query: Fundamental of mathematics
positive_passages.docid: 17515
positive_passages.text: Why is negative times negative = positive?
negative_passages.docid: 52110
negative_passages.text: About the second fundamental form
negative_passages.docid: 73352
negative_passages.text: Subjects studied in number theory
negative_passages.docid: 101944
negative_passages.text: Fundamental invariants of the electromagnetic field
negative_passages.docid: 95229
negative_passages.text: Qualifying Exam Question On Elementary Group Theory
negative_passages.docid: 153969
negative_passages.text: The "elements" of a real number
negative_passages.docid: 109964
negative_passages.text: the converse of Pythagoras Theorem
negative_passages.docid: 106157
negative_passages.text: Proof of Euclid's lemma using fundamental theorem of arithmetic
negative_passages.docid: 30879
negative_passages.text: Environment for Mathematics
negative_passages.docid: 122665
negative_passages.text: Help finding the fundamental group of $S^2 \cup \{xyz=0\}$
negative_passages.docid: 71918
negative_passages.text: Mathematical Induction
negative_passages.docid: 119050
negative_passages.text: Fundamental group of $S^2$ with north and south pole identified
negative_passages.docid: 95042
negative_passages.text: Textbooks on set theory
negative_passages.docid: 149472
negative_passages.text: Interesting topics to research in mathematical physics for undergraduates
negative_passages.docid: 60577
negative_passages.text: Understanding the intuition behind math
negative_passages.docid: 89843
negative_passages.text: Is the center of the fundamental group of the double torus trivial?
negative_passages.docid: 50240
negative_passages.text: Can you provide me historical examples of pure mathematics becoming "useful"?