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Schopenhauer ventures into math and concludes that space begets geometry, while time begets algebra. He also trashes Euclides theoretical approach; i'll update the post with some quotes later.
Reason is feminine in nature; it can only give after it has received. Of itself it has nothing but the empty forms of its operation.
--- Arthur Schopenhauer.
There is no absolutely pure rational knowledge except the four principles to which I have attributed metalogical truth; the principles of identity, contradiction, excluded middle, and sufficient reason of knowledge. For even the rest of logic is not absolutely pure rational knowledge.
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§ 11. In this regard the direct opposite of rational knowledge is feeling, and therefore we must insert the explanation of feeling here. The concept which the word feeling denotes has merely a negative content, which is this, that something which is present in consciousness, is not a concept, is not abstract rational knowledge. Except this, whatever it may be, it comes under the concept of feeling. Thus the immeasurably wide sphere of the concept of feeling includes the most different kinds of objects, and no one can ever understand how they come together until he has recognised that they all agree in this negative respect, that they are not abstract concepts. For the most diverse and even antagonistic elements lie quietly side by side in this concept; for example, religious feeling, feeling of sensual pleasure, moral feeling, bodily feeling, as touch, pain, sense of colour, of sounds and their harmonies and discords, feeling of hate, of disgust, of self-satisfaction, of honour, of disgrace, of right, of wrong, sense of truth, æsthetic feeling, feeling of power, weakness, health, friendship, love, &c. &c. There is absolutely nothing in common among them except the negative quality that they are not abstract rational knowledge.
--- Arthur Schopenhauer, The World As Will And Idea.
Logic is, therefore, without practical utility; but it must nevertheless be retained, because it has philosophical interest as the special knowledge of the organisation and action of reason.
But it has its real value, in relation to philosophy as a whole, in the inquiry into the nature of knowledge, and indeed of rational and abstract knowledge. Therefore the exposition of logic should not have so much the form of a practical science, should not contain merely naked arbitrary rules for the correct formation of the judgment, the syllogism, &c., but should rather be directed to the knowledge of the nature of reason and the concept, and to the detailed investigation of the principle of sufficient reason of knowing.
-- Arthur Schopenhauer, The World As Will And Idea.
https://www.gutenberg.org/cache/epub/38427/pg38427-images.html