müller contracted Hungarian Fever along with their remaining children.  By the following year, he was forced out of Prague for his beliefs. He eventually moved to Linz, Austria where he took a teaching and district mathematician position. Soon after their move, his seven year old son and his wife died. He was extremely distraught by his family’s tragedy. 

Widowed, exiled, and grieving, Kepler spent the next two years of his life in Linz “speed-dating” to find someone to take on the childcare of his remaining kids. He ended up marrying Susanna Reuttinger, to take over his household, someone who was half his age. They had seven children, for which only two survived. 

After an observation of the inappropriate volume of the wine in the wine barrels at his wedding, he published his treatise Stereometria Doliorum Vinariorum (The Stereometry of Wine Barrels). In this publication, Kepler objected to the standard methods for determining how much wine to put in each barrel. Originally, the volume of wine was calculated similarly no matter the shape, length, or volume of each barrel. Kepler determined that the wine should be calculated differently, to take into consideration volume and length. 

Even in Linz, he could not avoid religious politics. Most of his work got put under seal by Catholic authorities;  his family and he were forced to convert to Catholicism, and attend Mass. To distract himself from the constant unrest, he continued researching harmonies in the world in the fields of: geometry, music, metaphysics, astronomy, astrology, and any principles related to the “soul”. He published his findings and his third law of motion in Harmonic Mundi (Harmonies of the World). His third law states:

The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. 

Kepler Is Forced Out Of Linz

In 1625, the conflict between the Protestants and the Catholics reached an all time high and by 1626 the city of Linz, was placed under total siege. Kepler moved his family back to Ulm, Germany so he could continue his work without disruption. 

He published one of his final works Rudolphine Tables which included logarithmic calculations and provided tables for calculating the present and future planetary positions. It was this publication where he demonstrated the transit between Mercury and Venus happening in 1631. Unfortunately, he was not able to witness this transit, as he fell ill in Regensburg, Germany. He died on November 15, 1630. 

Before his death, he made several firsts. One of which was that he coined the term “satellite” in his pamphlet Narratio de Observatis a se quatuor lovis sattelitibus erronibus. He also was the first to explain the connection between the high or low tides of the ocean caused by the Moon cycles. He also predicted the year of the birth of Jesus, which is now the most universally recognized today. 

He was an extraordinary astronomer, astrologer, and mathematician despite all the difficulties that plagued his life. 

Our Blog

June 27, 2022
Évariste Galois, The Rebel Rousing Mathematician

Read about the French mathematician Évariste Galois, who split his time between his rebellious political beliefs and his mathematical pursuits.

Elephant Learning

June 20, 2022
Niels Henrik Abel, The Consistently Overlooked Mathematician

Learn more about the Norwegian mathematician Niels Henrik Abel, who’s math career never quite took off, while alive.

Elephant Learning

June 13, 2022
Charles Babbage, The Father Of The Computer

Discover more about the life and work of Charles Babbage, the father of the computer.

Elephant Learning

June 6, 2022
Carl Friedrich Gauss, The Most Brilliant Mathematician of His Time

Find out why Carl Friedrich Gauss was considered the most brilliant mathematician of his time.

Elephant Learning

May 30, 2022
Joseph-Louis Lagrange, The Metric System Mathematician

Discover how Joseph-Louis Lagrange convinced the French Academy of Sciences, during the heightened threat of death during the French Revolution, to adopt the widely used metric system.

Elephant Learning

May 23, 2022
Johannes Kepler, The Fleeing Mathematician and Astronomer

Discover the many mathematical and astronomy “firsts” Johannes Kepler made while having to continuously dodge the religious politics of his time.

Elephant Learning