The library's activity room.
Facing the half-filled whiteboard, Lu Zhou lowered his marker, took two steps back, and looked at the board.
"...To resolve the question of unifying algebra and geometry, we must strip 'numbers' and 'shapes' of their usual forms of expression and seek their common ground in abstract concepts."
Standing beside Lu Zhou, Chen Yang pondered for a moment before suddenly asking,
"The Langlands Program?"
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"Not just the Langlands Program," Lu Zhou said earnestly. "There's also motive theory. To solve this problem, we must understand the connections between different cohomology theories."
In fact, this problem encompassed a very broad field.
If the question of "the connections between different cohomology theories" were subdivided again and again, it could yield tens of thousands, or even millions, of unresolved conjectures-or mathematical propositions.
The Hodge Conjecture, an unresolved problem in algebraic geometry, was one of them, and the most famous.
Interestingly, however, despite the many extremely difficult conjectures standing in the way, establishing motive theory did not require solving all of them.
The relationship between the two was as tenuous as that between the Riemann Hypothesis and its generalization to Dirichlet functions.
"...On the surface, what we're studying is a problem in complex analysis, but in fact, it is also a problem in partial differential equations, algebraic geometry, and topology."
Looking at the whiteboard, Lu Zhou continued, "At the strategic level, we need to find a factor that can connect numbers and shapes in their abstract forms. At the tactical level, we can start with the common features of a series of cohomology theories, such as the Künneth Formula and Poincaré duality, as well