«Science History»
Zeuthen, Hieronymous

Hieronymous Georg Zeuthen

Born: 15 February 1839 in Grimstrup, West Jutland, Denmark
Died: 6 January 1920 in Copenhagen, Denmark

Hieronymus Georg Zeuthen's father was the minister in Grimstrup where his son was born and began his education. However Zeuthen's father moved in 1849 from a church in Grimstrup to a church in Soro and at this time Zeuthen began his secondary education. After completing his schooling in Soro in 1857 he entered the University of Copenhagen to study mathematics.

At Copenhagen Zeuthen studied a broad mathematics course attending courses on topics in both pure and applied mathematics. In 1862 he graduated with a Master's degree and was awarded a scholarship to enable him to study abroad. He decided to visit Paris and there he studied geometry with Chasles. This was extremely important for Zeuthen since his research areas of mathematics were firmly shaped by Chasles during this period. The first topic on which Zeuthen undertook research was enumerative geometry.

In 1865 he submitted his doctoral dissertation on a new method to determine the characteristics of conic systems to the University of Copenhagen. Haas describes the thesis in [1]:-

In this work Zeuthen adhered closely to Chasles's theory of the characteristics of conic systems but also presented new points of view: for the elementary systems under consideration, he first ascertained the numbers for point or line conics in order to employ them to determine the characteristics.
Up until 1875 Zeuthen worked almost exclusively on enumerative geometry. He was appointed as an extraordinary professor at the University of Copenhagen in 1871 and, in the same year, he became an editor of Matematisk Tidsskrift, a position he held for 18 years. He was the secretary of the Royal Danish Academy of Sciences for 39 years, during which time he was also a lecturer at the Polytechnic Institute. He continued teaching at the University of Copenhagen where he was promoted to ordinary professor in 1886. He was twice Rector of the University.

After 1875 Zeuthen's contributions to mathematics became more varied. He began to write on mechanics and he also made significant contributions to algebraic geometry, particularly the theory of algebraic surfaces. As we mentioned above, he developed the enumerative calculus, proposed by Chasles, for counting the number of curves touching a given set of curves. The move towards rigour in geometry led to this theory being neglected for many years but recently some of the remarkable numerical results produced by it have been confirmed.

He was also an expert on the history of medieval mathematics and produced important studies of Greek mathematics. He wrote 40 papers and books on the history of mathematics, some of which have become classics. Unlike many historians of science Zeuthen explained the ancient texts in the manner of a colleague of the ancient mathematicians.

His historical studies covered many topics and several periods. In a major work in 1885 he looked in detail at the work of Apollonius on conic sections and showed that Apollonius used oblique coordinates. Caveing, in [3], looks at Zeuthen's ideas on the discovery of irrational numbers. Zeuthen argued that Pythagoras himself discovered that 2 was irrational when computing the diagonal of a square. The passage from Plato's Theaetetus where it states that Theodorus proved the irrationality of 3, 5, ... 17 was also carefully studied by Zeuthen. He suggested that the end of Theodorus's proof somehow involved the continued fractions for 17 and 19, a conjecture which is very much in line with modern ideas about Greek mathematics.

Zeuthen's largest historical work was published in 1896. It looked in detail at the work of Descartes, Viète, Barrow, Newton and Leibniz as he traced the development of algebra, analytic geometry and analysis.

In [7] Lützen and Purkert compare the historical approaches of Moritz Cantor and Zeuthen. They write:-

Moritz Cantor and Hieronymus Georg Zeuthen were probably the two most outstanding historians of mathematics at the end of the 19th century. However, their methods of work differed strikingly. Moritz Cantor was an encyclopaedist who ... followed the development of mathematics in a survey of an almost innumerable collection of original and secondary sources from antiquity to the end of the 18th century. ... Zeuthen's papers and books, on the other hand, present deep mathematical analyses of the methods found in classical works mostly from antiquity and from the 16th and 17th centuries in an attempt to capture their fundamental ideas.
Kleiman gives an interesting biography of Zeuthen in [6]. This indicates that:-
[Zeuthen] was in many ways a leading light of the burgeoning intellectual life of his country, and with a selfless and generous disposition he seems happily to deserve Coolidge's epithet of the "ever kindly".
Finally we quote Hass's comments in [1] on Zeuthen's style. He writes:-
Zeuthen saw things intuitively: he constantly strove to attain an overall conception that would embrace the details of the subject under investigation and afford a way of seizing their significance. This approach characterised his historical research equally with his work on enumerative methods in geometry.

Article by: J J O'Connor and E F Robertson

March 2001
MacTutor History of Mathematics
Search All Ebay* AU* AT* BE* CA* FR* DE* IN* IE* IT* MY* NL* PL* SG* ES* CH* UK*
Becoming by Michelle Obama (New Hardcover Book – 2018)

End Date: Wednesday Jan-9-2019 7:02:36 PST
Buy It Now for only: $13.79
Educated : A Memoir by Tara Westover (2018, Hardcover) - NEW - FREE Shipping...

End Date: Thursday Jan-10-2019 10:58:04 PST
Buy It Now for only: $14.90
Becoming by Michelle Obama (New Hardcover Book – 2018)

End Date: Sunday Jan-6-2019 8:17:29 PST
Buy It Now for only: $16.99
Educated : A Memoir by Tara Westover (2018, Hardcover)

End Date: Wednesday Jan-9-2019 23:14:02 PST
Buy It Now for only: $3.84
All About Me: The Story of Your Life by Keel, Philipp

End Date: Wednesday Jan-9-2019 11:01:52 PST
Buy It Now for only: $23.01
Becoming by Michelle Obama Hardcover (FREE 2 DAY SHIPPING)

End Date: Saturday Dec-29-2018 9:23:54 PST
Buy It Now for only: $0.99
12 Rules for Life - An Antidote to Chaos by Jordan B. Peterson (PDF)

End Date: Wednesday Jan-9-2019 6:59:24 PST
Buy It Now for only: $13.99
In Pieces by Sally Field (2018, Hardcover) NEW FREE SHIPPING

End Date: Thursday Jan-10-2019 20:15:56 PST
Buy It Now for only: $13.00
Датский цойтен керамика чаша средневековый органическая форма

3 328,33 руб.
End Date: 31.12 22:59
Buy It Now for only: US 3 328,33 руб.
Buy it now |
Цойтен Дании середины века сливки и сахар

863,01 руб. (0 Bids)
End Date: 19.12 03:54
Винтажный датский современный керамика Мухомор красный-гриб, солонка и перечница в цойтен

6 577,20 руб.
End Date: 10.01 01:51
Buy It Now for only: US 6 577,20 руб.
Buy it now |
Цойтен Дания датский керамической середины века redware ваза

2 656,79 руб. (0 Bids)
End Date: 13.12 18:41
Цойтен Дания датской студии керамика

3 328,33 руб.
End Date: 19.12 01:56
Buy It Now for only: US 3 328,33 руб.
Buy it now |
Цойтен керамика ~ милый середины века белый в горошек красной керамики копилка ~ Дания

2 790,33 руб.
End Date: 16.12 03:03
Buy It Now for only: US 2 790,33 руб.
Buy it now |
Цойтен керамика ~ середины века белый в горошек красной керамики квадратная чаша ~ Норвегия

1 727,35 руб.
End Date: 16.12 03:04
Buy It Now for only: US 1 727,35 руб.
Buy it now |
Лот из 8 штук цойтен керамика дания redware керамика-выпуклые узор в горошек

8 636,06 руб.
End Date: 31.12 22:49
Buy It Now for only: US 8 636,06 руб.
Buy it now |

Nationwide and free delivery on orders over ?150

Start: 14 Jul 2017 | End: 28 Feb 2018

Sign up to our newsletter and enjoy $20 off your first box at HelloFresh.ca!

Start: 04 Apr 2017 | End: 01 Feb 2018

Save 15% off Virtual Private Servers at Heart Internet. Enter AFFVPS15 at Checkout.

Code: AFFVPS15

Start: 02 Oct 2017 | End: 30 Apr 2018

Search All Amazon* UK* DE* FR* JP* CA* CN* IT* ES* IN* BR* MX
Booking.com B.V. is based in Amsterdam in the Netherlands. Ready for some statistics? Our 1,534,024 properties, including 860,482 holiday rentals, are located in 123,105 destinations in 229 countries and territories, and are supported internationally by 198 offices in 70 countries.
2013 Copyright © Techhap.com Mobile version 2015 | PeterLife & company
Skimlinks helps publishers monetize editorial content through automated affiliate links for products. Affiliate programm.
Terms of use Link at is mandatory if site materials are using fully or particulary.
Were treated to the site administrator, a cup of coffee *https://paypal.me/peterlife