/sci/ - Science & Math

How many people here actually understand the mathematical results of Godel, Turing, Church, Kleene, Post?

i.e. stuff about:
Incompleteness, Decidability, Turing Machines, Lambda Calculus, Post Machines, Computability, Mathematical Logic?

Why is there such a strong focus in Analysis/Algebra for Math majors but not Logic, or Geometry?

Computability theory, Set theory, Model Theory, Proof Theory, Algebraic Geometry, Differential Geometry etc are other areas in mathematics, math majors should know about.

>>2603748
Congratulations, I got published at the end of last year as a math major as well. I am an undergraduate, are you as well?

>>2477403


To understand Computability Theory one should have an understanding of basic results in Propositional Calculus, First Order Logic, Set theory (countability, uncountability, cardinality, Godel's Completeness + Incompleteness Theorems etc). This can easily be taught to Math undergraduates. I'm not sure why you think Computability isn't worth studying, because Computability theory is a topic in Math that happens to have applications in CS, in fact it happens to be the very foundations of CS. Computability theory wasn't created for Computer Science, it was created to study problems posed by Hilbert in a very pure mathematical sense. It just so happens that results (some) can be applied to CS, but Computability theory is mostly an area of pure mathematics. Turing machines (a true Turing machine) is not physically possible to build, nor are Oracle Machines. NFA one day may be possible with the existence of quantum computers. DFA do exist. But that isn't the point. To dismiss logic is ignorant.

Is it possible for Riemann Hypothesis or Twin Prime Conjecture to be undeciable (i.e. have no proof)

What do you guys think of Recursion theory?