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The most serious... oversight in mathematics is certainly the (standard)
inconsistency of
Set Theory (any standard set theory: ZF with or without C, von
Neumann... Cantor...), but there are others.
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Fundamental... Oversights
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When faced with evidence of e.g. the inconsistency of set
theory, many mathematicians resort to... “oversighting”
the fundamental
formal definitions of e.g. “theory”
and “inconsistency”...
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- Set Theory is Standardly
Inconsistent
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Some “paradoxes of
infinity”
are actually formal theoretical inconsistency...
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Paradox... Oversights
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The are many paradoxes in mathematics
that have been... oversighted
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- Automata Theory’s
Computable and Incomputable Functions (short; deserves
tweaking)
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Are there only countably infinitely many computable functions?...
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- Applied Mathematics has Problems With Its
Formal Validity (very much under construction)
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Abstraction renders applied math formally invalid, and the science
that depends on that formal validity...
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- Russell’s Great... Oversight (reasonably short; deserves
expansion)
- How flawed is Russell’s Paradox? and what implications does this have
for logic and set theory?
(also found in Paradox...
Oversights)
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- Zermelo’s Great... Oversight (reasonably short;
needs tweaking)
- How flawed is Zermelo’s
Axiom of Separation?
What is the Axiom
of Separation Paradox? and what implications does all this have for
logic and set theory?
(also found in Paradox...
Oversights)
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