# Questions tagged [big-picture]

Questions designed to get an overview of a specific subject or body of results or to understand the relations among similar definitions, techniques or concepts appearing in different sub-fields of mathematics. While such questions by their very nature sometimes cannot be made very narrow and focused, it can be helpful to keep in mind that the design of MathOverflow does not make it a good fit for questions that are too broad.

**0**

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### Mathematics based only on real numbers [closed]

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### What are some interesting relationships between pi and phi? [closed]

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### Analogues over finite fields of certain integers defined multiplicatively in $\mathbb Z$

**8**

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### Why is modular forms applicable to packing density bounds from linear programming at $n\in\{8,24\}$?

**4**

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### Why does the Lax pair formalism look so similar to the Hamiltonian equations, and what is the significance of this?

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### Update on “Hopf algebras: their status and pervasiveness” by Hazewinkel

**5**

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### The Idea of Kroneckerian geometry

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### Geometric intuition behind this chain homotopy

**3**

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### Theories requiring dual continuous and discrete constructs

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### Daniell integral of “generalized (of some sort)” functions?

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### Understanding the reason for the particular formulation of the definition of a concrete reflector (as stated in The Joy of Cats)

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### What is the logical progression in algebraic tools for studying spaces (varieties -> schemes, sheaves, topos etc.)?

**2**

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### How should I think about concrete functors and in particular about concrete isomorphism?

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### On earlier references for $P=BPP$ and Kolmogorov's possible view on modern breakthroughs involving randomness?

**35**

**3**answers

### A map of non-pathological topology?

**10**

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### Hausdorff dimension and von Neumann dimension

**77**

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### Theorems that impeded progress

**3**

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### Regarding learning Algebraic Topology [closed]

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### Arithmetic that corresponds to combinatorial rectangles and cylinder intersections?

**20**

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### Motivation behind Analytic Number Theory

**16**

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### Axiom of Choice versus V=L in opposition to large cardinals

**5**

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### Grothendieck letter to Jun-Ichi Yamashita on tame topology

**4**

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### Is there a simple algebraic setup to accomodate fibres and cofibres at the same time?

**2**

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### Fundamental groupoid and fibration

**58**

**4**answers

### Why did Voevodsky consider categories “posets in the next dimension”, and groupoids the correct generalisation of sets?

**9**

**1**answer

### Three theorems on the number of nonzero coefficients of a polynomial

**11**

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### Poincare duality spaces vs. manifolds via lifting maps, the obstruction theory and the role of simply connectedness

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### What is the big picture of algebraic geometry? [closed]

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### Floer cohomology from mapping spaces of $\infty$ categories

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### Viewing parts of $\mathbb{V}$ 'from the top down' or 'from the bottom up'

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### Which constants are ambivalent and why?

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### What to expect from spectral algebraic geometry

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### Transformation or correspondence between language and real number

**2**

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### Any proved connection between Roth theorem and hartmanis stearns conjecture?

**17**

**8**answers

### Concepts in topology successfully transferred to graph theory and combinatorics with non-trivial applications?

**13**

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### Can the methods of classical algebraic geometry be made rigorous with a synthetic approach?

**7**

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### What are the uses of coefficient systems for arithmetic cohomology theories?

**3**

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### Is there a Fourier Analytic way to approximate volume?

**34**

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### Why is the definition of the higher homotopy groups the “right one”?

**4**

**1**answer

### Maximality without Zorn

**1**

**1**answer

### On Shannon information theoretic capacity to coding distance metric translation

**3**

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### How much can analogy between $\Bbb Z$ and $\Bbb F_q[t]$ work out to give better distance measures in information theory?

**8**

**1**answer

### Steps in Geometric Complexity Theory

**23**

**2**answers

### Interpretations of permanent

**16**

**2**answers

### Measuring a presheaf's failure to be a sheaf?

**6**

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### How to decompose cuspidal representations?

**2**

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### Is there a physically realizable inductive turing machine that can solve Hilbert's $10$th problem and can it overcome Church-Turing Hypothesis?

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### categorification of q-series

**39**

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### Is algebraic geometry constructive?

**5**

**2**answers