First published Wed Apr 17, 2002

Friedrich Daniel Ernst Schleiermacher (1768-1834) probably cannot be ranked as one of the greatest German philosophers of the eighteenth and nineteenth centuries (like Kant, Herder, Hegel, Marx, or Nietzsche). But he is certainly one of the most interesting of the second-tier philosophers of the period. Nor was he only a philosopher; he was also an eminent classicist and theologian. Much of his philosophical work was in the philosophy of religion, but from a modern philosophical point of view it is probably his hermeneutics (i.e. theory of interpretation) and his theory of translation that deserve the most attention. This article will attempt to provide a fairly broad overview of his philosophical thought. One thing which will emerge when this is done is that although he has important philosophical debts to many predecessors and contemporaries (including Spinoza, Kant, Friedrich Schlegel, and Schelling), he was above all following in the philosophical footsteps of one predecessor in particular: Herder.

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In a work ahead of its time the German mathematician Hermann Grassmann (1809–1877) published in 1844 one of the landmark works in mathematics, his Ausdehnungslehre or Calculus of Extension. It contained the main theorems that make up what is today called linear algebra. The significance of the book was not recognized at first and it took even longer before any connection was publicly made between this work and Grassmann's training for the ministry. This was in spite of the strong influence on his thinking in general that he described coming from his teacher at Berlin, the theologian Friedrich Schleiermacher.

The Divine Truth of Mathematics and the Origins of Linear Algebra

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Friedrich Schleiermacher was born at Breslau. His father, a clergyman of the Reformed Church sent him to the Moravian Brothers for his schooling. He then studied theology at the University of Halle, where he also became interested in philosophy. He was ordained in 1790 and worked as a tutor before taking up pastoral posts in Landsberg and then Berlin in 1796. While there he was in close contact with Friedrich von Schlegel and other figures of the Romantic movement. He was appointed to a university chair at Halle in 1804, and in 1810 he became professor of theology at Berlin, lecturing also on ethics and hermeneutics

One of Schleiermachers sources was Plato, and of course one of Platos sources was Pythagoras.

I have spent some time on Pythagorean theology and on Euclids Stoikeioon.This was fortunate, for the recent redearch into Die Geometrie reveals a distinct lack of understanding of Euclid's Stoikeioon. Instead of using the Stoikeioon as a gateway into Pythagorean theology, Early 19th century Geometers used it to define a subject called Geometrie. Before this time geometry was loosely associated with Euclid, because it was known that much of Euclid was applicable to land measurement. But with Descartes came a distinction between practical geometry for architectural, artistic and land measurement purposes, see for example Duerer's work, and a more abstact analyticaland algebraic approach. Also at about this time Geometers began to be distinguished from mathematikers, who by and large believed they held a more general view of the "science".

As a consequence, and in a general lack of knowledge about the connection of Euclid to Pythagoras, the Stoikeioon began to be trivialized. Thus, in the time of Jakob Steiner, Riemann Grassmann etc Grometry was born as an axiomatic subject, being raised from the dustbin of obsolescence and seated anew at the table of fundamental enquiry. However, now mathematicians had to define themselves as well as a new topic, and in so doing they started with their diminished understanding of Euclid's Stoikeioon.

Grassmann was different. He was not "miseducated" but he educated himself, and in particular he was somewhat influenced by Schleiermacher. His own study would have taken him past schleiermacher's work to Plato. From their he would have gleaned the connection to Pythagorean theology. thus he would have gained his inspiration to develop a new branch of science dealing with space but independent of any other mathematical branch.

http://books.google.com/books?id=PUifpzKWhLkC&pg=PA109&lpg=PA109&dq=Grassmann++and+pythagorean+Philosophy&source=bl&ots=ads8Fv5CEH&sig=unkGevg2VLzxJBydaidjUN14Rvw&hl=en&ei=MV-OTqWlLpCY0QW46akU&sa=X&oi=book_result&ct=result&resnum=1&ved=0CB4Q6AEwAA#v=onepage&q=Grassmann%20%20and%20pythagorean%20Philosophy&f=false

http://www.religion-online.org/showarticle.asp?title=2850

http://webcache.googleusercontent.com/search?q=cache:S6gEPZxvy4QJ:www.maths.ed.ac.uk/~aar/papers/johnson1.pdf+Grassmann+and+pythagorean+Philosophy&cd=27&hl=en&ct=clnk&client=opera

http://www.cosmosandhistory.org/index.php/journal/article/view/109/218

http://www.gap-system.org/~history/HistTopics/Abstract_linear_spaces.html

AS much as i can find does not confirm a Pythagorean theological influence beyond that generally adopted by the church theologians, and that is more down to Plato than direct Pythagoreanism. But certainly Schelling and Schleiermacher and his brothe Robert had some influence on Grassmann's thinking. It is clear that that thining did not follow academia in developing from an aiomatic system, but rather developing from an abstract system find one instance of it in Euclideab geometry as thougt at the time. This is precisely the method used by Euclid to organize his teaching material.