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Some (huge) updates

So I am in college now! Specifically, I am a fresher in the Electronics and Electrical Communication Engineering Department at IIT Kharagpur. After 2 years of  JEE being the all-important goal, I thought I would feel empty. Well, I did for the two months between writing the exam and coming to the campus. But, one word to describe college, is chaos. Chaos, spreading across space and time. One hour, you're cycling around this huge (large enough to fit in the other 8 IITs) campus, and the other hour you rush to a seminar, pedalling with the vigour you didn't even imagine you had.  Long periods of silence followed by long streaks of things to do.  And coming to college does something to 18-year-old, star-stricken newly-adults who were deprived of life for the past two years. Don't get me started on the number of goofy things we have done after just one month of coming to campus. And we go for a night out after watching a movie every freaking Friday! Since there are plenty of ...
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Peano Axioms and Arithmetic: How we define how we count

Caution It's another expository post (*I mean it's better than just ranting, but Samyak please stop playing an expert*). The same cautions ahead(I'm no expert; I may be wrong). With that out of the way, let's begin: Foreplay  Introduction So! How do you define natural numbers? As is the case with other topics in intro analysis, you'll think (I definitely thought) that this is so boringly obvious . I mean, it's just how we count right? But many things about $\mathbb{N}$ aren't so obvious. For example, how would you prove that $a+b=b+a$ for $a,b\in \mathbb{N} $? You'd say it's blindingly obvious , but commutativity is not obvious for many other things(try, for example, rotating a Rubik's cube and you'll get it). Note that you can't justify with examples (you'd have to give infinite examples to prove this property) Now, this was a problem that presented itself in the mid-to-late $19^{th}$ century. People always assumed that numbers, in g...
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Long time no see?

 Well.., The thing is I haven't been so faithful to write even one piece of writing a month. Let's just say I definitely won't be able to write more in the next months. But, I may just happen to post some random thoughts as a "blog". Who knows? Till then, Happy Holiday Season!
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I found out something beautiful

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When walking, I know that my aim  Is caused by the ghosts with my name.  And although I don’t see  Where they walk next to me,  I know they’re all there, just the same. -David Morin (Introduction to Classical Mechanics, 2008) Sounds eerie, right? But, in a certain interpretation of the notion of action of a path in physics, this is actually true, and the math behind it, calculus of variations, is truly fascinating in itself. Taylor Series: An overview For those of you who know calculus, it's taught late into differential stuff that we can find minimas and maximas of a function, say $f(x)$ by looking for the points where $f'(x)$ turns zero. Later on, in the same course, we get an intuition for why this is true, in the $\text{Taylor series}$, a powerful way to make sense of any ( differentiable) function, by using simple polynomials. So for any random differentiable function $f(x)$, the Taylor series, of $f(x)$ around the input $x=a$ looks like: $$f(x-a)=\sum_{n=0}^{\i...
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Your thoughts?

 Well! I am in my last year of school now! I don't seem to be getting any ideas though? (Haha! unintentional) What do you wanna have on this corner of the Internet? Type it in the comments section or mail it to me at samyakshirsh1234@gmail.com ! Au revoir!
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Happy Pi Day everyone!

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 3.14.2021 Happy Birthday, Einstien! RIP Stephen Hawking. Some of my favourite ways to celebrate today: Warning!!! There are the same Pi hater and Tau lovers down there. Go there at your own discretion
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Some Poetry

Oh, tell the people what matters Death doesn’t care about your money, As for family, it’ll probably end, Well before the last stars cease to remain sunny Oh, if perhaps, from this hopelessly large, Chessboard, if you find the rules, Maybe, we all will get closer To the “bright point of light”, Which we all can’t seem to stop thinking about I don’t fear failure, not even if it becomes my whole life For each Michelson-Morley experiment, There may be bound to appear, The Laser Interferometer Gravitational Observatory (Sidenote: Michelson and Morley were pretty successful in their own right) I don’t want to hear that, “God does not make mistakes” If he does exist, he probably made too many Otherwise, how would we marvel,  at this marvellous world, where man didn’t take the risk it takes?
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