Within the lens of the other religion probably. Except from hardcore zealots, religious people often agree on true things that they find in common between religions (eg idol worship being a sin, murder, adultery, etc etc).
I don't think that's a problem: if there are uninteresting languages, then you must study them, then work hard to prove that they are uninteresting first. That is, mathematics indeed does study uninteresting languages.
.. mathematics is the same for me as GP said: you have a set of symbols, a set of rules, now derive true statements. (Or at least this is a good view, but other views can be also good.)
There are uninteresting languages that can be considered, but nobody considers them unless a reason arises to do so.
Attempting to prove that they are uninteresting is not itself an interesting problem, because it is easy to prove that such proofs do not generally exist. Indeed things become interesting not because they are inherently interesting in and of themselves. But because something else that is already interesting turns out to connect to the not yet interesting thing, and studying the not yet interesting therefore becomes relevant to the interesting one.
The uninteresting languages are still part of mathematics though. It’s just that we choose not to explore them because we don’t think there’s any value. If you limit it just to the languages that we find interesting, then “what is mathematics” is a fluid definition depending on what we choose to focus on today whereas my definition is a bit more durable.
Also, on the topic of “uninteresting”, if I recall correctly number theory (or discrete math) was explored by a mathematician claiming it’ll never have any application and that’s why he was doing it, only for cryptography to come by within a century after that. At least if I recall the apocryphal story told to me in class correctly. Erdos seems like he’d line up time wise and focus wise but I can’t find any quotes from him to that effect so maybe I’m misrembering?
I don't hold with drawing the strokes too broadly. If we take a broad definition of mathematics, both computer science and chess would be branches of mathematics. Such a definition doesn't capture what I want to think of as mathematics.
There is one comforting conclusions which is easy for a real
mathematician. Real mathematics has no effects on war. No one
has yet discovered any warlike purpose to be served by the theory
of numbers or relativity, and it seems very unlikely that anyone
will do so for many years.
Given that he wrote this in 1940, relativity was a bad prediction. The theory of numbers also become useful thanks to cryptography.
He also makes reference to a belief that Gauss said something like, "if mathematics is the queen of the sciences, then the theory of numbers is, because of its supreme uselessness, the queen of mathematics..." But he argues this only to undermine it.
I don’t follow. Computer science is a branch of mathematics though, at least it’s considered as such by many university curricula. Technically, I’d say it’s more of a label to a cross sectional combination of branches of mathematics or viewing existing branches through a computational lens, but plenty of mathematical proofs use bridges across branches to solve problems that neither branch could alone. CS covers number theory, graph theory, game theory, discrete math, Boolean algebra, trigonometry, geometry, etc etc etc. Granted there’s a bit of inherent element of engineering in most of it too because “see the math running in reality” is a natural desire. That and computers offer faster feedback loops to playing around with mathematical ideas.
Chess is 100% covered by the branch of mathematics connecting game theory and search and you can translate computational problems onto chess boards in a fashion [1]. So if computational math is part of math and chess is part of computational math, then chess is math.
I think the discomfort you face is that nearly everything can be described with math which means nearly everything is a part of math even if we haven’t described it mathematically yet. And then if everything is math, setting up rigid boundaries between “math” and “not math” is difficult, but I don’t think that’s a bad thing - binary classification is famously problematic when trying to apply to the real world (eg genuses in biology are a valiant but ultimately futile attempt).
Granted it’s possible the language definition is necessary but not sufficient. Something about formalism maybe? Not sure. What does math mean to you?
Thanks for that quote btw - it’s 100% the quote I recall reading.
* edit: here’s a relevant quote from Hardy’s Wikipedia page:
> A chess problem is genuine mathematics, but it is in some way 'trivial' mathematics. However ingenious and intricate, however original and surprising the moves, there is something essential lacking. Chess problems are unimportant. The best mathematics is serious as well as beautiful - 'important.'
> Also, on the topic of “uninteresting”, if I recall correctly number theory (or discrete math) was explored by a mathematician claiming it’ll never have any application and that’s why he was doing it, only for cryptography to come by within a century after that.
I know a version that the motivation was that they can't use it in wars (so the mathematician was a pacifist instead of an arse). I can't find a source for this anecdote either. I probably heard it about Paul Turán, but anyone doing discrete math at that era (number theory, graphs, combinatorics) would do.
Makes sense. I never thought the mathematician was being an arse. To me it was just a reminder that no matter how well versed you may be in mathematics, any prognostication about the uselessness of a mathematical field is likely to be proven incorrect in the long run.
English grammar can be. Buffalo is an animal, a city, and a verb meaning "to bewilder and confuse". As a result the following can be proven.
The word buffalo, repeated any number of times, can always be parsed into a valid English sentence. If the number of times it appears is prime, it can only be parsed into ONE possible English sentence.
No, it is a mathematical statement about linguistics. It should not be surprising that mathematics can be used to describe things. Everything in the universe can be described by mathematics--even truly random, acausal events have probability distributions which are described by mathematics. But being described by mathematics does not make it mathematics. That's a type error.
I think so, but it wouldn’t be very interesting. The rules of Japanese grammar mathematically could only tell you if something is in the Japanese language or not. The other challenge is that human languages tend to be filled with exceptions and intentional violations of rules for creative effect. That kind of stuff doesn’t really fly in mathematical languages.
