> I agree for the most part, as I'm somewhat of a mathematician myself (theoretical computer science).
Haha, see? You can call yourself a scientist and nobody will bat an eye! Computer Science was once a branch of mathematics; and now it's a full-fledged field. But as you note, the pure-math roots still shine brightly. I'm somewhat of a computer scientist myself; I peddle in algorithms, graph theory, and more generally discrete math. Which brings me to a point I forgot to make: fundamentally, I'm an experimentalist. Not all mathematicians are.
> However, you state "mathematics is one of the only sciences that finds absolute ground truth", which I would argue sets it apart from being a science: science does not deal with absolute truth.
Happy to live with this disagreement, but not all mathematicians find ground truths. For example, there's a significant industry on "conditional proofs" in number theory -- they assume that the Riemann Hypothesis, or even the Generalized Riemann Hypothesis, is true, and discover results based on that. Others work on the Birch and Swinnerton-Dyer conjecture. They collect evidence, and report on it; similar to the 5-sigma proofs I derided earlier -- the distinction is that they only call things proofs when they're actual proofs.
In our shared world, there is the question of P vs NP. We've got a hypothesis (I tend to believe that NP won't be constructively equal to P; but I wouldn't be terribly surprised by a nonconstructive proof). Folks devote their lives to examining this dichotomy: given a problem class, resolve it into P or NP -- I call that an experiment!
I claim that endeavors like the above are actually following the scientific method. Only we use somewhat different language. I've seen snobbery on both sides^ -- scientists and mathematicians are happy to build and maintain a fence. And I find that sad.
Haha, see? You can call yourself a scientist and nobody will bat an eye! Computer Science was once a branch of mathematics; and now it's a full-fledged field. But as you note, the pure-math roots still shine brightly. I'm somewhat of a computer scientist myself; I peddle in algorithms, graph theory, and more generally discrete math. Which brings me to a point I forgot to make: fundamentally, I'm an experimentalist. Not all mathematicians are.
> However, you state "mathematics is one of the only sciences that finds absolute ground truth", which I would argue sets it apart from being a science: science does not deal with absolute truth.
Happy to live with this disagreement, but not all mathematicians find ground truths. For example, there's a significant industry on "conditional proofs" in number theory -- they assume that the Riemann Hypothesis, or even the Generalized Riemann Hypothesis, is true, and discover results based on that. Others work on the Birch and Swinnerton-Dyer conjecture. They collect evidence, and report on it; similar to the 5-sigma proofs I derided earlier -- the distinction is that they only call things proofs when they're actual proofs.
In our shared world, there is the question of P vs NP. We've got a hypothesis (I tend to believe that NP won't be constructively equal to P; but I wouldn't be terribly surprised by a nonconstructive proof). Folks devote their lives to examining this dichotomy: given a problem class, resolve it into P or NP -- I call that an experiment!
I claim that endeavors like the above are actually following the scientific method. Only we use somewhat different language. I've seen snobbery on both sides^ -- scientists and mathematicians are happy to build and maintain a fence. And I find that sad.
^and, oops, I did that with my 5-sigma dismissal