Scientist Carl Friedrich Gauss Is In A Class By Himself
March 10, 2021 at 11:26 p.m.
By Max [email protected]
Gauss is a strong contender for the greatest mathematician of all time, ranked with such stalwarts as Archimedes, Isaac Newton and Leonard Euler. I have written about Euler and Newton in earlier columns. Archimedes (287-212 BC) may have been the greatest intellect of antiquity.
Gauss not only made a number of significant astronomical discoveries but also worked and lectured in other fields, in particular, land surveying, geodesy (the branch of mathematics dealing with the shape and area of the earth), and physics and made highly important contributions to each of these fields. Several examples will follow.
Discoveries
Gauss invented and operated the first electromagnetic telegraph of the world. He measured and computed the earth’s magnetic field in great detail and developed new mathematical methods, including, for instance, what is now known as the Fast Fourier Transform, the Universal Transverse Mercator coordinates, and so on. In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.
Also, he taught a fairly large number of astronomers who later became famous, among them Heinrich Christian Schumacher (1780-1850), founder of the Astronomische Nachrichten, and Benjamin Apthorp Gould (1824-1896), founder of the Astronomical Journal (both journals still exist).
Mathematics
Mathematics enters the modern era with the peerless researches of Carl Friedrich Gauss. Gauss began in number theory, sealed his reputation in celestial mechanics by predicting the reappearance of the newly discovered asteroid Ceres and made major advances regarding complex numbers, least-squares data fitting and non-Euclidean geometry, though he published nothing on the latter because he feared it was too far ahead of its time and would attract ridicule.
He and Janós Bolyai are now recognized as the rightful founders of non-Euclidean geometry, which can be interpreted as the natural geometry of a surface with constant curvature. Gauss was basically right to believe that the idea was ahead of its time.
Early Life
Born the son of a poor workman, Gebhard Gauss, and his wife Dorothea (née Benze) in Brunswick in 1777, Carl Friedrich’s talents became evident at an early age. He was a prodigious child, at the age of three informing his father of an arithmetical error in a complicated payroll calculation and stating the correct answer. At the age of 7, Carl Friedrich Gauss started elementary school, and his potential was noticed almost immediately. His teacher and his assistant, were amazed when Gauss summed the integers from 1 to 100 instantly by spotting that the sum was 50 pairs of numbers each pair summing to 101. He was rare among mathematicians in that he was a calculating prodigy, and he retained the ability to do elaborate calculations in his head most of his life.
Impressed by this ability and by his gift for languages, his teachers and his devoted mother recommended him to the duke of Brunswick in 1791, who granted him financial assistance to continue his education locally and then to study mathematics at the University of Göttingen from 1795 to 1798. Gauss’s pioneering work gradually established him as the era’s preeminent mathematician, first in the German-speaking world and then farther afield, although he remained a remote and aloof figure.
In 1788, Gauss began his education at the Gymnasium, where he learnt High German and Latin. After receiving a stipend from the Duke of Brunswick-Wolfenbüttel, Gauss entered Brunswick Collegium Carolinum in 1792. At the academy Gauss independently discovered Bode's law, the binomial theorem and the arithmetic- geometric mean, as well as the law of quadratic reciprocity and the prime number theorem.
Gauss returned to Brunswick where he received a degree in 1799. After the Duke of Brunswick had agreed to continue Gauss's stipend, he requested that Gauss submit a doctoral dissertation to the University of Helmstedt. Gauss's dissertation was a discussion of the fundamental theorem of algebra.
During his career, Gauss published works on number theory, the mathematical theory of map construction, and many other subjects.
In the 1830s, he became interested in terrestrial magnetism and participated in the first worldwide survey of the Earth’s magnetic field (to measure it, he invented the magnetometer). With his Göttingen colleague, the physicist Wilhelm Weber, he made the first electric telegraph, but a certain parochialism prevented him from pursuing the invention energetically. Instead, he drew important mathematical consequences from this work for what is today called potential theory, an important branch of mathematical physics arising in the study of electromagnetism and gravitation.
Final Thoughts
There is a story that in 1807 Gauss was interrupted in the middle of a problem and told that his wife was dying. He is purported to have said, "Tell her to wait a moment 'til I'm through." An excellent book about his life is “The Prince of Mathematics” – written by Margaret Tent.
Max Sherman is a medical writer and pharmacist retired from the medical device industry. His new book “Science Snippets” is available from Amazon and other book sellers. It contains a number of previously published columns. He can be reached by email at [email protected].
Gauss is a strong contender for the greatest mathematician of all time, ranked with such stalwarts as Archimedes, Isaac Newton and Leonard Euler. I have written about Euler and Newton in earlier columns. Archimedes (287-212 BC) may have been the greatest intellect of antiquity.
Gauss not only made a number of significant astronomical discoveries but also worked and lectured in other fields, in particular, land surveying, geodesy (the branch of mathematics dealing with the shape and area of the earth), and physics and made highly important contributions to each of these fields. Several examples will follow.
Discoveries
Gauss invented and operated the first electromagnetic telegraph of the world. He measured and computed the earth’s magnetic field in great detail and developed new mathematical methods, including, for instance, what is now known as the Fast Fourier Transform, the Universal Transverse Mercator coordinates, and so on. In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.
Also, he taught a fairly large number of astronomers who later became famous, among them Heinrich Christian Schumacher (1780-1850), founder of the Astronomische Nachrichten, and Benjamin Apthorp Gould (1824-1896), founder of the Astronomical Journal (both journals still exist).
Mathematics
Mathematics enters the modern era with the peerless researches of Carl Friedrich Gauss. Gauss began in number theory, sealed his reputation in celestial mechanics by predicting the reappearance of the newly discovered asteroid Ceres and made major advances regarding complex numbers, least-squares data fitting and non-Euclidean geometry, though he published nothing on the latter because he feared it was too far ahead of its time and would attract ridicule.
He and Janós Bolyai are now recognized as the rightful founders of non-Euclidean geometry, which can be interpreted as the natural geometry of a surface with constant curvature. Gauss was basically right to believe that the idea was ahead of its time.
Early Life
Born the son of a poor workman, Gebhard Gauss, and his wife Dorothea (née Benze) in Brunswick in 1777, Carl Friedrich’s talents became evident at an early age. He was a prodigious child, at the age of three informing his father of an arithmetical error in a complicated payroll calculation and stating the correct answer. At the age of 7, Carl Friedrich Gauss started elementary school, and his potential was noticed almost immediately. His teacher and his assistant, were amazed when Gauss summed the integers from 1 to 100 instantly by spotting that the sum was 50 pairs of numbers each pair summing to 101. He was rare among mathematicians in that he was a calculating prodigy, and he retained the ability to do elaborate calculations in his head most of his life.
Impressed by this ability and by his gift for languages, his teachers and his devoted mother recommended him to the duke of Brunswick in 1791, who granted him financial assistance to continue his education locally and then to study mathematics at the University of Göttingen from 1795 to 1798. Gauss’s pioneering work gradually established him as the era’s preeminent mathematician, first in the German-speaking world and then farther afield, although he remained a remote and aloof figure.
In 1788, Gauss began his education at the Gymnasium, where he learnt High German and Latin. After receiving a stipend from the Duke of Brunswick-Wolfenbüttel, Gauss entered Brunswick Collegium Carolinum in 1792. At the academy Gauss independently discovered Bode's law, the binomial theorem and the arithmetic- geometric mean, as well as the law of quadratic reciprocity and the prime number theorem.
Gauss returned to Brunswick where he received a degree in 1799. After the Duke of Brunswick had agreed to continue Gauss's stipend, he requested that Gauss submit a doctoral dissertation to the University of Helmstedt. Gauss's dissertation was a discussion of the fundamental theorem of algebra.
During his career, Gauss published works on number theory, the mathematical theory of map construction, and many other subjects.
In the 1830s, he became interested in terrestrial magnetism and participated in the first worldwide survey of the Earth’s magnetic field (to measure it, he invented the magnetometer). With his Göttingen colleague, the physicist Wilhelm Weber, he made the first electric telegraph, but a certain parochialism prevented him from pursuing the invention energetically. Instead, he drew important mathematical consequences from this work for what is today called potential theory, an important branch of mathematical physics arising in the study of electromagnetism and gravitation.
Final Thoughts
There is a story that in 1807 Gauss was interrupted in the middle of a problem and told that his wife was dying. He is purported to have said, "Tell her to wait a moment 'til I'm through." An excellent book about his life is “The Prince of Mathematics” – written by Margaret Tent.
Max Sherman is a medical writer and pharmacist retired from the medical device industry. His new book “Science Snippets” is available from Amazon and other book sellers. It contains a number of previously published columns. He can be reached by email at [email protected].
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