# Dogmas and Mathematics

What are the dogmas that restrict or promote the development of mathematics?

I know that a dogma is a set of beliefs that is accepted by the members of a group without being questioned or doubted. However, dogmas are usually religious, and it is here that I am stuck. Should I be looking for religious dogmas that impacted mathematics, or should I be looking at the dogmas (axioms) of mathematics?

• You might be looking for stuff more on the lines of Platonism, Realism, Formalism (or Finitism), ... – Git Gud Nov 4 '13 at 22:43
• What is your context? It sounds like you've been tasked to write an essay on a topic or something... it would help greatly if we knew both your background and that of the target audience, more details about what specifically you're supposed to research, related topics you've been studying, et cetera. – Hurkyl Nov 4 '13 at 23:00
• You may want to look at this article in the Stanford Encyclopedia of Philosophy: plato.stanford.edu/entries/philosophy-mathematics (Although note that most ideas in the philosophy of mathematics would not qualify as dogmas; mathematicians love to doubt things.) – Trevor Wilson Nov 4 '13 at 23:02
• Besides looking at non-mathematical (e.g. religious) beliefs, or at the formal axioms of mathematics, there is also the third option of looking at mathematicians' informal ideas about mathematics (their answers to questions like: what is a rigorous argument, what is a number, do mathematical objects really exist, is mathematics a process of invention or of discovery, what should the axioms of mathematics be, etc.) – Trevor Wilson Nov 4 '13 at 23:10
• Given that in math everything follows a rigorous way, I would define a dogma as one (or a set of) axioms one chooses to follow or develop, even though alternative axioms would also lead to consistent conclusions. In this sense, one could say that Euclidean Geometry is based on the dogma that two parallel lines have no point of intersection. In a similar reasoning, one could say that Religion is a set of theorems based on the axiom that God exists. – Leo Azevedo Jan 29 '14 at 22:04