15.09.2024—planning for the upcoming week. this year is going so fast
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you don't want to look back and wish you had worked a little harder.
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11 August 2024
I was studying German all day 🫶🏼
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John William Waterhouse “Lamia” 1905,detail.
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Sorry for wasting time on my phone, that wasn't very Rory Gilmore, straight A+, speech champion, top of the class, academic weapon, relentless writer, future IVY student, 10 AP classes, graduating early, perfect score, Honors student of me.
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I often think what advice I would offer a younger version of myself at the beginning of my mathematical studies. To the extent I have accumulated any wisdom, it would have to be the following:
Try to avoid over-specialising before you have to. Even subjects which are unpleasant at a first glance can become beautiful when viewed from the right perspective. Give things time to sink in and intermix with other areas of math.
Your identity as a mathematician is validated by merit of putting in serious effort to learn and connect with mathematics. Do not tie your self-esteem to external markers of success in this process. Focus on whether or not you are improving with respect to where you were before.
Seek mentors and listen to them even when you do not like what they have to say. There are many research projects which would have gone better for me had I been less stubborn in my ways. Be especially concerned if you are not merely seeking a proof, but trying to seek a specific style of proof, or a proof that avoids powerful methods on the basis of aesthetic considerations. You can always return and find a more pleasing proof later on when time permits.
More important than anything else is the social network you build with your fellow mathematicians. Great work is usually done in collaboration with other minds, and there is no greater pleasure in life than to be found than sharing in the hunt for a hidden solution with another who really gets it.
Examining special cases is truly one of the most powerful problem solving mechanisms. When you are stuck, just keep making the problem more and more concrete until you hit something manageable. Do not be afraid to use computers to generate examples and counter-examples.
The distinction between pure and applied mathematics is largely nonsensical and harmful. It is not a distinction entirely without content, but when it becomes an ideological framework it has gone too far and hindered productivity.
Study by upgrading your notes to include extra lemmas and theorems from other textbooks, and thinking about how you would present the material in book form yourself.
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Let me introduce myself...
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