Ashika Jayanthy’s Blog

 For a long time, my close relative's work in law and public policy felt foreign to me. It seemed distant from the kinds of problems I was used to thinking about, governed by a different language and a different set of concerns. Over time, I’ve come to realize that it isn’t foreign at all. At its core, her work is about choosing objectives and then figuring out how to maximize them under real constraints. The constraints happen to be legal, institutional, and political rather than mathematical, but the structure of the problem is the same. I wanted to understand how legal training shapes that way of thinking, and how it helps turn ideals into something that can actually operate in the world. Abhijit Banarjee and Esther Duflo  Q: Good evening! Thanks so much for doing this. When you first started law school, what kind of thinking did you have to unlearn? I don’t think I had to unlearn anything in a strong sense. When you’re that young, you don’t yet have a very fixed or fully ...

Nitin (4 yo brother): Baabaa boo boo gee gee ga ga  Nitya: NITIN STOP BEING SO ANNOYING Nitin: I don't want to So that's the introduction for my family but there's more. First of all, there is a lot of shouting and messiness. Second of all, we always like have it really loud outside in our backyard. Its really annoying too. Then, me and my brother are always getting into fights and one of the parents have to shout at Nitin or me but they dont know which one started it. So they basically blame one of us. I have no time to give you an example so let me just say these three things. And I want you to remember these three things. Fighting, noisiness and messiness. So that was the third part of my blog. For now. 

N:  hi this is me again and this is my blog about brainvita! so today we played brainvita and you know that you have four options in the beginning and they're all the same. A: Are they exactly the same? N: Yeah, basically. So we started with one of the four options we had and we kept going and in the end we just kept ending up with 4. It was really interesting. Then we asked ChatGPT what the strategy was. When I was reading what ChatGPT had written for us, my aunt (A) experimented with the game and she got 2 surprisingly. I asked her what she did, and she said "I cleared the edges first". A: So what did you make of that N: We learnt that if you clear the edges first and preserve the middle parts, you could get a lot of pegs out and less pegs in.  And that was my blog. 

 today we drew pictures, colored and played brain vita. here are some pictures we drew. we were playing a game where each of us draws something random and hands it over to the other, and we are supposed to finish the drawing. I got the idea from a friend of mine. maybe you could play this game with your family and friends too!

I did not expect a pencil sketch of a hand to explain anything about how I learn number theory, but looking at this drawing again, the analogy is almost too accurate. When I draw, I never start with the details. I start by blocking in the large forms: the angle of the palm, the direction of the fingers, the overall gesture. Only when that structure feels correct do I move inward and work on the internal planes, the shading, and the tendons. The finished drawing looks detailed, but those details only work because the underlying structure was stable.  Also, I'm double jointed so some of the hand poses might seem a bit contrived.

  As I work through introductory number theory, I have started noticing that my mistakes are not random. They cluster around a very specific behavior in my mind. I tend to switch viewpoints too quickly. Instead of staying inside one definition or one structure long enough, I jump to a more general interpretation before the foundation is stable. This shows up clearly in modular arithmetic. For example, when I first learned that two residue classes [ i ]  and [ j ]  in Z / n Z \mathbb{Z} / n\mathbb{Z}  are equal if and only if i ≡ j ( m o d n ) i \equiv j \pmod{n} , I understood the definition but immediately tried to generalize it. I started reasoning about the classes almost as if they were single numbers, not sets, and occasionally I would try to compare them by looking directly at representatives instead of the congruence relation. The definition had not yet settled into my mind as an object. Another example: when working with congruence equations, I sometimes tr...