Summary of My Own Math Journey

by Justin Skycak (@justinskycak) on

Grinding it like a video game, running a secret self-study op inside traditional classes, taking talent development seriously while making every rookie mistake, and how it unlocked a life I almost certainly never would’ve found otherwise.

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Summary of my own math journey:

  • grinding it like a video game,
  • running a secret self-study op inside traditional classes,
  • taking talent development seriously while making every rookie mistake,
  • and how it unlocked a life I almost certainly never would’ve found otherwise.

$>$ middle school kid in indiana
$>$ likes math but only does what’s covered in class
$>$ algebra 1 in 7th, geometry in 8th, good grades

$>$ sent to parochial high school for “better education”
$>$ algebra 2 in 9th, obv precalc next
$>$ private school accelerated math track is weird af
$>$ “our top students do geometry in 10th, just take it again lol”
$>$ fight admin to get into precalc
$>$ head of math gives me trig/precalc workbook packet
$>$ intended to demoralize me but i think it’s a challenge
$>$ work through half of it in 2 days, hundreds of problems
$>$ write in pencil all over his master copy
$>$ hunts me down across campus
$>$ “WHERE ARE MY NOTES”
$>$ has to erase 50 pages of my pencil work
$>$ “ok this kid is actually doing the work & solving problems correctly
$>$ …fine you can take precalc in 10th as long as you take geometry again too”

$>$ summer after precalc in 10th, calc next year
$>$ always been low-key interested in sci-fi & astrophysics documentaries
$>$ always thought those ∫ and dy/dx symbols were many levels away
$>$ holy shit that’s the math i’m learning next year?!
$>$ can’t wait, wanna learn it now
$>$ fck it, imma self-study
$>$ find free online ap calc bc course
$>$ hole up in my room grinding calc problems most waking hours
$>$ learn it all in ~4 weeks
$>$ realize school pace is comically slow
$>$ math is better than videogames
$>$ infinite progression, infinite worldmap
$>$ you keep your skill equips in real life
$>$ parents confused but allow unlimited screentime because it’s math

$>$ now addicted to math
$>$ wtf comes after single-var calc
$>$ i need it now
$>$ discover mit ocw
$>$ grind linalg, multivar calc, calc-based physics rest of summer
$>$ oh shit, school’s starting, how do i keep learning
$>$ guess i’ll just self-study during school
$>$ calc-based prob/stats, more physics, some diffeq
$>$ sneak self-study math contraband into all classes
$>$ participate just enough to keep it don’t-ask-don’t-tell
$>$ “justin never looks like he’s paying attention
$>$ …but he answers correctly when called on
$>$ …eh whatever”

$>$ high school actually has one great thing
$>$ research class
$>$ cold-email professors, set up research project, do science fair
$>$ join dark matter detection lab in 11th grade
$>$ improving signal propagation in a bubble chamber
$>$ experimental physics not my fav but it’s still great
$>$ honestly not using most of my self-study math in lab
$>$ but serious physics knowledge is huge advantage with science fair judges
$>$ finalist in intel international science & engineering fair
$>$ mind blown how far life jumped in one year

$>$ think i’m hot stuff
$>$ i should do original math research
$>$ pick partial fractions as playground
$>$ can I get a general formula for the partial fractions decomposition of a rational function?
$>$ work on it entire summer
$>$ compile tables of concrete examples, identify patterns, prove formula for subcase
$>$ later realize my “discovery” is made trivial by residue method in complex analysis
$>$ hard lesson learned

$>$ fall back to another experimental physics project in 12th grade
$>$ improving signal propagation in a particle accelerator
$>$ bring partner along for fun
$>$ teacher warns “don’t, it halves your chances, funding sends kids not projects”
$>$ do it anyway because teenager brain
$>$ project is good but not 2x good
$>$ doesn’t even make state
$>$ hard lesson learned

$>$ mit ocw gets thin for real analysis & abstract algebra
$>$ go straight to the actual books
$>$ apostol for analysis because “serious math”
$>$ theorem-proof-theorem-proof
$>$ concrete examples are for babies
$>$ git gud at symbol pushing under logical constraints
$>$ weak intuition for tangible meaning of theorems
$>$ hard lesson learned

$>$ more ups and downs
$>$ fumble dream college apps :(
$>$ full ride to hometown uni :)
$>$ spin wheels with more unfruitful research :(
$>$ done with two-thirds of degree after 1st year :)
$>$ lose interest in pure math :(
$>$ summer intern in los alamos :)
$>$ lose interest in academia :(
$>$ data sci intern 2nd year, full-time thru 3rd/4th year taking bare min courseload :)
$>$ lose interest in data sci :(

$>$ been tutoring math 20h/week since highschool, love it
$>$ fck it, imma graduate move to big city & tutor
$>$ goin wild doin all sorts of math ed
$>$ years pass
$>$ can’t do this forever, unclear how to monetize, wtf is my future
$>$ actuarial exams look appealing, maybe i do that
$>$ feels like settling
$>$ but idk what i’m holding out for

$>$ been helping out w mathacademy doing algo/quant coding
$>$ got the opportunity bc background in datasci & math ed & helping w other mathacademy stuff
$>$ completely aligned w mathacademy philosophy
$>$ not a stable situation, no customers, bootstrapped
$>$ but lemme see where this one last thing goes
$>$ takes longer than necessary bc i’m shoring up weak software eng chops
$>$ but first time in my life i got rly gud guidance
$>$ we grinding for years but things coming together
$>$ finally make it
$>$ nothing i’d rather be doing

$>$ ok get to the point unc
$>$ final takeaway
$>$ self-study is major life accelerant
$>$ helps you find your place before walls of time close in and force you to settle
$>$ self-study didn’t just teach me math
$>$ didn’t just get me internships/jobs
$>$ it bought me time

$>$ but i spent lots of that time crashing into walls
$>$ almost settled for something other than a dream
$>$ despite going harder than anyone i knew
$>$ efficiency matters more than you think
$>$ even if you’re going hard
$>$ many people put in the work
$>$ but don’t find their dream
$>$ due to lack of efficiency

$>$ longterm goal
$>$ build the machine
$>$ thermodynamic engine
$>$ convert work into skills
$>$ as efficiently as possible
$>$ thing i wish i’d had
$>$ obsessed with building it
$>$ core motivation behind what i push for in mathacademy

(discussed ~1:22:00)


Follow-Up Questions

Q: Do you grind research level math now in your free time or you’re content with your current level & not as obsessed with math as before?

A: Currently I have very little free time (I mean that in the “good problem to have” way), so I’m focused entirely on Math Academy.

But it turns out that often requires developing theory about knowledge graph geometry, custom graph algos, and “good enough” practical solutions to research-level problems, so it scratches my itch.

Can’t go into too much detail on proprietary stuff but I occasionally write about it at a high level, will post a few links if interested:


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