I happen to know enough math to understand that. 
Nevertheless, there are many similarities between the different fields of math: set of axioms + rules to derive from them.
Look, Iām not going to get into admissions at individual schools.
I certainly didnāt mean to offend, especially because Iāve forgotten most of the math I learned. 
I simply buy into the same theory as @ucbalumnus, there are only so many hours in the day.
I certainly agree. But college, and to an extent high school are the place and time to explore things before we get stuck with the same ā¦ math for the rest of our life.
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At least 3 of 13 are home schooled.
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I agree, but the problem is that thereās more than math. That said, my son took a numerical methods class that he enjoyed (he essentially enjoys all math) and never uses now. After he graduated he self-taught discrete. It wasnāt part of his ME curriculum even though he concentrated in mechatronics. He does some DSP now though.
I would argue that ANY math that he studied helped him later to self-study at a much faster rate. I believe that most fields of math require the same basic brain circuits. Not sure about topology though, that stuff is unbelievable hard.
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Video games have their place, though that is a conversation for another day. I have been impressed by some of the real life skills kiddo has built under the guise of āwasting his time playing video gamesā. Mostly, though, they have kept him sane (and social) during the pandemic, without getting in the way of any of his academic and extracurricular obligations.
These days esports are ginormous, the pros make gobloads and colleges are fielding teams and offering scholarships. The viewership numbers are stunning. I would wager there are plenty of math competition alums that are in the industry in one form or another.
In the industry of making video games? For sure! In the industry of playing them? Unlikely.
I wouldnāt know how to track it down, but I really do think they are there.
I say this based on two observations: (1) gaming is huge in Asia, and (2)(more anecdotally) the students at kiddoās boarding school who are the mathiest (do local competitions, 3 years advanced in coursework) are also the ones biggest into video games and are also Asian. They may not be competing at the highest level of math or gaming, but if the kids I know are representative, the intersection of competitive gaming, competitive math and country of origin is strong and well-populated.
There are video game play-testing jobs, but they are not typically considered the ābestā jobs in the industry.
And are their parents immigrants who first came to the US on graduate student or skilled worker visas? And do similar students of other race/ethnicity also have similar parents in this respect?
Not so fast. Esports!
Probably the perfect summer job for a high school student.
In my opinion esports is the worst of both worlds. Worst thing you can do on a computer (itās probably just me, but nothing is as much fun as programming on a computer), and worst as a sport (again, maybe itās just me, but I donāt see how something done sitting on a chair can be a sport, and yes, I donāt consider chess a sport).
But thatās another completely separate topic.
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I didnāt see @CateCAParent reference esports. Sorry for the redundancy.
I must say, as a summer employee, I think my dad was the ultimate. During summers in medical school, he worked as an engineer. He had a BS/MS from MIT and 7 years of experience. The dream intern!
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At anything but the highest level in which kids spend the summers is special camps and have a lot of parental pressure to dedicate everything to competition, Iād expect a large portion regularly play video games. I mentioned the math-CS correlation earlier, which often extends to other computer related activities, including video games. However, Iād expect the greater correlation relates to having a personality of generally enjoying solving problems based on fixed a deterministic set of rules, which applies to both math contests and video games, as well as things like certain types of board games, puzzles, etc. Anecdotally I used to be really in to video games as a kid and probably spent more hours on video games than any EC. If I remember correctly, I listed a first person to complete video game type award on some of my college applications
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Contestants who advanced to a very high level (before qualifying for the national training camp) in a national/international competition arenāt likely to get much further support in US HSās (with a few exceptions). Homeschooling isnāt really an impediment. These homeschooled kids were probably coached by their parents or people their parents knew.
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The state UIL math champion from our HS in my D20ās class is at MIT. She was also highly ranked in Science. Quit band early on to max out GPA in AP and pre-AP classes. Yes, Iād say MIT values math and science contest winners. She wasnāt a leader in sports, art or student council but was an academic star and well liked by peers. If MIT is filled with students like her, yes, itās a top school. Unsustainably competitive? There are other top schools to choose from.