I'm trying to drill down to the core branches of mathematics and it seems to me that Algebra, Analysis and Geometry are the fundamental branches of mathematics––every other 'branch' (topology, number theory, combinatorics, probability, statistics etc.) rest on these three in one shape or form. For example, vector analysis is the interaction between algebra (linear algebra, specifically) and analysis and when applied to (metric) spaces, links geometry. However, I cannot find anything to support this nor is my breadth of mathematical large enough to verify this. Is this perspective correct? I'm happy to be corrected on this.
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2I’m far from a definitive source on this, but I’d say this division is good enough, simply because it’s impossible to draw clear lines separating areas. I would say that statistics is a different area in and of itself, though – Gauss Feb 16 '24 at 12:00
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I agree with Gauss. Probability and Statsitics are highly intuitive and I would treat them as separate from Algebra, Analysis and Geometry. – geetha290krm Feb 16 '24 at 12:11
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1What about logic and set theory? – J. W. Tanner Feb 16 '24 at 12:31
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@geetha290krm To the discontent of some probabilists that field was to a large extend "Bourbakisized" during the last seventy or sixty years. Not sure when that will happen with statistics. – Kurt G. Feb 16 '24 at 14:58