Day 6

2:20 am 5 August 2023
I have always known there is going to be a day, where im just going to decide to go get it. after which ill just spend every single waking second getting better. just enjoying the journey. Leraning cool math, solving difficult problems, building cool shit all day every day. living the experiment I have always wanted to. Where I just wake up every single day excited to work , work all day, no girls, no distractions nothing. just me having fun all day. improving so much every single day, and then going to sleep satisfied. Being so fucking confident and just happy all day. Having so much urgency and getting so much done every single day that people are just confused. I have always known that i can do anything. and I have always known that the day I decide to go get it, is the day I will have already achieved everything.

5 August 2025, that day is right now. WITNESS HISTORY.
2:40 am
So perfect, lose yourself started playing. life really is a movie huh, trynna figure out what I wanna work on right now...
3:16 am
So basically this was my dillema; which i basically asked chatgpt:
yup that's the point, day 6 should be legendary... so since it's like 2 am and whatnot i thought the best thing i could work on right now (since i can do math when im fresh only lmao) is programming... So you know already, first I wanna build a view counter, then a comment feature, and then an IP Map thingy... the thing is my aims are kinda two fold, or like i have a few things i want you to think about when suggesting the plan... 1)first is, i wanna get this shit done today... 2) secondly, yk im learnmaxxing. like the point of doing this shit is via building small projects i wanna learn programming... i know basic php right now (ch-2 of that novice to ninja book) So basically tell me what's the best way for me to proceed right now, basically i want a path to building this feautre thats like a) kinda generalisable, like for example, my whatsapp bot projectusing selenium was kinda useless cos selenium is kinda useless, so like dont tell me a random view api and i spend time learning that api and in the end all i know is how to make a view counter, no actual skills b) on the other hand, since i do want to get this done today, i actually wanna build stuff soon, so like dont tell me to go read this 2000 page book and then I can build a view counter, then read 2k more pages and i can build comment etc... Please think about this carefully and answer... This is the start of a wonderful journey
o3 just said a bunch of bullshit, so i used the deep research thingy, it asked me three question:
1) am i open to sqllite instead 2) am i using vps on my mac approach 3) do i wanna write javascrip code myself too?
my answers were:

Deep research seems really cool, its just thinking right now... while its thinking, lemme read the AI book (Norvig Russell) {cos im somehow taking COL 333/671 w/ prof Mausam} this is btw the first time im kinda excited for a class, the prof is actually cool, and this might be the perfect startupy CS topic (no. 17 on 60 day :D ) and I really feel like AI could be the thing I dedicate my life to, and if it is, I will actually change this field forever. I’ll say more about this I think later on in this blog... but yeah im just going to read the book till Im bored and wanna get back to roleplaying as ZUCK :)
Reading ch-1 rn, “The quest for “artificial flight” succeeded when engineers and inventors stopped imitating birds and started using wind tunnels and learning about aerodynamics. Aeronautical engineering texts do not define the goal of their field as making “machines that fly so exactly like pigeons that they can fool even other pigeons.” lmaooo
dang its kinda tough for me to read non math texts man, cos i just keep re-reading ts cos i dont know if i read it or just read it if that makes sense. ill get better tho
3:53 am
Well, just read the first section, 1.1 is complete.... very interesting... things like these really really excite me so much, cos like i just get excited cos im following the mony method (go read this blog, i will have re-written this to actually say what it is by the time this blog post is up) like this excites me so much to go read the probabilistic method, maybe read dynamic programming by bellman ford, watch additive combo yufei zhao in my freetime; just think of new things and new ways and question every decision, this is so fun, so exciting man... ahahahahha lets go, im living the dream life yay
4:09 am

bruh philosophy actually seems just retarded to me. my philosophy is I can achieve everything, and since everyone is like me, anyone can achieve anything, you just gotta want it and then go get it. and if you disagree, you can come suck my dick bitch.
4:15 am
ahh ive heard of computable so many times, it kinda makes sense now,.. “Turing also showed that there were some functions that no Turing machine can compute. For example, no machine can tell in general whether a given program will return an answer on a given input or run forever.”
so i mean i guess a good exammple is just the length of collatz orbit.
I will study this in more depth soon, computability and logic both seem interesting... dang so much stuff to do,,, exciting stuff :D
4:32 am
hmmm i really really do not understand how to read this part of the text lmao... ig ill just read through, and in the future if it causes some problem, ill get back to it, cos like trying to understand everything is just taking tooo much time, i wanna get to the mathhhhhhh
btw im also so excited to learn game theory, and stuff like thatttt woohoo... oliviu calin or smthng deep learning, compression, information theoryyyy, so much exciting stuff brodie lets get it
4:42 am
“Futurists make much of these numbers, pointing to an approaching singularity at which computers reach a superhuman level of performance (Vinge, 1993; Kurzweil, 2005; Doctorow and Stross, 2012), and then rapidly improve themselves even further.”
this actually seems true, i mean i was thinking about this the other day, cos ai is now imo gold level, by the end of this year, i will be more than imo gold level too btw (42 in 25 ;) )olympiad blog post but yeah i need to become very good very fast, cos if the best models are smarter than me, theres really no point right... i need to be succesful before that happens ;)
4:58 am
Section 1.2 finally complete... noam chomsky huh, i used to hear his name all the time when i was obsessed with aaron swartz... anyways, this was prolly a waste of time lmao.. lets get back to programming :D deep research is prolly over lmao... mony playlist on shuffle again, i was debating going on a scooty ride, but i just feel like workinggggg, lets get it... so excited to read the roadmap!!!
5:02 am
yup here it is, deep research is completeeee. if after reading this blog, y’all wanna learn how to learn all this stuff in one day, or are just curious, check out the report... this technology is seriously so cool damn.
5:10 am
hmm ok perfect, i read the view counter part of the report... literally perfect... it understood exactly what i was trying to do:
“General approach: Store a counter in the database and update it on each page load. We’ll keep it very simple – no unique visitor tracking, no IP filtering (so if someone refreshes 10 times, that’s 10 increments). It’s essentially a page load/hit counter. This simplicity means you can implement it fast, and it’s a stepping stone to understanding database operations in PHP.”
literally exactly what i wanted man... im actualy so inspired by this wow man...
So i guess the first point of order is to understand MySQL by reading a couple chapters of novice to ninja ... before that tho, im going for a small scooty ride, cos i mean the point of life is to have fun man. in two weeks when i come back to meerut, ill go on this exact ride and reflect :D right now tho, just have funnnn
btw a couple tangents, i just changed my ig profile pic to this, cos i really dont give a singular fuck about my loooks now.

and secondly, i just found out in j cole’s verse on ‘a lot’ he was talking about markelle fultz man... damn thats crazy.
5:49 am
Yay im back, got so many cool ideas while scootying. just enjoying the ride, and also excited about how much i wanna get done today!!! and making this blog and day legendary haha... rn i gotta unfortunately pack for college but yessirski life is perfect, just keep this goinggggggg... 2 weeks, when im back in meerut again ill have done so much lol. infact ill have done so much before sleeping today but i digresssssss...
9:26 am
lmao something really funny happened this morning... so yk how i started studying norvig’s ai book today right... well while i was leaving for college i found and put on a very amusing shirt...

then when i was in the car, i remembered that when i was in high school, i remember reading about this google or meta researcher who wore funny shirts, and i remember thinking it was quiet funny...

lmao this is a crazy coincidence. is it a sign that ai is going to be a really fun part of my lifeeee... hmmm maybe maybe not, it is funny tho...
anyways, now im back in my college dorm room, ig i slept for some time in the car, let’s get back to work then... confidence hoodtrap remix playing
aima book!!! just have funnn...
9:37 am
wow yann lecunn has a turing award?! btw the word encode seems really cool to me idk why... i’ll rediscover gray coding 1000% when doing diestel pretty soon lesgoo... now just focus focus focus focus focus focus ok.
10:19 am
couldnt really focus, fuck it... moving onto chapter 2... i think imma save all the papers they mention in chapter 1 and read them, idc how old they are. im trying something no one ever has lol.
10:48 am
watched this on loop a few times... Section 2.1 is complete... I mean I guess the only useful thing i learned here was, an agent is something that can preceive things and act on them... so you get a percept sequence, and then you can make a decision based on that sequence. You can represent the agent by either a tabular form, in which given every percept sequence you tell me what its action was, or you can just tell me what the agent does as a program... lets go to this class now :D
11:05 am
lmao im in my ai class dressed as peter norvig, this is funny asf.
7:48 pm
I had slept directly after class, when i woke up I had messages from Muskan didi and Manoj bhaiya (BlocSoc presidents)... Manoj bhaiya told me to register for the mumbai hackathon

i mean i guess why not, just free will maxxing right... so rn im reading bitcoins whitepaper and avalanche consensus. lesgo, i got like 2 hours for this. mushroom ridge final lap music playing haha this is cool
9:30 am
Wow i just spent the last hour and half reading the bitcoin whitepaper and avalanche consensus docs... this was actually sooo interseitng. i had no idea it would be this cool lmao.... i understand their random sampling consensus very well now i think.... lots of interesting math going on here, i think ill sit down and work out the math soon too, very cool, i mean the main point that i understood by the way was this: (mainly reading docs and chatgpt’s help...
so ig the point is all 10 ppl sample together, like curerntly these 10 ppl are going to be in a state, say its (0,0,0,1,1,1,0,1,1,1); then according to what subset they choose, we'll have a new state, like say everyone sampled the 4 guys next to them including themselves (so the guy at first pos. samples 1,2,3,4 and obv mod 10, so guy at pos 8 samples 8,9,10,1...) then we reach a state: say alpha is 0.51 btw; (0,0,1,1,1,1,1,1,0) ... then you'll do this again and so on, so i mean say beta was just 1, so then things at every pos except 3,7,10 (cos they changed pref) are now fixed on their decision, only the 3,7,10 guys will sample now right? and then ig also till what time do we do this? till everyone says 1? like is that consensus?
i mean yeah this example i thought about made everything clear to me... crypto is a very interesting field too damn... i mean all of this shit is just math, and im great at math so i can really decide to work on whatever i feel like working on, so many interesting choices... just work all day man.
btw this felt soooo good, just listening to mario kart music understanding math wow, literally the dream life :D...
the ai class w/ mausam sir was so much fun too btw... life is just perfect, i can just sit and do math cs and programming stuff all day, what else could i ask for....
we locked in twin :D and life is so good when youre locked in haha. less sleep wtv doesnt matter, the only point of every moment for me is to just do cool shit woohoooooo (can you tell im excited lmao, cos i found another cool thing that i could dedicate my life, well the next few years, too haha)
2:23 am
Well this presents an interesting dillema btw... i met muskan didi and talked about cryptography for a while, then I went to the crypto club meet where Manoj Bhaiya was talking about some blockchain stuff... I mean like going to hackathons and speerdunning stuff and like going to mumbai etc would be fun right... Maybe I’ll learn stuff too. but the problem is then I’ll just be like everyone else who goes to hackathongs and builds stuff. The differeniator for me has got to be the Mony Method right, like I deeply learn stuff, and all that... I think I’m going to stick to this then... and do this my way... ik it takes conviction, but i mean obv i have that in loads lmao... im gonna write the mony method blog post now and then go to sleep for a while...
4:17 am
I wrote the mony method blog post... this is it man. good night, lets wake up and get right to it.
Mony Method.
the decision is made man, go live out our dreams.
12:37 pm
We just woke up, I’m straight away getting to work, gonna atleast set up mysql before even leaving my bed hehe... got some cool hackathon news
7:58 am 9 August
At night I was reading Algebraic combo on words by Lothaire (interesting name lore btw), like i’ve been very sick so I was moreso just skimming through really. I didn’t really get much done cos I was going on IG or youtube and whatnot in the middle, but yeah while I was lying on my bed skimming the book I was suddenly like wtf, this is it.
Like I understood how I’m going to make really fast progress; ALL DAY.
ok so like basically I’ve imagined my life as this anyways but I really thought about it and was like yeah… but what does All DAy mean?
like yeah I’m going to work really hard, but like when I’m bored, I’ll go and skim a math book, or a CS book, or maybe a paper, when I’m tired I’ll maybe code something, or do an Olympiad problem, but the point is to do *something* math related all day. I know I started the day w/ the decision that changed my life but I feel like really this is THE small piece that will actually change my life…
Like yeah, im sleeping now, will wake up, im at mummys house, got a car too, just me alone in the house, perfect, gonna do *something* all day, along w obv lots of really focused work, thats a given, no time to waste man, and yeah that means like I guess no internet tomorrow? well, that’s fine w me… I wrote that messsage to Sagnik btw… I really can’t falter today man, I even posted an ig note haha, lets go get it todayyyyyy woohoooo!!! so pumped for this man, 9 August 2025. special.

wrote this while listening to ‘little child running wild- curtis mayfield’
life changing frfr, just do it then..
4:13 pm
I woke up at 3ish, could really sleep again, so i decide yk what, fuck 8 hours, when i wake up is when i’m fresh. yuh, so now w/ the basics out the way, we back to work, imma decide what i wanna study and then study that :D
Ok I have decided I feel like doing apostol analytic nt, im at ch-3, finally one of the most inspiring parts of math for me is starting, averages of arithematical functions, lesgetit then.
5:19 pm
Dang, my eyes were paining etc, just feeling sleepy, so it took me so long to prove Euler’s summation formula,

which is actually supposed to be so simple… I lied down for a while, watched some of my old videos, and I was just like, no time to waste man, bad health, sleepy wtv doesnt matter, do something, so yeah lets do somethinggg woohoo.
5:43 pm
just ate a brownie and sandwhich while reading Vitalik’s blog post on ZK-STARK, adventure of a lifetime playing, back to math ;)
11:59 pm
I think I studied some more time, but I’m like genuinely sick, so I just went to sleep… I woke up just now, ordered food and now I feel so fucking fresh and excited woohooooo letsgooooo man… I woke up and was like perfect, math all day let’s get it then bro :)
12:46 am

Well I just proved all these 4 results myself (like I had hidden the answers w/ that red thingy and then I proved all these myself… also I figured out how to add latex to my blog, so yay!
ok but the cool thing here is, how you can find some constants, like when we’re doing part a), you can easily get
$$ \sum_{n \le x} \frac1n = \log x + [1 - \int_{1}^{\infty} \frac{t-\lfloor t \rfloor}{t} ] + \mathcal{O}(\frac{1}{x}) $$
Then you can just call the thing in the square bracket C (cos its bounded ofc) and then just say as $x$ becomes large, you straighaway get that $C=\gamma=\sum_{n\le x} 1/n - \log x$ (euler maccaroni (yum!) constant)…
I mean yeah this is a cool technique… I also independently proved that the thing inside square bracket is $\gamma$ btw.
Also my taco bell and blinkit order had come, so I just ate the cinnamon chips (so good lol) while doing this…. woohoo this all day math thing is actually fun man, lets keep going, imma read something while eating something now… also this latexing takes too much time, I don’t think I wanna waste timme doing this, sorry lmao.
One problem btw is I had brought a finite amount of A4 sheets w me to mummys house, cos I was pretty sick so I wasnt sure how much I could do, so at some point I might run out of paper lmao… So I’m writing a page and then immediately erasing everything on that page from now….
Ok man Also, This is so good, this is literally my dream life, like this is literally my dream, just me alone in a house, doing math all day, like cool food drinks w me, just me alone at a table just studying cool shit and locked in and becoming the best right, so dont forget to enjoy it also :D.
2:18 am
it’s interestng, i dont feel particularly excited or inspired right now, but i guess i just gotta keep studying, and see how i will feel in the night… i opened ig and looked at a few peoples stories, and yeah man i just gotta be the best ever.
2:36 am
wow wtffff, i am literally the best ever nigga woohoohohoho wthelly…. I just proved (d(n) is the divisor function, number of divisors of n)
$$ \sum_{n \le x} d(n) = x \log x + (2 \gamma - 1)x + \mathcal{{O}}(\sqrt(x)) $$
The standard way to do this is something called the Dirichlet hyperbola trick, but since I’m following the mony method (seriously go read it haha) I wanted to prove this myself.
So my method was, obv first use double counting to see the sum is just $\sum_{n \le x} \lfloor \frac{x}{n} \rfloor $ and then i split this into normal part minus the fractional part, and using the bounds we’ve prove above it sufficed to prove that $\sum_{n \le x} \{{\frac{x}{n}\} = (1-\gamma) x + \mathcal{{O}} (\sqrt{x})}$
So I split the sum into $n \in [\frac{x}{k} , \frac{x}{k+1}]$ and then we only need to go till $k=\sqrt{x}$ cos after that the range is less than 1, and it’s ok cos the error we get is just $\mathcal{O}(\sqrt{x}$) anyways, and yeah then we for the kth range, we get $\frac{x-kn}{n}$ and then just use your brain and we’re done!!!!
Wait was this just the dirichlet hyperbola trick in a new phrasing??? idk lol wtv this was an independent proof and that’s the point, and now imma go read Apostol’s proof.. I felt so inspired and Happy the moment I proved this, like I was on top of the world, but then I scrolled down and saw this

haha people are proving such advanced things in 1922, i really have such a long way to go still… lets keep working then man… btw A head full of dreams by coldplay, what a fucking album, so inspirational man, every song. ate a couple churros, lets go back to work… I guess when you’re working, I shouldnt stop to write blogs in the middle of it right, I’ll write blogs when im bored and tired or wtv, cos i need to go FASTTTTTTTTTTTTT
3:55 am
wtv man, its just me and my mind. this world is mine.
5:37 am
well, we’re finally doing this shit…
listening to logic’s suicide song on loop, I found $\sum_{n \le x} \sigma_{\alpha} (n)$ for all possible $\alpha$
I have wanted to do analytic number theory for so long, and now im finally doing it… i remeber being in school looking at tough olympiad problems thinking I wanna study analytic nt and use advanced theory for these problems, little kid in lucknow man, maybe gurgoan too… and now im doing it, just work. yessirski lets just work…
Im very excited and happy again, what do i feel like studying rn then…
I guess let’s just complete ch-3 of apostol right, perfect mix of fast progress and some thinking, like perfect for my exctied mood right now woohoooooooo
btw im happy that im working hard but agian this is just a prereq to getting what you want, have more urgency bro. lets go have fun, just be the best ever…
listening to BOSS BATTLE Mario Kart DS song
5:52 am
Well, I got the
$$ \phi(1)+\phi(2)+\cdots \phi(N) \sim \frac{N^2}{2\zeta(2)} $$
result pretty easily by thinking about the probability two numbers uniformly chosen in [1:N] are relatively prime… now how do we get the exact analytic bound hmmmmm…
switched to TITLE SCREEN MUSIC
3:33 pm
Well I had just slept last night, good morning, lets get back to work… my health is completely fine now!
3:45 pm
Prfect, just got the result
$$ \sum_{n \le x} \phi(n) = \frac{x^2}{2 \zeta(2)} + \mathcal{O}(x \log x) $$
And I did this by rewriting the sum as $\sum_{a \le x} \mu(a) \sum_{b \le \frac{x}{a}} b$ and then using that $\sum_{n > x} \frac{\mu(a)}{a^2} = \mathcal{O}(\frac{1}{x})$ and that $\sum_{a \le x} \frac{\mu(a)}{a} = \mathcal{O}(\log x)$ phew thats a lot of latex
I remember when I was speedruning c++ I used to tell myself I know latex, which is jsut a programming laguage so oyu can learn c++ fast too, and I mean it worked, I became top 60 (or even better) off like 2 weeks of focused work… so the thing is when I focus I improve soooo quickly, I remember feeling like day before inoi, i learnt soooooo much stuff in one day, i remember feeling wait if ijust do this every day, i will literally be the best ever, and that is the truth… so let’s just do that every single day…. btw someone had come to kill the wasps near our window, and it’s 4 now… lets work woohoooo!!!!
btw the fact that $\sum_{n \ge 1} \frac{\mu (n)}{n^2} = \frac{1}{\zeta(2)}$ is interesting, I found the proof by looking at it like $\prod_{p \ \text{prime}}(1-\frac{1}{p^2})$ and then noticing $\zeta(2)=\prod_{p \ \text{prime}}(1+\frac{1}{p^2} + \frac{1}{p^4} \cdots) = \prod_{p \ \text{prime}}{{\frac{1}{1-\frac{1}{p^2}}}}$ and you’re done woohooo
lmao i just love writing in latex, sorry no more time waste haha (4:15 now)
4:23 pm
welp I guess I found my next challenge… PNT here I come :D


interesting….
one more thing is i need to be much more consistent, like when i just did apostol chapter 2, all of this stuff was so much more fresh in my mind, if you keep going in a flow and are consistent w it, we wont need to waste time revising the stuff we have already studied (boringggg) and we’ll make much quicker progress … 448 lets get it
5:59 pm
lmao sometimes i forget to just be in the moment damn… man just have fun right, youre literally living your dream and achieving everything you ever wanted right here… in the name or urgecny, I prolly have a blockchain club meet tonight, im still at mummys house, so before taking an uber for college, I wanna complete apostol ch-3, cryptopals as many sets as i can, crypto 101 block ciphers chapter… hmm lets get it…
6:22 pm
Ok this is very clever, we can prove $|\sum_{n \le x} \frac{\mu(n)}{n}| \le 1$
The way to do this, is first using the generalised convolution we had seen, we can prove, if you let $\sum_{n \le x} f(n)$ that
$\sum_{n\le x} \sum_{d \mid n} f(d) = \sum_{n \le x} f(n) \lfloor \frac{x}{n} \rfloor = \sum_{n \le x} F(\frac{x}{n})$

So when you do this for $f=\mu(n)$ you get $\sum_{n\le x} \mu(n) \lfloor \frac{x}{n} \rfloor =1$
So we're almost done at this point, rewrite the sum as
$x\sum_{n \le x}\frac{\mu(n)}{n} - \sum_{n \le x} \mu(n) \{{\frac{x}{n}}\}$ where {.} is ofc the fractional part...
Then you know this is 1, so you get
$x\sum_{n \le x}\frac{\mu(n)}{n}=1+\sum_{n \le x} \mu(n) \{{\frac{x}{n}}\}$
I mean i got to this point pretty easily, this is where you gotta be a lil careful technically tho, abs value of rhs (by triangle inequality or wtv is at max
$1+\mid \sum_{n \le x} \mu(n) \{{\frac{x}{n}}\}\mid = 1 + \{{x\}} + \sum_{n > 1}^{x} \{{\frac{x}{n}}\}=1+\{{x\}}+\lfloor x \rfloor -1 =x$ so dividing by x you get absolute value of that term is atmost 1… gg
Wow I feel so good writing latex, like I guess it’s jsut practice man, so if you practice with any language, you’ll become this good at it… its literally just that, you know you’re smart so just go do it man, you can be the best programmer too woohoo…
7:30
meet is at 8:30 hmm, lets see, work non stop man :D
3:18 AM 11 august

it’s really it man. lets’ go then.
im stuck on this really tough analytic nt problem, i really cant figure it out or think about it rn at all..
let’s just do cryptopals right now man, idgaf.
just trust youreslf and trust the plan, i can do anything. its time to do everything then