Feb 17, 2026 · 43 min · 22 segments
In this conversation, Ravi Vakil discusses the beauty of mathematics, the impact of AI on the field, and the importance of human interaction in mathematical education. He emphasizes the social nature…
Ravi VakilGuest
Noah GiansiracusaHostAutumn PhaneufHostspeaker_6Host[upbeat music] All right, so Ravi, let's start by hearing what makes you most passionate about mathematics or the mathematics profession?
I guess for me, for me, definitely it starts with the mathematics, so it's what's beautiful.
And so that guides a lot of other things which seem like they might be primary, but for me it's just what's amazing about nature and beautiful about it.
And then that relates to why people matter in it as well because if something's incredibly beautiful, you want to both share it with people and also the way in which you create it is, is with people as well.
That's something when you're really tiny, when you see beautiful things that you just want-- it makes you happy and squeal with joy, it's the same thing you get to be happy about decades later, and you always want to share them with other people and, and hear about them from other people.
So beauty is, is tricky to define in art, and I would say it's just as tricky if not trickier in mathematics.
So beauty is tricky in art and it's tricky in mathematics, but the amazing thing is that we agree on it so much, that if you get a bunch of people in a room and they're open to seeing something beautiful, they tend to agree on it.
Maybe in art it can be more complicated sometimes, but somehow in mathematics and in science I feel like it's sometimes easier, where somehow an entire room can have an aha moment at the same time.
Or when you're sharing, sharing a, a drink with someone or a coffee with someone and you hear something amazing or they, uh... or you, or, or you get to say something amazing, everyone's li-- eyes light up at the same time.
So it, it, it is somewhat, uh, cliché to say you know it when you see it, but, uh, but there are some commonalities that are always there.
Uh, the word epiphany is a, uh, is a phrase that, that, that mathematicians say and really feel, and I, uh, uh, that feels a little bit religious as well.
When something so amazing happens that you remember years later when you first heard it.
So, so I, I think there is this commonality, and that's that developing of mathematical taste and appreciation that we can agree on even if we can't really describe where it happens.
But it really accompanies where things are powerful, and somehow when suddenly you see the Grand Canyon, you don't just see something beautiful, you also see something very far away.
When you climb an amazing mountain, then you have a view as well as y- you've exerted yourself, but you've also achieved something, and you see farther than other people do as well.
[upbeat music] All right, so Ravi, let's start by hearing what makes you most passionate about mathematics or the mathematics profession?
I guess for me, for me, definitely it starts with the mathematics, so it's what's beautiful.
And so that guides a lot of other things which seem like they might be primary, but for me it's just what's amazing about nature and beautiful about it.
And then that relates to why people matter in it as well because if something's incredibly beautiful, you want to both share it with people and also the way in which you create it is, is with people as well.
That's something when you're really tiny, when you see beautiful things that you just want-- it makes you happy and squeal with joy, it's the same thing you get to be happy about decades later, and you always want to share them with other people and, and hear about them from other people.
So beauty is, is tricky to define in art, and I would say it's just as tricky if not trickier in mathematics.
So beauty is tricky in art and it's tricky in mathematics, but the amazing thing is that we agree on it so much, that if you get a bunch of people in a room and they're open to seeing something beautiful, they tend to agree on it.
Maybe in art it can be more complicated sometimes, but somehow in mathematics and in science I feel like it's sometimes easier, where somehow an entire room can have an aha moment at the same time.
Or when you're sharing, sharing a, a drink with someone or a coffee with someone and you hear something amazing or they, uh... or you, or, or you get to say something amazing, everyone's li-- eyes light up at the same time.
So it, it, it is somewhat, uh, cliché to say you know it when you see it, but, uh, but there are some commonalities that are always there.
Uh, the word epiphany is a, uh, is a phrase that, that, that mathematicians say and really feel, and I, uh, uh, that feels a little bit religious as well.
When something so amazing happens that you remember years later when you first heard it.
So, so I, I think there is this commonality, and that's that developing of mathematical taste and appreciation that we can agree on even if we can't really describe where it happens.
But it really accompanies where things are powerful, and somehow when suddenly you see the Grand Canyon, you don't just see something beautiful, you also see something very far away.
When you climb an amazing mountain, then you have a view as well as y- you've exerted yourself, but you've also achieved something, and you see farther than other people do as well.
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