[FabHK]

Just because something seems obvious does not mean that it is.

Famously, for example, Bertrand Russell and Alfred Whitehead prove in Volume II of their Principia Mathematica, using theorem 54.43 from page 379, Volume I, that 1+1=2 (adding that "the above proposition is occasionally useful.")

Now, that is clearly obvious to everyone, and yet what Russell and Whitehead achieved in the intervening 400+ pages was more than just obfuscation.

[bitL]

Also, consider this - nowadays fewer and fewer academicians achieve groundbreaking results in their young age. It's more common for people to study 30+ years before they really contribute something important to science. Often it is because one has to study huge amount of previous results to come up with something new and validated. This time-to-result is likely going to increase in the future. Either we manage to continuously prolong lifespan while keeping brain elastic or we would have to make serious changes to the underlying math to keep math still rigorous, correct but more accessible to the way human brain operates, otherwise there won't be anyone living long enough to come with new results.

[bitL]

I am actually suggesting that current mathematical language is not sufficient to describe real world and the language itself has self-imposed structural problems preventing it from achieving higher precision in describing the real world in fewer symbols. Now with computers doing all the menial work we should be able to tackle on the challenge of improving the mathematical language itself stuck with over-simplistic mental models so popular at the beginning of 20th century.

Try to use mathematics to describe an artistic work. Or even precise muscular movement of a human arm in a ballet in its wholeness. Good luck with that!

[bitL]

FYI, this might shed light on some problems introduced by Russel and Whitehead in Principia Mathematica: http://www.academia.edu/13159243/2015_Pragmatism_the_A_Prior...

See also Hempel's raven paradox.