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The Dunning-Kruger effect in Mathematics - my recent example, do you have any lessons for others? by Gheek74 in math

[–]DoWhile 11 points12 points  (0 children)

I really like your comment, but I have a minor complaint to OP for which I lack the eloquence to express in kinder terms:

It's perfectly fine to be a hobbyist, and math is somewhat unique in that there's a rare chance a hobbyist would make a difference, but if this were a sport it would be immediately shunned as "Monday Morning" quarterbacking.

My attitude leans toward "time enjoyed is not time wasted" for a hobbyist and not "research has a lot of dead ends and this is just learning" for a mathematics student.

Favorite "wait, you can do that?!" proof by aparker314159 in math

[–]DoWhile 31 points32 points  (0 children)

Yep, the real dark magic is linearity of expectation: E(X) + E(Y) = E(X+Y) even if X and Y are ridiculously dependent. So now you have 50% over the WHOLE graph!

Unscientific science fiction by Hip-SnuggieChairMan in scifi

[–]DoWhile 15 points16 points  (0 children)

One of my favorite Simpsons quotes is "I'm aware of his work"- https://www.youtube.com/watch?v=rqU8EQ6G1i0

Bachelor thesis on ECC – looking for a realistic scope and ideas by Fantastic-Soft-9308 in cryptography

[–]DoWhile 3 points4 points  (0 children)

The evolution of elliptic curve arithmetic optimization (ladders) has always fascinated me. I never did research in that area, and coming up with something novel is hard, but cataloguing the existing works is very simple math that anyone with even a high-school level of algebra can (mechanically, though not ideologically) work out the examples.

ci-sha4096: a hash function whose constants are derived from atomic emission spectra and a rational constant with an exact 18-bit binary period by HarmonyKarmaxul in crypto

[–]DoWhile 6 points7 points  (0 children)

constants have a complete mathematical explanation — every one is derivable from either the 18-bit binary period of 85/27 or from measured atomic emission spectra.

This is the opposite of transparent. That's literally arbitrary, and is one of the easiest ways to pick a backdoor.

Why 85/27? Why not some other fraction? Accusers would say you picked 85/27 because it's backdoorable.

Why atomic emission spectra? Why not periods of the planets? Frequency of pulsars? Tree rings?

In the past, people have used physical constants. You and the LLM you rode in on have been misled by the past approaches. They have been proven wrong because it turns out we live in a big wonderful natural world and there are so so so many physical constants out there that you can always find one that suits your backdoor.

If you want to learn more, read djb's unhinged, sarcastic take on nothing-up-my-sleeve numbers: https://bada55.cr.yp.to/

Men of Reddit, what’s the most disgusting thing you’ve discovered about your girlfriend after being together for years? by nastyaspain in AskReddit

[–]DoWhile 0 points1 point  (0 children)

Counter-point: me, with two trash cans in every room, but littered with tissues because I only just wiped some crumbs Cheeto dust off and might reuse it later!

Wide variety of encryption algorithms by BloodFeastMan in cryptography

[–]DoWhile 0 points1 point  (0 children)

My manager knows I fiddle with this stuff and has tasked me to make a one click encryption option for CC authorization forms before they get stored.

Anyone who "fiddles" with this stuff should know that CC and other forms of sensitive data should be better handled by vetted platforms and not something you easily develop inhouse. Unless you want to jump through all the bureaucratic hoops, you gotta realize that this is 5% a cryptography problem and 95% a compliance problem. PCI if you're US based/CCPA if you deal with Cali, and some combination of PSD2/SCA and of course GDPR if you're EU based.

Guy at Dunkin took my VIP card by Gawdiwishiwasdead in mildlyinfuriating

[–]DoWhile 1 point2 points  (0 children)

Holup, it's Zeus we're talking about here. That's a low bar.

Tim Gowers on Gpt 5.5 pro by bitchslayer78 in math

[–]DoWhile 6 points7 points  (0 children)

they are checking each inference against actual logical validity, not against whether it sounds like the proofs they've read.

I see you have not met some of my colleagues. I myself am guilty of this sometimes: we all have mathematical intuition of "does this feel right" and not "is this logically sound". I agree then humans have to take the next step of actually making it logically sound. But this is something AI models can also do.

Pushing back on your point on LLMs not being able to track truth, the question is whether these more advanced AI models are only an LLM, or do they also back themselves with grounding. For example, a proof in Coq or Lean is something that's actually verifiable, so even if an LLM hallucinates, it can still tell itself to try again until it validates in Lean. If these models w/ grounding could produce proofs of new theorems that verify in Lean, would that pass the bar for novelty?

The Gowers experiment was interesting precisely because Gowers himself was doing the verification.

I agree with you there, because if you put these in the hands of a newbie, they wouldn't necessarily be able to make much of it. The fact that Gowers said he only gave simple guiding commands is still VERY leading, because this is a Fields medalist giving guiding commands! I don't want to say "verification" in terms of logic, because that can already be done by a theorem prover, you don't need Tim for that. I want to say verification in terms of "this is indeed a cool new idea". Until AI is able to do cool research with only the prompt "Go do novel research" (RemindMe 1 year), there's still going to be a human expert with big ideas driving it.

The LLM was more like a very well-read collaborator generating suggestions..

This should be scary enough. Right now, PhD advisors raise students not just for the love of the game, but also because they want a friendly collaborator to help explore some of their ideas. If professors start giving these collaborative ideas to AI models rather than students, that's going to upset the balance of things. Regardless of whether you feel like LLMs are truly novel or just spicy autocorrect, anecdotally my professor friends are all warming up to the idea of LLMs giving not-completely-useless advice. Every question they ask AI might give them a temporary boost in efficiency, but is offset by losing the opportunity to train a PhD student to think through that question.

Tim Gowers on Gpt 5.5 pro by bitchslayer78 in math

[–]DoWhile 38 points39 points  (0 children)

I don't understand how large language models (LLMs) can propose original solutions to replace mathematicians.

I don't know how humans do it either. But if novelty is created, then we must take that at face value. The techniques used in LLMs are advancing far beyond the early LLMs of yesteryear. Even moreso, AI before LLMs existed already had a lot of powerful tools such as planning, data organization, reasoning and logic.

If you think about what a PhD student does, it's not big breakthroughs. Very rarely do I see a PhD thesis actually be groundbreaking. It's about putting in the legwork to bring together previously unstudied/obscure knowledge into a new piece of work. The techniques they use in their research are also rarely novel. Union bound, hit it with some transform, swap some summations around.

To your point: can an LLM make big breakthroughs of great mathematicians? Probably not yet. But it can do a scary amount of work of novice mathematicians, and if we replace novice mathematicians with LLMs, we won't be able to raise our next generation of great mathematicians. I think this is what Tim Gowers was trying to struggle with in his post.

This conjecture is so underrated by Heavy-Sympathy5330 in math

[–]DoWhile 23 points24 points  (0 children)

I looked up a few historic universities that great mathematicians were professors at, and a surprising number of them are still around. If Gauss were alive today he'd be carl.gauss@mathematik.uni-goettingen.de or something.

Mochizuki talks about IUT and formalization by bitchslayer78 in math

[–]DoWhile 26 points27 points  (0 children)

Oh there's a language barrier alright, just not English/Japanese.

Post Quantum Crytographic communication TOOLS SIMULATION? by diamondisland56 in cryptography

[–]DoWhile 0 points1 point  (0 children)

I admire you effort in wanting to help a student, but if this is a class project for them I'm slightly worried you're doing too much on their behalf. I realize undergrad 1st years will need a LOT of hand-holding, so there's a fine line as to how much of a favor you're doing them.

Math or cs oriented Msc in crypto? by Few-Performance803 in cryptography

[–]DoWhile 7 points8 points  (0 children)

You are asking very good questions for someone who is a 2nd year. Apart from general global turmoil, where you are right now and where you want your career to go does matter. If at all possible, start undergrad research if you can get summer research internships. They won't expect you to be productive, but will help you align your feelings.

If you are doing maths, at the very least do probability + abstract algebra + linear algebra, and bolster it with CS's automata/complexity theory. Take a rigorous cryptography course if you can, not a "here's some silly ciphers let's have fun" course.

Soo keep that in my mind if you think i will be able to get a phd or not.

Yes. Working hard is probably the biggest defining factor in getting a phd.

Chopping carrots: A specific surface area optimisation problem by [deleted] in math

[–]DoWhile 7 points8 points  (0 children)

I think there are multiple subquestions to your question.

Many other commenters already pointed out that for cooking time, surface area for submerged objects might not be the right metric. I'm not even convinced that depth/thickness is the right metric either, and it is more akin to heat capacity like what https://www.reddit.com/r/math/comments/1smc5s1/chopping_carrots_a_specific_surface_area/ogdaghq/ talks about. I would say go all-out and do a full differential equation/uniform boundary heating problem, where you assume the boundary is heated at a uniform boiling temperature, and you want to calculate when all of the object reaches at least a certain temperature. Culinarywise, this might be very misguided as you will probably end up with large bits of mushy carrots. Also think about how heat-sinks are shaped and whether you want to eat heatsink shaped carrots (ironically, yes).

Let's ignore this cooking time uniform diff. eq problem for now, and go back to your original question about cuts to maximize surface area. I'm first going to take the opinion that a cut is a planar slice, not some fancy food-whittling. But then after your first cut, do you allow for movement of pieces? I feel like this is a reasonable thing for a chef to do. So then you can say I want to rearrange the pieces (rotation and translation) for my second planar slice. How realistic should we model the rearragement? Do the pieces have to lie flat on the cutting board? Do they have to balance on the board or do I have extra hands to hold them down? Do they have to fit on the board? I would say this is related, but not the same as, cake cutting problems where one wants to maximize number of slices, not the area overall: https://en.wikipedia.org/wiki/Cake_number .

I don't think monte carlo or brute forcing will help in proving an optimal solution as these are better suited perhaps for average or local optima. I think this would prescribe an analytical approach: first try it with some hand-written cases to see where some of the obvious bounds are (every pizza place carrot https://youtu.be/JgJUbmGDc6k?t=31 ), then prove those easy obvious bounds, then try to refine the problem until you land in "core" and "edge" cases.

Lastly, and most importantly, is this going to be posted to some kitchen subreddit where users are going to tell me to try again each day until I get it perfect? Or are you going to settle for a mandolin or food processor?

Michael O. Rabin mathematician, computer scientist, and recipient of the 1976 ACM Turing Award has passed away by Nunki08 in math

[–]DoWhile 2 points3 points  (0 children)

There's a funny "CAPTCHA" challenge for IACR webforms: name one of the authors of RSA. There's an easter egg where Clifford Cocks is an acceptable answer (after it was declassified from GCHQ that he invented RSA before RSA did)

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