At my first math competition in 2011 I was able to only answer the following question:
"How many great-grandfathers do all your great-grandfathers have in total?:
Needless to say I didn't get past that first round.
A year later I came across a notebook from a former math competitor from which
I learned how to mimick proof writing.
That notebook got me past that first round after which I met the person they called "Sef"(Shef).
With his guidance I passed all the way to the state competition where I fell short.
In 2013 I passed the state junior TST and got my first bronze medal at the Junior Balkan Math Olympiad in Turkey.
Two years later I passed to the International Math Olympiad and got my first IMO bronze medal.
Two years later I went to my final International Math Olympiad in the beautiful Rio de Janeiro,
winning my third bronze medal. It was here that I realized how beautiful
this opportunity to do math competitions is.
My bronze medal got me into an Ivy League school which I started in September 2017.
In September 2020 I decided to start Shefs of Problem Solving to, among other things, give you a roadmap from 0 to the IMO.
Now I decided to take it a step further by introducing Shef's Scholars.
Over my time as a math competitor, I've learned a lot about what it
takes to get to and perform well in math competitions.
I've talked to a lot of competitors about their thinking,
trying to see if there is an algorithm for solving problems
they have that I don't or some secret to better performance.
As far as I can tell, it's implausible to try to come up with
a descriptive universal algorithm for solving general competitive
math problems.
But there are certain heuristics or rules of thumb to follow when
solving problems like:
- exploring the problem
- playing around with
small cases
- looking for patterns in small cases
- guessing the
solution or construction
- starting simple before moving onto complexity
- being flexible with your approaches
and many more
All of these heuristics take a ton of time and practice to
truly master.
You can definitely do all the practice by yourself and get yourself to
the IMO and potentially even win a medal.
However, a mentor who has gone down the same path as you can greatly help you with the selection of practice problems.
On top of that, having a community of competitors from around the world
can motivate you to get better.
You can learn a lot about your own problem solving by talking to other
problem solvers about their approaches to problems.
Before the Internet, you would've needed to be very lucky to be born in a
place where there are a lot of math competitors around.
Today, and hopefully with Shef’s Scholars, that need no longer be a requirement
for success.