this post was submitted on 12 Jun 2025
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Isn't that true of almost all the sciences?
Not quite. Science is empirical, which means it's based on experiments and we can observe patterns and try to make sense of them. We can learn that a pattern or our understanding of it is wrong.
Math is inductive, which means that we have a starting point and we expand out from there using rules. It's not experimental, and conclusions don't change.
1+1 is always 2. What happens to math is that we uncover new ways of thinking about things that change the rules or underlying assumptions. 1+1 is 10 in base 2. Now we have a new, deeper truth about the relationship between bases and what "two" means.
Science is much more approximate. The geocentric model fit, and then new data made it not fit and the model changed. Same for heliocentrism, Galileos models, Keplers, and Newtons. They weren't wrong, they were just discovered to not fit observed reality as well as something else.
A scientific discovery can shift our understanding of the world radically and call other models into question.
A mathematical discovery doesn't do that. It might make something more clear, easier to work with, or provide a technique that can be surprisingly applicable elsewhere.
You're contradicting yourself.
Is no different than:
Science isn't changing, our understanding of it is. Same with math.
There's a difference between an advance that repudiates prior understanding and one that doesn't. You can, in maths - and I assume this is the point - know that you are right, in a way that you can't with a more... epistemological science. Of course it's more complex than that, and a lot of maths is pretty sciency, like deriving approximate solutions for PDEs is more experimental than you might imagine, but even though we might make improvements there, we'll never go 'oh actually those error bounds are wrong'. They might be non optimal but they'll never be wrong