Shakuntala Devi is often described as "India's most famous woman mathematician". Her biopic led discussion like what does a mathematician do? Is mathematics all about performing massive computations? Or is there more to it?
A 🧵on Indian women mathematicians by @kaneenikasinha
https://t.co/Rsb2aLv4v1
Prof. Ramdorai has also worked with the Indian government in several capacities for mathematics education in India. She was a member of the PM's Scientific Advisory Council from 2009-14.
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Ok, it's time for a #FUNctionalAnalysis thread! Let's talk about Hilbert spaces. (I hope you like linear algebra, because that's what we're
If you want to impress people, you can just say a Hilbert space is just a complete infinite dimensional inner product space and leave it at that, but let's talk about what that actually means.
When you first learn about vectors, you talk about them as arrows in space; things with a magnitude and a direction. These are elements of R^n where n is the number of dimensions of the space you care about.
You also talk about the dot product (or inner product) as a way to tell when vectors are orthogonal. (I'm purposely saying "orthogonal" instead of "perpendicular" here, but when you actually think about arrows, it's the same thing.)
As my linear algebra students are about to see, R^n is far from the only interesting vector space. A classic example is the space of polynomials of dimension less than or equal to n
— syzygay (@syzygay1) August 9, 2020
If you want to impress people, you can just say a Hilbert space is just a complete infinite dimensional inner product space and leave it at that, but let's talk about what that actually means.
When you first learn about vectors, you talk about them as arrows in space; things with a magnitude and a direction. These are elements of R^n where n is the number of dimensions of the space you care about.
You also talk about the dot product (or inner product) as a way to tell when vectors are orthogonal. (I'm purposely saying "orthogonal" instead of "perpendicular" here, but when you actually think about arrows, it's the same thing.)
As my linear algebra students are about to see, R^n is far from the only interesting vector space. A classic example is the space of polynomials of dimension less than or equal to n
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1/ Here’s a list of conversational frameworks I’ve picked up that have been helpful.
Please add your own.
2/ The Magic Question: "What would need to be true for you
3/ On evaluating where someone’s head is at regarding a topic they are being wishy-washy about or delaying.
“Gun to the head—what would you decide now?”
“Fast forward 6 months after your sabbatical--how would you decide: what criteria is most important to you?”
4/ Other Q’s re: decisions:
“Putting aside a list of pros/cons, what’s the *one* reason you’re doing this?” “Why is that the most important reason?”
“What’s end-game here?”
“What does success look like in a world where you pick that path?”
5/ When listening, after empathizing, and wanting to help them make their own decisions without imposing your world view:
“What would the best version of yourself do”?
Please add your own.
2/ The Magic Question: "What would need to be true for you
1/\u201cWhat would need to be true for you to\u2026.X\u201d
— Erik Torenberg (@eriktorenberg) December 4, 2018
Why is this the most powerful question you can ask when attempting to reach an agreement with another human being or organization?
A thread, co-written by @deanmbrody: https://t.co/Yo6jHbSit9
3/ On evaluating where someone’s head is at regarding a topic they are being wishy-washy about or delaying.
“Gun to the head—what would you decide now?”
“Fast forward 6 months after your sabbatical--how would you decide: what criteria is most important to you?”
4/ Other Q’s re: decisions:
“Putting aside a list of pros/cons, what’s the *one* reason you’re doing this?” “Why is that the most important reason?”
“What’s end-game here?”
“What does success look like in a world where you pick that path?”
5/ When listening, after empathizing, and wanting to help them make their own decisions without imposing your world view:
“What would the best version of yourself do”?
