Sorry, I am more of a Leibniz person

I think these are what a functioning transport system are for.

Ha, because I bold stuff. Yeah that does look a bit like LLM on retrospect.

But you can see these are not AI generated, because they like repeating trivial conclusions reached in previous paragraphs, which I hope I didn’t do. :)

Also grammar mistake is another giveaway.

I am not a mathematician, but sometimes I get accused of being one; so given that no real mathematician have answered, I guess I can give it a shot.

Mathematician are in charge of building mathematical tools that are used by physicists, computer scientists, and many other subjects, including artist.

Why is math useful: mathematics are used in social science, physics, computer science and many other subject. Take a simple example from computer science: everyone is very excited about quantum computing, but what questions can be answered faster by a quantum computer than a classical computer? This is both a computer science question and also a math question. Many mathematicians are working on problem like these.

What is the difference between mathematican, computer scientists, physicist, and so on: although people from other subject also use advanced mathematical tools and work on similar questions as mathematicians (I guess why I was accused of being a mathematician), the difference is in their approach. Typically, for non-mathematicians (like me), proofs and math tools are means to an end. We often want to prove a very concrete problem (like are two reasonable ways to define the meaning of a program are equivalent), and usually we prefer the proof the takes the least amount of effort to get to the conclusion. Whereas mathematician often makes connection between different approaches, generalize, and just explore things that they feel is interesting. The mathematical approach often is slower but also gives deeper understandings: although it is common for many of their insights to be lost through time, it is also quite often for these exploration leading to important breakthrough in other fields.

What is the life of a mathematician like: like every other academic: teaching, research, writing grant to feed yourself, and sometimes traveling to discuss ideas and start new projects. I imagine OP is most interested in is mathematical research. I feel the most apt analogy is the creation of art: for an artist, they usually have a emotion trying to express, either something they see or feel. Then they do a couple sketch, see what detail/style works in expressing their ideas and what doesn’t, then paint the painting. For mathematicians, they often have a question in mind, then they try some examples to see what steps closer to their goal and what leads to dead ends. Through these excersices they gain a intuition of what conditions are important for the desired conclusions, then they paint the full painting by finishing the proof.

These proofs can be exceptionally time consuming: even for computer scientists, they can easily take couple researcher a year of work to do a proof. Most of the sketches will be thrown away, either because they are too convoluted or because they don’t lead to the correct conclusion. Usually, a proof by computer scientists like me can easily take 20-30 pages to explain properly, if not more; and the proof that were thrown away can double that quantity. I can only imagine proofs for mathematicians will be even more energy consuming.

I feel yields different result than 5 ∪ 7 in the classical set theoretical encoding… I believe 5 ∪ 7 = 7 in the standard encoding of set theory. Because ∪ is the join operation in the natural number lattice (every total order give a lattice structure), yet the lattice structure in ideals of natural number ring is different: the join is LCM and the meet is GCD.

I guess my objection is that the ∪ and ∩ in the set theoretical encoding is rather trivial: the lattice structure in a total order is not terribly informative. Yet the standard encoding of natrual number in category theory (the category generated by one arrow on one object) is slightly more interesting, as composition encodes addition, which is arguably the most interesting opration on natrual numbers.

That being said arguing about encoding of natrual number is not the most informative discussion. but I feel set theory in general is very low level, yet people usually think in more algebraic and high level way, which aligns more closely with category theory.

Counter point, no lawful theory shell let 5 ∪ 7 type check.

The continent of America is called 美洲, as in “the beautiful continent”

If function composition is chaotic, then set intersection is certainly not lawful.

I have never seen the original scene, only the meme. Since the meme refers to the floor, I always thought he is standing on the floor.

Wait, is he standing on a bed the whole time?! I always thought he is standing on the floor?

Left 3 Dead

And the poor npc

last time I checked, life savers are not food.

Thank you, for the detailed answer, and I am sorry for the abuse by your parent.

(again, sorry for the personal question, feel free to disregard) Do you know how dod they immigrated to the U.S.? As a immigrant myself, I thought you can only go to the U.S. if you have work/study here, or being a refugee.

Just to say that MA has a pretty IMO idiotic flat state income tax rate of 5%, and having a income over 1m only increase the rate by 4%.

This increase is really negligible compare to the tax rate by the federal government and the cost of living difference between MA and other states.

If anything, I feel MA still don’t really have a “fair” income tax system yet, but one step at a time.

Sorry if this is personal, feel free to not answer. What made your family move to the U.S. and what did they need to prep financially to support the move?

My main concern is the kid might feel entitled to what they are provided from their parents. That is not necessarily a problem in of itself, but I would be worried if my kids are not aware of how hard it would be to get a house or a car from nothing, because they never need to work for it. And I would be very upset if they cannot empathize with people who are not provided these things by their parents, hence doesn’t support public projects that benefit the less fortunate.

I growup with my mom preping me for “moving out at 18”, in the end, they did support me during college and give me some down payment for my apartment.

I still feel quite bad asking my family for money till this day, because I was taught that way. If it isn’t my wife pushing to get an apartment, I probably will rent until I can pay for my own place. I am honestly quite grateful for them paying for my college because it is not a small expense; and I understand most people don’t have these luxuries.

I feel their teaching let me save when I can, built up a lot of tolerance towards my environments and people around me, and develop a lot more empathy. I don’t know if there is a causal link, but I find people around me who talk a lot about “everyone should bootstrap themselves” often comes from richer families and they get much more than what I got from my parents. Quite honestly, I am very grateful I do not think like them, and I prefer my kid to not think like that as well.

To be completely clear, I am not claiming I am unlucky or have bad parents. My parent, despite forcing me to be independent, are still a great safety net for me. I try my hardest to live on my own and I happens to not need anything else from them (besides enormous college tuitions and down payment 🤣), but I am sure they will provide me whatever I need if I truly needed it.

Vegans/Vegetarians are not a small base in many parts of the world, but most vegan I know also don’t consume like of impossible meats very much (once or twice per week at most?).

Sorry but what does “highest use of our military” even mean?! Are they pretending to be stupid to gain attention, or are they really not able to speak their own language.