First of all, the stylistic differences between Greek and Western mathematics emphasized by Oswald Spengler [in his book The Decline of the West] should not become overvalued in their importance: the correctness of mathematical theorems is completely independent of them. ...
Or are there real differences, say, between German and French mathematics? Recently that has actually been asserted: the stylistic differences between German and French mathematics are immensely large and it could be asserted that an occupation with German mathematics - and careful avoidance of French mathematics - would uncommonly strengthen the schoolchild or student in their German consciousness. These theses probably arose from the worry that from a widespread aversion to "objective science" must arise a negative valuation of mathematics - and the conviction that it may be easier and richer in prospects to recommend mathematics through veiling its objective character, than to limit the objections against objective science to their legitimate amount. However, one renders National Socialism no service if one offers as bases for the detail of its decisions points of view that are selected only according to convenience, without regard to their truth content.
The distinctions between German and French mathematics are not more real than the distinctions between German and French machine guns. Therewith is recognised that there actually are also in the mathematical sciences certain very fine differences of style of a national sort. If one (and the opportunity occurs now and then in the cinema) compares the appearance of Japanese warships with European ones, one recognizes distinctly that even in such an instrument of technical precision, Japanese feeling for style is able to assert itself: somehow also the shape of such a warship shows the characteristically un-European features that represent Japanese art to us. Perhaps a very sensitive analysis could reveal indeed a rationally determined difference in style between a German and a French machine gun. However, the value of a weapon rests directly not on this: what matters is solely the effectiveness of the machine gun, and for this question there prove to be standards from military experience of "objective" validity going beyond the differences in taste and style of the different nations.
Therefore it completely misses the nub of the matter if one wishes to recommend mathematical-school instruction by the assertion that the students may gain from German mathematics a strengthened German consciousness. If therein lay the actual task and value of mathematical instruction, then it were high time to completely abolish this torment, since for this end there are better means. However, as is well known, our youth capable of defence will not be instructed in the use of a machine gun for the reason that they experience in their association with German weapon factories a strengthening of their Germanhood (while through the use of French factories they must become Frenchified ... On the contrary, the education in a machine gun occurs because of the importance of this instrument for international intercourse, and nations who must buy their weapons in foreign countries pay not for the finest traces of national peculiarities of style contained therein, but for objective effectiveness.
These considerations suggest that also the concept of scientific objectivity is a politically definable concept. Objective standards, i.e., standards of supranational validity, exist for all things that possess a connection to war. War is the most distinguished means for creation of objective historical facts - i.e., such facts whose factuality must also be recognized by the conflicting nations. And war represents the objective test for the relation of the forces and weapons on both sides.
It reminds us - compared with the grotesque misunderstandings with which we must occupy ourselves - that the computation of bullet trajectories, of airplanes and armoured ships, depend upon nothing else as solely and exclusively as the objective correctness of the computational results. Therefore, that the mathematical-physical sciences perhaps present in the most refined secondary traces turbidity of their objective content brought about by national peculiarities of style must not be cultivated but overcome.