As a brief follow-up to my last post, I reread some pages in Tobias Dantzig’s book Number and, on one of them, he is critical of early 20th century formalists when he says about symbols in mathematics:
To me the tremendous importance of this symbolism lies not in these sterile attempts to banish intuition from the realm of human thought, but in its unlimited power to aid intuition in creating new forms of thought.
The question I wanted to raise in my last post is this. Perhaps symbol has flourished so well in mathematics that our thorough comprehension of them is actually lagging. That we can’t quite see some of the windows they open up to our intuition.
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