Source: https://www.math.inc/a-conversation-with-terry-tao

However, I think this is still likely a very significant achievement/milestone.

I have no exact prompt to share, but he does write:

> Appreciate the insight! If it's at all of interest, this was a one-shot (supposed) solution in about 80 mins, unlike some other problems like 851 that took over 20 continuations totalling perhaps 15-20 hours of reasoning time.

Source: https://www.erdosproblems.com/forum/thread/1196#post-5365

Yes grandpa

Me when all the candidates for European Tree of the Year are from Europe

Please add an option to adjust the thickness of colored lines. Right now it's more of an eyesight test for me.

Options are almost never the right solution

Such an informative, well meaning comment

I might have missed it but how much did this cost in total?

Don't RTGs generate power constantly? That would make them impossible to use for a casual customer.

1) Sell the power back to the power company (granted, at the wholesale price)

2) Use the heat given off to generate more power

Such a convenient space heater wouldn't ya know?

Possibly. I'm not sure what you would do with it in the summer though. Even Arctic and Antarctica have pretty big seasonal temperature variations.

And how exactly did you come to the conclusion that this is relevant here?

By the fact that the geometric proof in the link wants to proof the formula, but only does so for a small subset of all a,b for which the formula is correct. This makes it a partial proof, at best.

Ok nvm I can't resist wasting my time and typing stuff on the internet again, probably gonna regret it later.

How is it not obvious to the dullest of the dull that this visual proof is not supposed to work for goddamn commutative rings lmao

It's probably not even supposed to work for negative reals, 0 or the case b>a. It's supposed to demonstrate the central idea of the visual proof. Also yes, by choosing suitable ways to interpret the lengths shown in the diagrams it's absolutely possible to extend the proof to all reals but I'm not convinced it's meant to be interpreted like that.

But bringing commutative rings into this... man you're funny

I know barely anything about welding, could you explain what a good weld would look like?

Some examples of a good weld:

https://s3.amazonaws.com/uploads.bmxmuseum.com/user-images/2...

https://s3.amazonaws.com/uploads.bmxmuseum.com/user-images/2...

Steady hands and a good rhythm are helpful.

I won the top welding student award at my high school. The competition wasn't great. Mostly, I just didn't smoke a ton of pot right before class.

You sure that top weld is by a human? It looks like one of the robotic welds.

It's both a good weld and a robotic one.