'Abtruse' is intended to signify 'complicated to understand' and 'perplexing'.

  1. This feels true, as intelligent laypeople can understand unsolved philosophy problems and competing possible solutions, but can't understand or how to begin unsolved math problems.

  2. Yet math and philosophy use logic, which feels mathematical enough to fall under math.

    Optional Information

    A friend apprised me of a leading fee-paying UK high school's experiment for Sixth Formers (i.e. seniors) to substantiate 2.

  3. Teachers notified all students that they'd be tested in 4 weeks, in 4.5 hours in class without notes, on 3 IMO questions from the Algebra section randomly selected from 2011-2016 papers whose solutions are posted.

    They were advised to study the solutions, if they remained baffled after trying. Yet on the test, nobody solved 1 problem or finished early. When asked why, students said that IMO problems needed too clever tricks or inventions or "machinated ploys" (as one student complained).

  4. After this IMO test, all students were instructed to read this list of unsolved philosophy problems for homework. In 2 weeks, they'd write a précis $\ge$ 300 words outlining the problems, on 4 randomly chosen topics from that list, in 2 hours in class without notes. Everyone aced this. Some finished before the time limit.

The snag: 4 weeks after this test, the teacher dispensed a pop test with the same format, but on another 4 randomly chosen topics. Yet everyone still aced it.

  • 6
    "Why's math more abstruse than philosophy ?" Who says it ? Try to read Euclid's Elements and compare it with Sartre's Being and nothing* or Deleuze's works. May 9 '18 at 15:00
  • 2
    You asked pretty much the same in math.educators. why the repeat? matheducators.stackexchange.com/questions/14049/…
    – bukwyrm
    May 9 '18 at 15:08
  • 1
    "This feels true, as intelligent laypeople can understand unsolved philosophy problems and competing possible solutions, but can't understand or how to begin unsolved math problems." source please? There's no way you can substantiate this claim, and either way this question is subjective and opinionated. A 300 page high school level essay is not even close to the rigor and technical application that is required for professional philosophy. Those students would not have gotten A's if they were being graded on the same level academic, publishable philosophy papers are graded.
    – Not_Here
    May 9 '18 at 21:31
  • "Problem", "solving" and "logic" have such different meanings in mathematics and philosophy that this feels like comparing apples to oranges. Each philosopher creates his own list of "unsolved problems", which is why Wikipedia's "formulations" are so vague, and proceeds to "solve" them using arguments whose "logic" is often disputed. In mathematics those problems are handed down for generations, and when a proof is given it is broadly accepted, barring mistakes. "Abstruseness" may simply reflect precision standards, it is more "abstruse" to cut wood to 0.1mm margin than to cut it "originally".
    – Conifold
    May 9 '18 at 21:49
  • 2
    None of the students solved the philosophical problems so I'm not sure what 'aced' means in this context. In the algebra test they had to solve problems but in the philosophy test they only had to define them. Not a fair contest.
    – user20253
    May 10 '18 at 16:12

This is the opinion of 'mathematician' (working on my mathematics PhD) who has studied a fair amount of (analytic) philosophy. I find it interesting that you feel this way, for I feel the very opposite is true. To my mind, philosophy seems to be just as difficult, if not considerably more difficult, precisely because of the high learning barrier and the fact that the problems aren't as well-defined (at least they take a rather long time to reach a state of well-definedness). With philosophy, there is just so much to read and the arguments in philosophy can be just as difficult/abstract as any mathematical argument, not to mention that arguments are sometimes hidden within pages of dense writing; and even if they are presented in premise-conclusion form, which is common in contemporary philosophy papers, they compensate for being in plain sight by being more difficult. So, dense philosophical texts combined with equally abstract arguments seems to indicate that philosophy is more difficult. I think that once you delve more deeply into philosophy, you'll find that the problems become much more challenging and nuanced. Moreover philosophy has great diversity, in terms of the problems and questions that fall within its purview, although it may be difficult to argue that philosophy possess greater diversity than mathematics, since mathematics is itself rather diverse.

As for why intelligent laypeople find statements of philosophical problems more comprehensible than statements of mathematical problems, I refrain from rendering any opinion as I am not a psychologist/sociologist. The only concerns I have are: which philosophical problems were they presented with; and were they presented superficially? Often these "unsolved" problems can be presented in a way that makes them seem simple; but, as I said above, once you delve more deeply into these problems they can become overwhelmingly nuanced. That said, present the intelligent layperson with detailed treatment of Plantinga's Free Will defense using ideas of modal logic and counterfactuals of creaturely freedom or Putnam's Model-Theoretic Argument against Metaphysical Realism, I'm sure they'd be just as lost as hearing a presentation of the Riemann Hypothesis or Connes' Embedding Conjecture.

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