Type theory and lean is more interesting to people who like computers than to people who like math.

The set theorists decided that mathematics is the overarching superdomain over all study of structure. You don't get to pick and choose. Either mathematics is a suburb of logic and these two things are separate, or they're not and ZFC dogmatics need to accept they don't have a monopoly on math.

I of course fully support reinstating logicism, but the same dogmatics love putting up a fight over that as well.

I think the most surprising thing I've learned taking formal math in college is just how much mathematicians are pragmatists (at least for my teacher with sample size n=1). They're much more interested in new ways to think about ideas, with a side effect of proofs for correctness. The proof is more about explaining why something works, not that it does.

I'm going to take a formal logic class in the fall, and my professor said something akin to "definitely take it if you're interested, just be aware that it probably won't come in use in most of the mathematics done today." The thing is the foundations are mostly laid, and people are interested in using said foundations for interesting things, not for constantly revisiting the foundations.

I think this is one reason most mathematicians don't see a need for formal proof assistants, since from their perspective it's one very small part of math, and not the interesting one.

This is not to say that proof assistants are a dead end—I find them fascinating and hope they continue to grow—but there's a reason that they haven't had a ton of traction.

Mathematicians use logic to talk about the mathematical world. But logic is not the world.

Not even the most dogmatic of the set theorists ever argued mathematics was possible without reason, however. For mathematics, logic is the world, as the copula makes no distinction between substance and existence. In the same sense that the earth is not matter itself, but it is a material thing.

Putting that aside, to make things more clear: computer science is mathematics. Computer scientists are mathematicians. That was a categorization decided long before you and I ever lived. In the sense that you mean, you're only referring to a very small fraction of what "mathematics" refers to In the true sense of the word. It is just as irreconcilably disjointed as Logic is, not unified and fundamentally non-unifiable.

I too think it would be better if "mathematics" was reserved for the gated suburb of ZFC. But that's not the world we live in, courtesy of the same people who pushed ZFC as a foundation to begin with.

> For mathematics, logic is the world, as the copula makes no distinction between substance and existence.

No. There are truths about the subject not captured in any single formal system. Which is why objects are studied form many perspectives.

> Computer scientists are mathematicians.

Some are and some aren’t.

citation needed, Tao certainly is on record using Lean and that carries some weight.

also, https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon... i.e. there's no reason it should be as you say.

The link is exactly what I’m saying. I only hear cs people talk about it.

For mathematicians a proof is a means to an end, or a medium of expression - they care about what they say and why.

The correspondence isn’t about C programs corresponding to proofs in math papers. It’s a very a specific claim about kinds of formal systems which don’t resemble how math or programming is done.

Mathematicians care about interesting ideas, not whether their theorems are true :-)

They care about if it’s true. But the role of the formal proof is a kind of spell checker or static analysis after they have the idea.

> They care about if it’s true.

Not always.

If it is NOT true, they sometimes simply play "what if" and construct a new system where it could be true.

Terence Tao, one of the most important living mathematicians, specifically embraces Lean and has been helping the community embrace it.

What you've done here is an overgeneralization. "People who like math" and "people who like computers" are massive demographics with considerable overlap.

> one of the most important living

Maybe. But more clearly one of the most popular online.

I think the number of instances should be a clue that you need to look at the layout.

Spivak is a different category of calculus text.

Did CAD make engineers better? certain products are only possible because of CAD but the pen and paper guys weren’t obviously less efficient, and I personally think they were very efficient.

When prototypes are harder to build you focus on answering the biggest questions. I feel like you spend more time iterating on details in CAD, even when the larger idea is invalid.

The effect of JavaScript or python code is well defined - they have an excellent model of what it will do.

The performance - how that is executed on the machine is what you were referring to. “As if” is the key to optimization

Economics is circular. The baker buys shoes from the cobbler, and the cobbler buys food from the baker.

Yes but the baker doesn't just give the cobbler money to buy bread and take a share in the shoe shop in return.

But there's nothing wrong with that. It's not a circle; it's an exchange. Like any transaction.

I like this abstraction. If the baker says “I could sell 10x more if only I had shoes that allowed me to bake faster” then the cobbler says, “split the growth with me and I’ll craft you all the shoes you want.”

The claim was circularity is evidence the business activity is fake.

Those are tangible items. Here, the baker is buying shoes from someone who says they're going to be a cobbler some day.

It’s no different with services. Making deals with potential cobblers seems like a fine market activity.

I didn’t expect him to describe his own field as illegitimate. Somehow knowing you are doing bad things is even worse than a rationalization. Why spend your time with people who don’t believe in what they do?

I am pretty sure most companies and people doing bad things know they are doing bad things.

I know this isn’t quite your point. But for the portfolio approach to be plausible you have to play as if all of them will succeed, and only later sort out the failures.

If you mentally say “well 90% fail so I’ll just throw in this dog shit to see what happens” then you increase the failure rate.

Yeah I can see that.

Another thing I was thinking as I was re-reading this thread is that for some VCs the fact that you can game your GH star count might in fact read as a positive signal. It shows you're willing able to play a kind of vicious PR game to get popularity.

Again, VCs not interested in pure technical excellence or geek "cred". They likely want you if you're the kind of person who can stand in front of a room and puff yourself up and make yourself look more important than you are, and frankly "acquiring" GH stars might just be part of that.

I think it's awful, and I could never do that and my values wouldn't let me buy stars or lie about my projects.

Hence I've been working in this industry for 30 years this year, and I'm still a wage labourer.

I think this is accurate. It’s a kind of promotion and commitment acumen.

In other words, VCs should be taking a risk primarily by being very early. They should not be taking risks on low quality people or projects on the off chance that something good comes out.

This is why I hate health science. Informed people can have the same information and come to opposite conclusions. The entire field is made up of contradictory explanations and principles, to the extent that it’s unknowable what’s true or not.

The flat earthers are why I hate astronomy.

Afaict, the grand parent poster is just very wrong. You do want to cause acute stresses to your heart (cardiovascular exercise) to get it work better.

It’s not really about this particular claim. It’s that I can read a comment that has a reasonable chain of logic and I don’t know if it’s true. This topic is just not easily studied and theories are hard to falsify.

Claims about flat earth are falsifiable with at-home experiment.