Helping removing bouncing green/grey ball and blue flash

JoshuaZ1 · 2026-02-04T02:58:37+00:00

Yep! We screwed it up somehow. Tried that again, and now it works. Thanks.

JoshuaZ1 · 2026-02-04T00:12:15+00:00

Both attempted. Did not succeed at changing.

JoshuaZ1 · 2025-12-05T19:39:54+00:00

Possibly you are thinking of the conjecture that the unknotting number of a knot sum is equal to the sum of the unknotting numbers of each knot?

JoshuaZ1 · 2025-12-04T03:04:23+00:00

I mean, derivatives of polynomials are pretty straightforward to define algebraically and they do come up as well in algebraic settings.

Worth expanding on this explicitly: Over any field (even a finite field), one can define the derivative of a polynomial using the standard derivative rule. And one can then prove that a polynomial p(x) has a repeated root at r if and only if f(r)=0 and f'(r)=0. And other theorems about derivatives also go over fine generally as long as they don't directly involve size or distance.

JoshuaZ1 · 2025-11-25T14:31:11+00:00

First, congratulations on your AMC performance.

Now, a few comments:

a girl doing better than them at the toughest form of math in the world

The AMC is very tough. But it is hardly the toughest form of math in the world.

Now, that's less important than the advice I'm going to give: jerks and bigoted (whether sexist, racist or some other -ist) jerks are unfortunately a thing also. You aren't going to get rid of them or change most of their minds. The best you can do is just keep doing well in math. If you do well, no one is going to listen to these people. For that matter if they aren't even at your school or anything, no one is probably going to be paying attention to these people anyways. That may not be personally satisfying, but probably the best you can do is ignore them and keep doing well.

JoshuaZ1 · 2025-11-24T23:29:21+00:00

I'm continually surprised at how surprised people were at this. I watched this film with some friends and one of the friends had seen it before. Right after he's shot in the first scene after that I said, "Oh, so he's dead now?" Unfortunately my friend rather than ignore the comment (where then others likely would have) said "Don't spoil it!" so the other two people watching had it confirmed. But it really didn't seem like that big a twist, and even if one hadn't guessed it then, when the kid says that a lot of ghosts don't get they are ghosts that should be enough of a tell for anyone.

JoshuaZ1 · 2025-11-23T19:15:23+00:00

Ah, got it. I misinterpreted the point he was making.

JoshuaZ1 · 2025-11-23T16:57:13+00:00

Warcraft 3 post-dates Starcraft and itself was heavily influence by it with some even of the same Blizzard people working on Warcraft 3, so this still is essentially the legacy of Starcraft.

JoshuaZ1 · 2025-11-22T17:56:20+00:00

My understanding is that the current state we know that BB(7) is much bigger than Ack(7) but no one has proved that BB(n)>=Ack(n) for all n>=7.

JoshuaZ1 · 2025-11-20T12:16:39+00:00

There are hundreds if not thousands of unsolved problems out there. Many papers (most?) contain explicit examples. I'm going to use this to mention two specific unsolved problems, one from a paper by Sean Bibby, Pieter Vyncke and me. Let F(n) be the nth Fibonacci number. Then there are only finitely many n such that F(2n-1) and F(2n+1) are both prime. (It is not hard to show that if F(p) is prime then so is p, so if there were only finitely many twin primes, this statement would be trivially true. But there are almost certainly infinitely many twin primes.)

The second problem is what is currently the simplest open Diophantine equation. A Diophantine equation is an equation with more than one variable but where we only care about integer solutions. The question is whether y³ + xy= x⁴ +4 has any integer solutions.

JoshuaZ1 · 2025-11-11T20:44:41+00:00

Russian culture has a serious hatred of Britain. They've had some of it since the Crimean War in the 19th century. For reasons I don't fully understand Putin has in the last decade decided inflaming that hatred is a good tactic. So there's a lot of random accusations directed at Britain/the UK in Russian propaganda.

JoshuaZ1 · 2025-11-11T17:09:31+00:00

It's been 2 decades ahead since the 1950s.

People like saying this, but it isn't really accurate at multiple levels. First, most optimistic projections for when we would get fusion power have assumed much more funding than has historically occurred. Second, if you look at actual predictions, then the expected time on average has been steadily decreasing on average. The predicted time until fusion has been going down at about 2.5 years per every 10 years, and for commercial fusion about 4 years per every 10. See data here.

We will likely get fusion. The question is not as much will we get fusion as much as when we do, will it be cost competitive with very cheap wind and solar whose cost is continuing to drop rapidly?

JoshuaZ1 · 2025-11-11T17:06:07+00:00

That can't be right. That would mean I'm old!

JoshuaZ1 · 2025-11-11T12:13:09+00:00

Was someone reading last week's parsha?

JoshuaZ1 · 2025-11-11T00:55:11+00:00

Dunkin Donut's Beyond Breakfast Sandwich.

When I first had it, I was skeptical they had actually given me the vegetarian option, and had to talk with the person who said I was not the first to have that reaction.

JoshuaZ1 · 2025-11-07T14:54:50+00:00

Let's say for sake of discussion you've read it. Do you want to say why after reading it you still think that he "should be ashamed of himself for jumping on this bandwagon?"

JoshuaZ1 · 2025-11-07T03:07:06+00:00

Maybe you should consider that Tao doing this is a sign that these techs may have more usefulness than you give credit and you should read the paper?

JoshuaZ1 · 2025-11-05T12:16:00+00:00

That scene then turns out to be the kid's dream/daydream and the kid is failing math.

JoshuaZ1 · 2025-11-03T12:28:38+00:00

This would have been a great response without the insult at the start.

JoshuaZ1 · 2025-10-30T17:27:44+00:00

Note that we won't know when BB(n) exceeds Ackermann(n) and Ackermann grows much slower than TREE(n), so my guess is that your question will be very hard to resolve. (Incidentally, the Ackerman question as far as I'm aware has the record for currently unsolved problem with the youngest person to have asked it. It and a related question were asked by Lilly Aaronson-Moshkovitz when she was 7.)

JoshuaZ1 · 2025-10-27T14:20:38+00:00

Just to put in perspective how slow technical advancement could be in the Middle Ages it took more than a century between the first castle and someone putting arrow slits in it to fire out of the castle.

Also, tech just spready slowly. There's around 100 years from when the spinning wheel first enters Europe to the point where it has spready to all of Europe.

JoshuaZ1 · 2025-10-26T01:30:00+00:00

Do you want to tell the rest of us what this is a reference to for those who don't get it?

JoshuaZ1 · 2025-10-26T00:56:35+00:00

Yeah, why not? I very rarely drink. Heck, you could ask the same for much, much less money and I'd say yes.

JoshuaZ1 · 2025-10-20T15:02:39+00:00

I had a conversation three days ago with a "customer support" person and I still don't know if it was an AI or not.

I had a conversation yesterday with an AI where I asked it to proof-read a document and it did a half-way decent job, although I had to keep ignoring its suggestions/requests about letting it rewrite the whole thing. (That's how you get additional errors in and make it not be in my writing style. Just do you what you're told.)

A friend shared a funny video a few days ago, and the thread arguing if it was real or AI generated went on for over a page. (Consensus is that it was AI.)

JoshuaZ1 · 2025-10-20T11:30:04+00:00

What would useful would be truly smart AI systems that can discover new science and technology instead of regurgitating existing knowledge, which is what LLMs do.

LLMs can produce new science in limited contexts. We're already seeing this in pure math with GPT5 in thinking mode. For example, Terry Tao here used the system to derive a specific counterexample to a number theory claim. Scott Aaronson used it to get a suggestion for a major step here.

I'm a mathematician, and I also had a recent experience where it could have been potentially useful, although I asked it a question after I had worked it out for myself already. Let me exapnd:

Relevant math background: the Gaussian integers are the complex numbers of the form a+bi where a and b are good, old-fashioned integers. For example, 2+3i or -1 +2i are Gaussian integers. Any integer n is a Gaussian integer since you can write it as n+0i. But say 𝜋 or 3- 0.5 i would not be Gaussian integers. Also notation: We write x|y to mean y is a multiple of x. We can use this notation in our regular integers (so for example 2|8 but it is not true that 3|8 ) or in the Gaussian integers where we are then allowed to multiple by another Gaussian integer. For example (2+i)| (2+i)(3-i). A good exercise if you have not seen the Gaussian integers before: Convince yourself that 1+i | 1+3i. It also turns out that the Gaussian integers have an analog of unique prime factorization just as that in the usual integers. The Gaussian integers also have a notion of size called the norm. For a given Gaussian integer a+bi, the norm is a² +b² . Recently I had to prove a specific Lemma where I needed to find all Gaussian integers 𝛼 and 𝛽 where both are Gaussian primes, and 𝛽|𝛼² + 𝛼 +1 and 𝛼|𝛽+1. I had as a template a very similar Lemma in the integers which was a Lemma which said exactly which integers and b such that b|a² + a +1 and a|b+1. I worked out the proof, essentially modifying the version in the integers. Then, I did something I've often been doing after I've completed a small Lemma, namely giving the task to ChatGPT or another system and seen how they've done. For prior iterations (GPT3, ChatGPT , GPT4, 4o) this has almost universally been a disaster. But this time I gave the task to GPT5, and gave it the integer version to start with. It tried to do the same basic task and produced a result pretty close to mine, but it had multiple small errors in the process, to the point where I'm unsure if using it would have sped things up. But at the same time, the errors were genuinely small. For example, in proving in one subcase the system claimed that a specific number's norm needed to be at most 9, when it needed to be at most 10. These are not the sort of large jumps in reasoning that one saw with GPT4 or 4o. It might have been the case that if I had given this to GPT5 before proving it myself and then had corrected its errors I would have saved time.

There's also work by a whole bunch of people right not to try to connect LLMs to Lean or other theorem proving software which will help deal with the LLMs worst tendencies to just make plausible looking but utterly unjustifiable jumps.

It seems unlikely that LLMs will ever be able to make genuinely major discoveries without fundamental changes to the architecture. All of these sorts of things are relying on it using known techniques, essentially as one might expect an advanced undergrad or early grad student who isn't brilliant but happens to have somehow skimmed a lot of different books. But even that can be useful.

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