Intereting Posts

Question about the totient function and congruence classes
Summation Theorem how to get formula for exponent greater than 3
Minimum and maximum determinant of a sudoku-matrix
Explicit bijection between ordered trees with $n+1$ vertices and binary trees with $n+1$ leaves
If D is an Integral Domain and has finite characteristic p, prove p is prime.
Proof a graph is bipartite if and only if it contains no odd cycles
We break a unit length rod into two pieces at a uniformly chosen point. Find the expected length of the smaller piece
For each $y \in \mathbb{R}$ either no $x$ with $f(x) = y$ or two such values of $x$. Show that $f$ is discontinuous.
When are we permitted to multiply or divide both sides of an equation by a variable?
Cardinality of a Hamel basis of $\ell_1(\mathbb{R})$
Show that there are infinitely many powers of two starting with the digit 7
For any positive integer $n$, show that $\sum_{d|n}\sigma(d) = \sum_{d|n}(n/d)\tau(d)$
Connection between rank and matrix product
How many groups of 4 primes exist such that their sum is a prime and that $p^2+qs$ and $p^2+qr$ are squares?
Minimality in the case of partial derivatives and Sobolev spaces?

Let us say that someone was able to prove that $0=1$ using ZFC, thereby proving it inconsistent. What impact would this have on the study of meta-mathematics?

Most mathematicians would just move onto a different set theory, since most mathematics is not sensitive to the exact axioms being used.

Meta-mathematics, on the other hand, is. In particular, I’m talking about model theory, set theory, proof theory, etc… What results would become meaningless, and which could be salvaged. What other set theories could be used instead?

- The standard role of intuitive numbers in the foundations of mathematics
- Why bother with Mathematics, if Gödel's Incompleteness Theorem is true?
- Mathematical structures
- How do you go about doing mathematics on a day to day basis?
- Definition of definition
- Why are all the interesting constants so small?

- Boy and girl paradox is driving me crazy
- St. Petersburg Paradox
- Explain why calculating this series could cause paradox?
- Proposition vs Theorem
- Why is “the set of all sets” a paradox?
- The set of all things. A thing itself?
- Paradoxes without self-reference?
- For x < 5 what is the greatest value of x
- Reference about the Banach-Tarski paradox
- The standard role of intuitive numbers in the foundations of mathematics

People will start paying more attention to results like Patey-Yokoyama on Ramsey phenomena, which show that a lot more mathematics than was thought earlier can done conservatively relative to a finitistic framework.

Another issue is the possible impact of a discovery of an inconsistency in ZFC on traditional beliefs in the existence of an intended model/intended interpretation of ZFC. Namely, in such a hypothetical situation of ZFC having turned out to be inconsistent, how will such beliefs evolve and what strategies will be developed to deflect the question “what is this supposed to have been an intended model of exactly”.

- What is the number of full binary trees of height less than $h$
- distinguishing probability measure, function, distribution
- Does the Extended Euclidean Algorithm always return the smallest coefficients of Bézout's identity?
- If $x^m=e$ has at most $m$ solutions for any $m\in \mathbb{N}$, then $G$ is cyclic
- Partitions and Bell numbers
- Find the limit without use of L'Hôpital or Taylor series: $\lim \limits_{x\rightarrow 0} \left(\frac{1}{x^2}-\frac{1}{\sin^2 x}\right)$
- Prove that $112$ divides the integral part of $4^m-(2+\sqrt{2})^m$
- Proving Cartan's magic formula using homotopy
- Projection of a 3D spherical distribution function in to a 2D cartesian plane
- Bourbaki exercise on connected sets
- Why is $P(X,Y|Z)=P(Y|X,Z)P(X|Z)$?
- A combinatorial proof of $\forall n\in\mathbb{N},\,\binom{n}{2}=\frac{n(n-1)}{2}$
- Is $M_g$ NEVER proper? And why does $T_g$ contain products?
- Theorems with an extraordinary exception or a small number of sporadic exceptions
- How generalize the alternating Möbius function?