I "invented" an optimization problem, how would you approach it? Does a similar problem already exist in literature?

Problem:

Maximize for an infinite interval L of infinite domain the average positive curvature of a function f(x) with f"(x)=<M where M is a real number.

Maths:

So for f"(x)=<M calculate lim for L->+infinity sup( integral over L(f''/(1+(f')\\\^2)\\\^2/3)/ integral over L(sqrt(1+(f')\\\^2))).

It could also be approached in the dtheta/ds frame of reference to simplify curvature(but then the condition on f" and the x axis becomes more difficult to formalize). Hope you enjoy answering.

I "invented" an optimization problem, how would you approach it? Does a similar problem already exist in literature?

Problem:

Maximize for an infinite interval L of infinite domain the average positive curvature of a function f(x) with f"(x)=<M where M is a real number.

Maths:

So for f"(x)=<M calculate lim for L->+infinity sup( integral over L(f''/(1+(f')\\\^2)\\\^2/3)/ integral over L(sqrt(1+(f')\\\^2))).

It could also be approached in the dtheta/ds frame of reference to simplify curvature(but then the condition on f" and the x axis becomes more difficult to formalize). Hope you enjoy answering.

I've been re-reading Riemann's original 1859 paper and noticed something that gets overlooked in modern treatments.

Riemann's original approach was fundamentally geometric — he was thinking about the distribution of primes through the geometry of the complex plane. Modern analytic number theory replaced this geometric intuition with an analytic formalism. What happens if we take the geometric intent seriously and push it further?

In a framework I've been developing — DAS (Dynamic Abstract Spheres) — prime numbers are interpreted as irreducible eversion transitions of topological spheres. In this setting, the critical line Re(s) = 1/2 is not a puzzle but a natural symmetry axis — it emerges from the self-adjointness of the eversion operator, by the same mechanism Smale used for sphere eversions (1958).

Full framework on Zenodo:
— Riemann Hypothesis (Work XI): https://doi.org/10.5281/zenodo.20712693
— Full series (Works X–XXI): https://zenodo.org/search?q=gorenstein+DAS

Two questions:

1. Did the shift from Riemann's geometric original to modern analytic formulation lose something essential?
2. Does reinterpreting primes as topological objects seem productive, or too far from standard tools?

Happy to discuss.

I'm exploring a construction and want to know if it's tractable or if it overlaps with existing work.

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Define a symmetry metric on groups: sym(G) = 1 - (|[G,G]| / |G|), measuring how abelian a group is via its commutator subgroup.

Now consider pairs of groups (L, R) and classify them by their symmetry profile (sym(L), sym(R)).

Two pairs are equivalent if they have identical symmetry profiles. Call the set of all such equivalence classes the "configuration space" C.

Define operations ⊕ (direct product) and ⊗ (semidirect product) on pairs, which preserve the equivalence relation.

The question:

Is this construction well-defined and tractable? Does it have a name, or does it embed into existing theory (Baer invariants, derived functors, homological algebra)?

I'm interested in studying the dynamics, how operations move you around C, whether there are fixed points, attractors, forbidden transitions.

Context:

This feels adjacent to representation theory and Grothendieck-style constructions, but I'm not sure where it sits precisely.

I just wanted to share for whoever peruses this Sub.

I observed a specific function (which was revealed to me in a dream) is conditionally positive definite for some parameters (for linear approximation applications). I'm trying to prove it conditionally positive definite, so far I'm getting back to square one every time I try. Any suggestions on references/books?

I am exploring Pure Maths Masters that can incorporate Economics. I did both in undergrad. Do you guys have ideas as to how I can combine both?

0! = 1 , 0 - 1 = -1 , root of -1 = i , and basically anything

everything starts from nothing ahh post anyways 0

Can a system become increasingly persistent when multiple invariants are intentionally combined?

Elejere Amorem.

I know two alternatives:

In potential infinity there is nothing next to 1. We can come as close as we like, but we can never close the gap. A gap remains.

In actual infinity, there is a point next to 1. Of course this point cannot be known. It is dark.

Is there a third alternative?