Pure mathematics is just such an abstraction from the real world, and pure mathematics does have a special precise language for dealing with its own special and technical subjects. But this precise language is not precise in any sense if you deal with real objects of the world, and it is only pedantic and quite confusing to use it unless there are some special subtleties which have to be carefully distinguished.
The Subtle Art of the Mathematical Conjecture | Quanta Magazine:
By Robbert Dijkgraaf
The highest summits are not conquered in a single effort. Climbing expeditions carefully lay out base camps and fixed ropes, then slowly work their way to the peak. Similarly, in mathematics one often needs to erect elaborate structures to attack a major problem. A direct assault is seen as foolish and naive. These auxiliary mathematical constructions can sometimes take centuries to build and in the end often prove to be more valuable than the conquered theorem itself. The scaffold then becomes a permanent addition to the architecture of mathematics.
I believe in new ideas, in progress. It’s faith. I’ve recently been thinking about faith. If you’re a religious person, which I’m not, you believe God created the universe. That’s why it works, and you’re trying to understand God’s works. There are many scientists who work in that framework. Scientists, outside of religion, have their own faith. They believe the universe is rational. They’re trying to find the laws of nature. But why are there laws? That’s the article of faith for scientists. It’s not rational. It’s useful. It’s practical. There’s evidence in its favor: The sun does rise every day. But nevertheless, at the end of the day, it’s an article of faith.
I feel a responsibility as a scientist who knows the great value of a satisfactory philosophy of ignorance, and the progress made possible by such a philosophy, progress which is the fruit of freedom of thought…to proclaim the value of this freedom and to teach that doubt is not to be feared, but that it is to be welcomed as the possibility of a new potential for human beings. If you know that you are not sure, you have a chance to improve the situation. I want to demand this freedom for future generations.
Always remember that it is impossible to speak in such a way that you cannot be misunderstood: there will always be some who misunderstand you.
A pioneering physicist explains why it’s okay to not have all the answers:
Interesting interview with theorist Brian Greene, I liked his concept of personalized education, I think he could be quite right on this.
“[…] I think in some number of years we’ll have a far more personalized approach to education. Kids are different. They come at things completely differently, different DNA, different experiences. If we could allow them to drive the right way to learn for their particular biochemical and neurophysiological make-up, how much more powerful would that be than a one-size-fits-all approach, which is what we do now?”
The coevolution of physics and math:
[The] relationship between physics and mathematics goes back to the beginning of both subjects; as the fields have advanced, this relationship has gotten more and more tangled, a complicated tapestry. There is seemingly no end to the places where a well-placed set of tools for making calculations could help physicists, or where a probing question from physics could inspire mathematicians to create entirely new mathematical objects or theories.
Beware of false knowledge; it is more dangerous than ignorance.