The moment I put my pen to the paper (metaphorically, for this blog), I'm out of content to write.
This is an interesting phenomenon -- I'm pretty sure I have a stack of ridiculous ideas somewhere in my brain, but once I told myself "time to spin up the good ol' writing machine, tim chu!" these thoughts escaped me, and I find that my brain is totally blank.
This is the "decide-to-write first" way of tackling things, where one detrmines what they should do and then tries to do it. In contrast, there's the "ideas first" school of thought, were thoughts and ideas float around in the brain and then coalesce into art.
This last item is a guess based on conversations with talented undergrad mathematicians, and how they come up with good ideas. I would estimate up to 40 to 90 percent of MIT mathematics students believe that the best undergraduate mathematicians "force" themselves to read math books, or tell themselves to do it and have a reserve of love or willpower that let them power through the books. From a brief conversation with the illustrious Amol Aggarwal (one of the top undergrads from MIT), this is a misconception. He takes me through the mental process he uses:
(1) Questions and ideas that flit in and out of the mind.
(2) Sometimes, it becomes clear that more knoweldge is required to think about the question more deeply .When this occurs, it appears reasonable to read a section of a book, or learn a particular branch of mathematics.
Where do the questions and ideas in (1) come from? According to Amol, his questions came from previous querstions, which came from previous questions, which .... eventually went down to a "seed idea" that his advisor, Alexei Borodin, proposed to him.
Thus the picture looks much less like "time to do math" and more like.... starting out with a seed idea from Borodin, which blossoms into a tree of questions, and books and references are accessed accordingly when they appear relevant to the question at hand.
3/12/2023 03:24:52 am
Great read thankyoou
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"All we ever want is indecision, all we really like is what we know." - Alexander Pope.