Tycho Brahe
1546 - 1601

He was an alchemist. This is intended to be a supreme compliment for his day. Yet, the modern perspective on alchemy does not offer Brahe the proper respect due for the many contributions he made to science and future mathematics. Tycho Brahe (Tyge Brage) had influences on Kepler, Newton, Nathaniel Carpenter, John Webster, and a host of others. To say that he was interested in mathematics is to say that Einstein was interested in science. He was passionate about math. In fact he even was involved in a sword duel with another man to end an argument as to whom was the greatest Danish mathematician.

In the mid fifteenth century Trevisan spent eight years in the lab keeping a fire going to distill gently two thousand hens eggs. This was done to create a strong reagent for use in finding the philosopher’s stone. Tycho Brahe did not need personal wealth and was not thought to have been seeking the philosopher’s stone. Rather his effort was directed more toward the medicinal and mystical developments in alchemy. Still, the slow patient work of the early alchemists may provide the basis for Brahe’s careful work over a long period of time. However, Brahe was quite wealthy and had a large number of assistants to help with the tedious observations. It is hard to determine just how much of the science labor was actually his, although most accounts note Brahe as a careful and tireless worker. He did seem to enjoy developing the best observational gadgetry of the day and had huge sums of personal wealth to devote to such things. During the 1580’s it is estimated that he held 1% of the entire worth of Denmark. At his island observatory he also was known to throw drunken parties … nobility does what nobility does. (For example, one night Brahe’s pet elk died while stumbling down some stairs after it had had too much strong beer to drink. Even in modern times partying is still used to counter the tedium of a day’s work.) He also ran his island (Hveen) as if it was a sovereign country and he was the king. His observatories at Hveen not only had the usual amenities such as precision equipment rooms, alchemist’s furnace room, and library, but also there was a prison for tenants who caused difficulty. Near the end of his stay he kept a tenant and his entire family in chains in spite of Denmark’s high court of justice. Even given the downside to Brahe, it appears that science was a product of fervent interest in the phenomena of nature.

In the early sixteenth century, Theophrastus Paracelcus took alchemy in a new direction. He was a man of medicine. Common to the time were strange medical practices such as the doctrine of signatures and the practice of sympathetic cures. In these pursuits a plant with a heart-shaped leaf might be thought to be good for dealing with heart ailments. An axe that cut a person’s hand might be bandaged in addition to bandaging the hand since it was impossible to determine if it was the hand or the axe that went astray and both might be in need of healing. Paracelcus came up with the novel idea of carefully observing an ailing patient and then prescribing cures based upon these observations. This revolutionized science. Much attention turned toward medicines, particularly the search for the “ilixir vitae.” Brahe studied the works of Paracelsus and was constantly trying to make medicines. Some of these concoctions were listed in the official Danish pharmacoepia. Since Paracelsus had a great influence, it is reasonable to believe that this was the source for Brahe’s interest in careful and tedious observations.

Telescopes were not invented during Brahe’s lifetime thus all of Tycho’s observations had to be done with plain eyesight. He believed that some of the errors in the astronomical works of Claudius Ptolemy and of Copernicus were due to poor instrumentation. He developed many “oversized” pieces of equipment such as a sextant that had five and one half foot arms and was calibrated in 60th’s of a degree. (This alone was not sufficient for Brahe as he created a table of corrections for the small errors that might be found while operating a piece of equipment.) Brahe also employed mathematical techniques that would help reduce the size of calculations and thus might help reduce errors from fatigue. One such technique was the use of the equation:

[sin(a+b) + sin(a-b)]/2
where in multiplying two large numbers one is regarded as the sine of an angle and the other as the cosine of a second angle. (Pitiscus had only tables of sines and so angle compliments were used.) If a person wanted to find the product of a problem such as 155 x 36, a person would find the angle values for the decimals of these numbers. Thus, sin 77o49’ = 0.15500 and cos 68o54’ = 0.36000. Thus, 36 x 155 = 105 [sin 77o49’ + sin (-59o59’)] / 2 = (97748 - 86588) / 2 = 5580. Some significant figures would be lost but for large numbers this procedure saves labor.

For more than twenty years Brahe plotted his careful observations of the six planets, sun, moon, and a variety of stars. He had a 5-foot diameter polished brass globe made for him so that he could record the courses of these objects. Some of his findings and the conclusions he drew contradicted Aristotle and the dogma of the Church. His status of nobility probably kept him from being punished. He believed in the improvement of astrology and was charged with making annual prognostications for King Frederick II. Likewise, in Bohemia (Czech Republic) he was the King’s mathematician and was employed because of his insights into the enigma and mysteries of the universe. In fact the job description which King Rudolph II had for Kepler (Brahe’s assistant and successor at Prague) required him to cast horoscopes for the worthies. Kepler referred to astrology as the daughter of astronomy who nursed her own mother.

Disputes of science, of religion have lead to the persecution and even the deaths of many people. Brahe rejected the belief of there being a dichotomy between the sublunary world and the perfect and immutable heavens, which was a common doctrine of the time. Brahe concluded from distance calculations of the sun, comets, and planets that the heavens could not be filled by solid spheres carrying the planets. He also could not accept the full heliocentric theory of Copernicus and insisted that the earth was the center of the universe. The idea of a moving earth seemed counter to the day’s interpretation of the Bible. Maybe it was also difficult for Brahe to deal with the idea of ascribing motion to the earth both in the terms of spin and of travel around the sun. With the earth as the center of the universe, Brahe could retain Aristotelian physics (the only physics available). Maybe the expense of twenty-five year’s of data recording on an extremely costly brass globe that would have to be discarded was a consideration as well. Still, Brahe’s collected data had many benefits for future astronomers and mathematicians.

One of the greatest legacies given by Brahe and Kepler was their fine example of collegiality. Remembering that Brahe was a man of strong belief and hot temper, it is interesting that he left his entire life’s work to Kepler even after the two had had many vehement arguments over Copernicus’ sun-oriented system. It is also amazing that Brahe did not “fudge’ data to support his own theories. This being the case, later on Kepler was able to use the measurements Brahe had recorded in order to develop his laws regarding elliptical motion. Thus, the “folly” of one scientist was able to be revised into a new form of mathematics and provide the continuation of a better science. Brahe’s idea of dual centerings for the universe was popular through the middle of the seventeenth century. Theological reinterpretations as well as Kepler’s work and the contributions of Galileo Galilei made it finally possible to let go of the idea that the earth was the center of the universe. Thus, a final benefit of good science seems to be the interest generated in the theological community to review, retranslate, and better explain Scripture.

General Summary:

Although timing was essential to the accomplishments of Brahe, merely showing up for work would not have produced the legacy he left. Still, it is important that he was of noble linage on both sides of his family. His mother, Beate Bille, was a member of the Bille family who had had a number of members on the Rigsraad. His father, Otte Brahe, was a member of the twenty-member oligarchy (Rigsraad) that ruled Denmark (now Sweden). Before birth, he had been promised to Jorgen Brahe, his wealthy uncle who was childless. After he was born, Tycho’s father refused to hive him up to his uncle. Later, a younger brother was born to Beate and Otte. At that time, the uncle kidnapped Tycho. Otte flew into a rage and vowed to kill Jorgen. It appears that passion ran deep in the Brahe family. However, Otte was comforted by the fact that Tycho was to be Jorgen’s heir.

At the age of seven Jorgen insisted that Tycho begin studying Latin. His parents objected (religious grounds?) but were told that this would help him to become a lawyer. On August 21, 1560, when Tycho was 13 and attending the University of Copenhagen, a partial eclipse of the sun occurred. Tyco was impressed that this event had been predicted long before its occurrence. As a result, he went out and bought a copy of Ptolemy’s “Almagest” (in Latin) and a set of astronomical tables based on Copernicus’ theory. By the time he was about sixteen, Tycho had lost interest in the law. In Leipzig, he was accompanied by a private tutor, Anders Vedel (age 20). He found numerous ways to ditch the tutor so that he could concentrate on astronomy. (The fact that he and Vedel remained friends throughout their lives was fortunate since Vedel went on to become Denmark’s first historian.) In Leipzig, finished his first self-made astronomical instrument, the Jacob’s Stave. In 1565, his uncle, Jorgen Brahe died of pneumonia. Jorgen had rescued the King of Denmark from drowning but it eventually cost him his life. Generally, Tycho’s family was unfriendly to star gazing thus he spent much of the late 1560’s away from Denmark. He fell into the company of some rich young astronomers in Augsburg. This is where he developed many of his ideas for building large equipment to get lines of sites on stars. It was shortly after this time that Tycho has his infamous duel regarding an argument over a new mathematical formula. Tycho lost the end of his nose, which he replaced with an alloy (some say copper, some say gold/silver) prosthesis. From 1568 through 1570, Tycho’s father paid for his educational and traveling expenses. In the early 1570’s he lived and worked with his maternal uncle, Steen Bille who founded the first paper mill and glassworks in Denmark. Steen had an alchemy lab set up at Herreved Abbey and was the only family member who approved of Tycho’s star gazing. On November 11, 1572, as Tycho was coming back from Steen’s alchemy lab, he noticed that a new star was in the sky which was brighter than Venus. This was significant for several reasons. First, it focused Tycho’s attention back on astronomy. Second, he wrote “De Nova Stella”. Third, he had to deal with the fact that the universe was mutable.

Tycho married a woman of non-nobility and was generally ostracized by the community. His children (eventually 5 girls and 3 boys) were all seen as illegitimate. Thus in 1575 he went abroad to visit with the world’s astronomers. In 1576, King Frederick II of Denmark provided Tycho with an island, an observatory, and an annual income. Besides the observatories, Tycho established a paper mill and a book printing house. Brahe spent twenty years or more at the island observatory. However, after King Frederick II died, Tycho was no longer in favor with the new king, Christian IV. After several years of staying in German towns, he moved his lab, family and assistants (par. Kepler) to Prague. He spent two years in service to Rudolph II and on October 24, 1601 he died apparently of a burst bladder at the King’s table. In those days no one left the table for any reason until they were dismissed. The works of Tycho Brahe have been compiled and published under the title “Tychonis Brahe Opera Omnia,” by the Society for Danish Language and Literature.

Contributed by W. R. White


  1. “The History Of Mathematics: A Brief Course,” Roger Cooke, 1977, John Wiley & Sons.
  2. “Crucibles: The Story Of Chemistry,” Bernard Jaffe, 1976, Dover.
  3. “Mathematics In Western Culture,” Morris Kline, 1982, Oxford University Press.
  4. “The History Of Mathematics: An Introduction,” Victor J. Katz, 1998, Addison Wesley.
  5. “Ancients And Moderns,” Richard Foster Jones, 1961, Dover.
  6. School of Mathematics and Statistics, University of St. Andrews, Scotland,http://www-history.mcs.st-andrews.ac.uk/history/Mathematics/Brahe.html
  7. Catalog Of The Scientific Community Brahe Compilation by Richard S. Westfall, Dept. of History, Indiana University,http://es.rice.edu/ES/humsoc/Galileo/Catalog/Files/brahe.html
  8. “Tycho Brahe” http://es.rice.edu/ES/humsoc/Galileo/People/tycho_brahe.html
  9. Neft’s Astro Scientific Tycho Brahe Homepage, Flemming Ravn Neft, M.A. & B.A., http://inet.uni-c.dk/~nefts/tycho.htm
  10. “Tycho Brahe,” Michael Fowler, http://www.phys.virginia.edu/classes/109N/1995/lectures/tychob.html
  11. “Tycho Brahe” maintained by Tycho Brahes Glada Vanner, http://www.nada.kth.se/~fred/tycho.html
  12. “Kepler’s laws” by Bill Drennon, Central Valley Christian High School, Visalia, Ca http://www.cvc.org/science/kepler.html

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