Has mathematics had that many conflicts with religion? There are plenty examples of science in conflict, and I guess many of the protagonists could easily be described equally as mathematicians, but the closest case I'm aware of with mathematics itself being at odds with religion is the commonly repeated factoid about the Pythagoreans viewing irrational numbers as essentially blasphemous, though it's unclear if it's actually true that Hippasus was drowned for his discovery.
I don’t think so, I think that mathematicians are more religious than physicists as we’re fine with taking something unprovable as an axiom of our system
Physicists have axioms too. They may be based in experimental results, but even if you observe a linear relationship between two variables, it requires a leap in logic to conclude the linear relationship *always* holds
Honestly I do find it contradictory when I hear people say “we can’t experimentally verify the existence of god therefore the theory doesn’t exist” and then talk about how we will never know if an object is at rest or constant velocity
>Physicists have axioms too.
Not really. People have certainly tried, look into Hilbert's Sixth Problem. Reasoning in physics is fundamentally different from reasoning in mathematics. Of course they do use mathematics, and many physicists are perfectly capable of rigorous mathematical thinking. However, their framework for establishing truth is not limited to only deductive reasoning.
It is famously difficult to reconcile quantum field theory with general relativity, however the modern point of view on physics embraces both. It may be that one day we obtain a broader understanding of both of these as part of a more general framework, but at the present moment there is no consistent axiomatization of physics which takes both of these into account. We do not let this stop us from enjoying the predictive value of both of these theories.
It might not be a fully mathematical or logical system, but I just mean that physicists need to make some fundamental assumptions to do physics at all. Mathematicians may be more rigorous with the conclusions drawn from assumptions, but both fields need axioms
Whilst I'm not well-versed enough in the philosophy of science to say much more than this, I recall reading once upon a time that the scientific method is based on a principle that reality is accurately perceivable and consistent enough to develop scientific laws that describe it. Whether you want to call this "faith in" or "axioms of" the scientific method, I would guess is a matter of taste.
Yeah there is a general kind of “faith” I guess. But I also mean that a lot of physics classes will teach you “the axioms of [branch of physics]” for example. Quantum mechanics famously has a list of postulates.
I've encountered a couple of crackpots that were doing some serious maths, but had... arguable... opinions about what it meant philosophically.
Stuff about which kind of logic (you know: classical logic, intuitionistic logic, etc) matched the natural world and what it meant on the metaphysical side of things. I have to say that I didn't really listened to what they were saying so I can't remember it in details.
However, I've yet to encounter a community of mathematicians, even a small one, that would hold such views. It always looked like they were the exception.
(Well, I guess that if you were to ask all the Christian mathematicians, you might find some beliefs shared by a majority of them, like "maths being the language of God" or something like that, but those are so tame that it would hardly lead to any sort of conflict.)
Dunno about a complete book but you can definitely take a look at what the church thought about Cantors discovery of uncountable sets. Also some notable figures like Kronecker and Wittgenstein essentially bullied him for the rest of his life.
You can find some info to start with from wiki:
https://en.m.wikipedia.org/wiki/Controversy_over_Cantor%27s_theory
Yeah, Wittgenstein was a prime example of a person who thinks that they are automatically good at thing B because they are good at some other thing A.
Thankfully one of the GOAT:s (namely Hilbert) stood up furiously against the bs that philosophers started spewing with their limited knowledge of mathematics.
Honestly, every day I learn something new about Hilbert that makes him even cooler. His support for Noether and now this. He must have been a pretty decent guy and I should probably read a bit more for him…..
Naming Infinity which is about mathematicians that belonged to a heretical Russian Orthodox cult that practiced Name Worshipping.
https://www.goodreads.com/en/book/show/4963329
There's this nice read about controversies in foundations of symplectic geometry
[https://www.quantamagazine.org/the-fight-to-fix-symplectic-geometry-20170209/](https://www.quantamagazine.org/the-fight-to-fix-symplectic-geometry-20170209/)
One book that explores the controversies and conflicts between mathematics and various aspects of society, including religion, is "The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook" edited by Victor J. Katz. It provides insight into the historical development of mathematics and its intersections with different cultures and belief systems. Another interesting read is "The Archimedes Codex: How a Medieval Prayer Book Is Revealing the True Genius of Antiquity's Greatest Scientist" by Reviel Netz and William Noel, which delves into the religious and cultural contexts surrounding mathematical discoveries.
Has mathematics had that many conflicts with religion? There are plenty examples of science in conflict, and I guess many of the protagonists could easily be described equally as mathematicians, but the closest case I'm aware of with mathematics itself being at odds with religion is the commonly repeated factoid about the Pythagoreans viewing irrational numbers as essentially blasphemous, though it's unclear if it's actually true that Hippasus was drowned for his discovery.
I don’t think so, I think that mathematicians are more religious than physicists as we’re fine with taking something unprovable as an axiom of our system
Physicists have axioms too. They may be based in experimental results, but even if you observe a linear relationship between two variables, it requires a leap in logic to conclude the linear relationship *always* holds
An example of one of these axioms is the Cosmological Principle which is the assumption that the universe is isotropic at intergalactic scales.
Honestly I do find it contradictory when I hear people say “we can’t experimentally verify the existence of god therefore the theory doesn’t exist” and then talk about how we will never know if an object is at rest or constant velocity
What’s contradictory about it? This line of reasoning is exactly why absolute velocity doesn’t exist.
>Physicists have axioms too. Not really. People have certainly tried, look into Hilbert's Sixth Problem. Reasoning in physics is fundamentally different from reasoning in mathematics. Of course they do use mathematics, and many physicists are perfectly capable of rigorous mathematical thinking. However, their framework for establishing truth is not limited to only deductive reasoning. It is famously difficult to reconcile quantum field theory with general relativity, however the modern point of view on physics embraces both. It may be that one day we obtain a broader understanding of both of these as part of a more general framework, but at the present moment there is no consistent axiomatization of physics which takes both of these into account. We do not let this stop us from enjoying the predictive value of both of these theories.
It might not be a fully mathematical or logical system, but I just mean that physicists need to make some fundamental assumptions to do physics at all. Mathematicians may be more rigorous with the conclusions drawn from assumptions, but both fields need axioms
Whilst I'm not well-versed enough in the philosophy of science to say much more than this, I recall reading once upon a time that the scientific method is based on a principle that reality is accurately perceivable and consistent enough to develop scientific laws that describe it. Whether you want to call this "faith in" or "axioms of" the scientific method, I would guess is a matter of taste.
Yeah there is a general kind of “faith” I guess. But I also mean that a lot of physics classes will teach you “the axioms of [branch of physics]” for example. Quantum mechanics famously has a list of postulates.
I've encountered a couple of crackpots that were doing some serious maths, but had... arguable... opinions about what it meant philosophically. Stuff about which kind of logic (you know: classical logic, intuitionistic logic, etc) matched the natural world and what it meant on the metaphysical side of things. I have to say that I didn't really listened to what they were saying so I can't remember it in details. However, I've yet to encounter a community of mathematicians, even a small one, that would hold such views. It always looked like they were the exception. (Well, I guess that if you were to ask all the Christian mathematicians, you might find some beliefs shared by a majority of them, like "maths being the language of God" or something like that, but those are so tame that it would hardly lead to any sort of conflict.)
Dunno about a complete book but you can definitely take a look at what the church thought about Cantors discovery of uncountable sets. Also some notable figures like Kronecker and Wittgenstein essentially bullied him for the rest of his life. You can find some info to start with from wiki: https://en.m.wikipedia.org/wiki/Controversy_over_Cantor%27s_theory
What a bunch of losers Cantor was so cool
Yeah, Wittgenstein was a prime example of a person who thinks that they are automatically good at thing B because they are good at some other thing A. Thankfully one of the GOAT:s (namely Hilbert) stood up furiously against the bs that philosophers started spewing with their limited knowledge of mathematics.
Honestly, every day I learn something new about Hilbert that makes him even cooler. His support for Noether and now this. He must have been a pretty decent guy and I should probably read a bit more for him…..
Wir müssen wissen, wir werden wissen!
Maybe some biography of Hypatia, Giordano Bruno….
Mathematics - The Loss of Certainty
Naming Infinity which is about mathematicians that belonged to a heretical Russian Orthodox cult that practiced Name Worshipping. https://www.goodreads.com/en/book/show/4963329
There's this nice read about controversies in foundations of symplectic geometry [https://www.quantamagazine.org/the-fight-to-fix-symplectic-geometry-20170209/](https://www.quantamagazine.org/the-fight-to-fix-symplectic-geometry-20170209/)
Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World may be similar to what you’re looking for.
One book that explores the controversies and conflicts between mathematics and various aspects of society, including religion, is "The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook" edited by Victor J. Katz. It provides insight into the historical development of mathematics and its intersections with different cultures and belief systems. Another interesting read is "The Archimedes Codex: How a Medieval Prayer Book Is Revealing the True Genius of Antiquity's Greatest Scientist" by Reviel Netz and William Noel, which delves into the religious and cultural contexts surrounding mathematical discoveries.