Do Mathematicians Have Modest Goals?

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SUMMARY

This discussion centers on the philosophical and mathematical implications of the paper titled "Cohomology Classes on Compact Projective Manifolds" (arXiv:2106.11285). The author humorously contrasts the lofty existential questions humans ponder with the more modest mathematical goals of proving results related to cohomology classes, the Hard-Lefschetz Theorem, and Hodge-Riemann bilinear relations. The discussion highlights the significance of these mathematical concepts while acknowledging the gap between abstract mathematics and fundamental human inquiries.

PREREQUISITES
  • Understanding of cohomology classes in algebraic geometry
  • Familiarity with the Hard-Lefschetz Theorem
  • Knowledge of Hodge theory and bilinear relations
  • Basic grasp of compact projective manifolds
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  • Research the implications of the Hard-Lefschetz Theorem in algebraic geometry
  • Study Hodge theory and its applications in modern mathematics
  • Explore the significance of compact projective manifolds in topology
  • Investigate the Riemann Hypothesis and its relevance to cohomology
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Mathematicians, algebraic geometers, and students interested in the intersection of philosophy and mathematics, particularly those exploring advanced topics in cohomology and topology.

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From the Introduction to
https://arxiv.org/abs/2106.11285

"Since the dawn of time, human beings have asked some fundamental questions: who are we? why are we here? is there life after death? Unable to answer any of these, in this paper we will consider cohomology classes on a compact projective manifold that have a property analogous to the Hard-Lefschetz Theorem and Hodge-Riemann bilinear relations."
 
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It would have been really cool if a paper began,

"Since the dawn of time, human beings have asked some fundamental questions: who are we? why are we here? is there life after death? Unable to answer any of these, in this paper we will prove the Riemann Hypothesis."
 
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