#mathematicalcomplexity 検索結果
Another case where huge combinatorial chaos collapses into a single invariant. Math keeps searching for balance beneath complexity. x.com/74wtungsteno/s…
#GreatBooks4Math Visual Group Theory Nathan Carter, 2009 #math #science #iteachmath #mtbos #elearning
What complexity exactly? Removing variables?
Attorney General Dorcas Oduor says the government cannot stop charging Kenyans fees to access eCitizen, citing the complexity of the system.
This problem appears in every field. I think it’s most salient in math due to the difference in symbols from natural language? Experts often struggle to explain concepts because their knowledge organization is interconnected and contextually complex where students’ are dispersed.
kompliziertheit kann nicht retrospektiv qualitarisiert werden, die quantität schwingt nie in qualität um, täuschung der großen zahlen, nur menschen lassen sich von zahlen beeindrucken, obwohl sich alle zahlen immer als zählsysteme kontingenter kontexturen erweisen.
there's nothing specifically complicated about this *notationally*, just conceptually; and, well, in math, notation is generally intended to be deobfuscatory for ease of use, unlike (ironically) in economics
“Is every problem that’s easy to verify also easy to solve?” uwaterloo.ca/news/mathemati… via @uwaterloo
This is completely understandable for anybody acquainted with mathematics. Math is abstract and very notation/vocab heavy. There is no way around it.
Some of the nonsense is about how to describe incompleteness. Is incompleteness “a hole at the center of maths”? No. That’s not what it is. Incompleteness identifies a limit to formal proof-analytic systems. Maths aren’t proof-analytic systems.
But still complexity is a hard boundary for the range of applicability of any theory or application because complexity is a source of irreducibility. Discreetness introduces irreducibility.
Computational irreducibility means you can't jump ahead to the answer with a shortcut. The only way to know what happens is to simulate each step and watch it unfold. There's no easy way out. #Complexity #Simulation
The graceful art of calligraphy meets the precise logic of mathematics. This beautiful writing is actually a complex mathematical proof.
geometry is troublesome. all physical theories want to map to some beautiful geometry (Fibonacci obvi does this perfectly). but in practice geometry provides cover for incomplete experimentation.
This banal looking equation has changed mathematics end thus modern science, forever! Its is over 450 years old, and is the one that triggered the definition of complex numbers.
Infinite dims is one thing, it’s the fact that even mildly nonlinear algebra (i.e. algebraic geometry) is much more complicated and much less tractable (Linear solvers are O(n^3), Gröbner bases are doubly exponential) that’s quite the bummer.
Mathematics demands precision. Even tiny rounding errors can lead to large mistakes. chatgpt.com/share/6922d7be…
Remarkably, both the equation and its solutions are complex. But the measurable quantities (the amplitude squared) are the real part. You can describe reality with imaginary mathematics, but you cannot measure it. ❤️
Real mathematics, or just the hieroglyphs? Mathematical systems exist beyond mathematical language. The formal language is an incomplete model — unable to describe itself, or the very reality it seeks to capture. Incompleteness means: unable to understand itself.
(TLDR is that a function like f(complex number) is annoying to work with, reason about, and compute with, so we want to transform this into (complex number)*f(real number). But if you do this in a naive way -- which works for basically every other function you've ever worked with…
x.com/i/grok/share/4… Any sufficiently powerful formal system that is consistent (doesn't prove contradictions) is incomplete — there are true mathematical statements that can never be proved using the rules of the system itself."
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