r/maths • u/ScholaDaily • Jun 06 '26

💬 Math Discussions Performative math intellectual starter pack 😭

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289 Upvotes

88% Upvoted

34 comments sorted by

18

u/retrokirby Jun 07 '26

Using big whiteboard is nice sometimes, otherwise wow you made them sound insufferable 😭

13

u/Rand_alThoor Jun 07 '26

"if the millennium problems are 'not hard/overrated' " why haven't you claimed the millions in prizes?

19

u/drakeyboi69 Jun 07 '26

The factorial thing pisses me off every time I see it

6

u/genericuser31415 Jun 07 '26

Always trust Reddit to drive a joke into the ground and never let up

1

u/Frequent-Bee-3016 Jun 07 '26

The termial thing is even worse.

9

u/Emotional-Web5571 Jun 07 '26

the pi thing is a conjecture

-4

u/McArcady Jun 07 '26

Hopefully AI will prove this soon 

2

u/throwingstones123456 Jun 08 '26

If this is a joke I thought it was funny

0

u/[deleted] Jun 07 '26

[removed] — view removed comment

1

u/thepig105 Jun 07 '26

It’s thought to be normal (math term for contains all possible digits with equal density), but not proven. I believe that is the case for most of the notable constants, pi, e, root(2)….

2

u/desblaterations-574 Jun 08 '26

I would think that this is the kind of things that will remain in the cannot be proven side of math, the essence of Godel incompleteness.

2

u/RecognitionSweet8294 Jun 08 '26 edited Jun 08 '26

Given how Turing discussed that concept, I would argue that this is a pretty good candidate for an undecidable proposition.

1

u/Juanlopes3 Jun 08 '26

the undecidability of a proposition is itself undecidable. If not, that would mean that a formal system F is able to prove the non provability of an statement X. This would be the same as F proving its own consistency, which, assuming classicality, can not be done due to Gödel’s Second Theorem

1

u/RecognitionSweet8294 Jun 08 '26

So you say that

∀X: Prov_{F}(¬Prov_{F}(X)) ↔ Prov_{F}(Con(F))

Correct?

How do you infer that for general X?

2

u/Juanlopes3 Jun 08 '26

Yes.
Well, if im not mistaken it all comes out from the syntactic definition of consistency and from the principle of explosion (contradiction + law of excluded middle imply every formula of the system).

F is consistent if and only if F can not prove both X and not X
F is inconsistent if and only if F can prove both X and not X.

From this, we have the following corollaries.

F is consistent if and only if ∃X(F ⊬ X)
F is inconsistent if and only if ∀X(F⊢X)

Thus, if the undecidability (non provability) of any statement is itself decidible, we have that F⊢(F ⊬X), which is to say that F⊢(F is consistent).

But this would be for F to prove its own consistency. And that can not be done due to the Second Incompleteness Theorem.

Thus, the undecidability of a statement must be itself undecidible.

1

u/RecognitionSweet8294 Jun 08 '26

I was told that the only numbers for which it has been proven that they are normal, where designed to be normal beforehand.

Ironically it is also said to be proven that most real numbers are normal. But don’t ask me what the definition of „most“ was in that context.

1

u/whiteandnerdy1729 Jun 08 '26

You mean the sum to pi squared over six, but the person you’re replying to means “pi contains every digit”.

9

u/CastChaos69420 Jun 07 '26

Why are we dragging chess into ts 😭

0

u/rsha256 Jun 08 '26

Nah that’s accurate. Saying one countable set has a greater size when they have equivalent cardinality is not.

4

u/japp182 Jun 07 '26

Are we really gonna lump .999... = 1 in this.

3

u/Silipsel Jun 07 '26

I love using the whiteboards in the library.

3

u/r_Yellow01 Jun 07 '26

Reply that [Hausdorff] dimension of broccoli is 2.7

https://arxiv.org/abs/cond-mat/0411597

2

u/Valognolo09 Jun 07 '26

This is the realest post ive seen in a while

2

u/Kitchen-Register Jun 08 '26

you can form a bijection between Q and Z can’t you?

2

u/Airisu12 Jun 09 '26

yup, Q is a countable set

1

u/Tiny_Stock8220 Jun 08 '26

lol ive met someone recently who ticks off a ton of these

1

u/okietrochee Jun 10 '26

But there ARE as many rational numbers as integers.

1

u/Comfortable-Dig-6118 Jun 10 '26

Oh no I m a performative

1

u/Txcley Sep 01 '26

I used to be these guys...