Math preferences

[Chris11]

The following question really only applies to those of us who are mathematicians. I was wondering if Intp thought preferences would lead us to pursue particular areas of math over others. For instance, would you prefer High end algebra to enumertive combinatorics? Algebra over graph theory? Graph theory over counting? Algebraic topology over point set topology? Algebraic topology over graph theory? Algebraic topology over high end algebra? Algebra over Analysis? Foundations over any of the above?

My suspecion (yes, I can't spell this word) is that most of us are drawn to the more abstract areas of math, so we would likly choose to pursue algebra over combinatorics (not that this area can't be very abstract), but I don't have a great deal of confidence in this 'hypothesis.'

 

[Octavian Starr]

Well, I agree. I don't think INTPs are the ones to put anything into practice, at least.

 

[Melllvar]

I'm not a mathematician, but I do like math a lot and I definitely find the more abstract stuff to be more interesting. I like how specific mathematical ideas can be abstracted on as special cases of more general concepts (e.g. sets or categories). Examples might be the real number system just being a special case of the complex number system, or addition, multiplication, etc. being particular types of binary operators. Which is to say, it's more interesting for me to get more abstract than more specific when studying mathematics. Personal favorites have included abstract algebra, tensor analysis and complex variables, as compared to stuff like differential equations or number theory (which seem more boring, for no particular reason I can think of). Recently I've become interested in category theory, which I think is about as abstract as it can get.

 

[Latro]

Pros and cons to each. I think even in concrete math, though, we generalize a lot, which keeps things pretty interesting even if you like abstraction.

+1 to category theory by the way, I've been reading up on that recently. I keep wanting it to "get to the point", and occasionally it does. Product diagrams are a really cool idea for example, as is duality. The idea that things about unions and things about cartesian products are essentially just flipped versions of one another, for example, is a really cool idea, which doesn't really get elucidated without the categorical perspective. Hopefully with a bit more work I can understand what the *hell* an adjoint functor is, since apparently they are everywhere.

 

[Chris11]

Pros and cons to each. I think even in concrete math, though, we generalize a lot, which keeps things pretty interesting even if you like abstraction.

+1 to category theory by the way, I've been reading up on that recently. I keep wanting it to "get to the point", and occasionally it does. Product diagrams are a really cool idea for example, as is duality. The idea that things about unions and things about cartesian products are essentially just flipped versions of one another, for example, is a really cool idea, which doesn't really get elucidated without the categorical perspective. Hopefully with a bit more work I can understand what the *hell* an adjoint functor is, since apparently they are everywhere.

Ah functor, you are such a beautiful word. I don't know a great deal of cat theory. In fact, all I know from it is from an advanced linear algebra course. It does seem like a subject that would interest me, but I don't know any good books on the subject.

 

[Vrecknidj]

I think that the convergence between logic, set theory, and mathematics generally would be appealing to INTPs.

Oh, and proofs. Definitely proofs.

Dave

 

[PhoenixofVindemiatrix]

I hate proofs.

 

[Agent Intellect]

I don't have a lot of math experience (highest I have is calculus 2) but I find that I like applied math more than abstract math. I think the fact that existence operates in a mathematical way is more interesting to me than just symbol manipulation. I like to try and discern mathematical relationships in real life phenomena, and often find myself trying to understand non-mathematical things using mathematical symbols.

That being said, I like statistics.

 

[Infinite Regress]

When I was completing my degree as an undergrad I liked abstract math, particularly real analysis and setting out all the proofs e.g. epsilon-delta criteria for continuity etc.

However as I moved towards my current career path, applied math became more interesting particularly probability and time series analysis in statistics.