Boy, I wholeheartedly disagree with this! I enjoyed Geometry the most of any math class I took and do still remember a lot of it, but I am in no way, shape, or form math major material! Geometry was probably my favorite math class, but I can’t remember a thing about Trig or Calculus — so not for me.
Geometry is divisive. Both my kids dislike math, but my super duper artsy oldest liked Geometry better because of the spatial aspects — works well with art, but my D22 hated it and found it worse than other math courses like Algebra.
I think sometimes people who are artistically gifted and who can visualize an object and manipulate it in their mind (something like flipping house plans in their mind’s eye) tend to enjoy Geometry more because it deals with more shapes and their brain already works that way.
I would put it a bit differently. I view going to great schools as potentially allowing you to get away with a bit less in terms of putting in the “hard work”. In other words the name and reputation of a super-elite school can count for quite a lot in your job search and career. But that’s only if you are good enough to still be seen as effortlessly brilliant, including by your professors.
The most talented people I knew in undergrad were able to do their work sufficiently quickly that they could then do other things with their time that made them stand out even more. In his spare time my closest friend redesigned the university newspaper, did original chemistry research, wrote for the Economist and ended up writing a textbook on financial mathematics.
It probably helped that we all did math, which is very conducive to problem sets that are quick and easy for the best students. I was lazy and switched to math because it was far less work (from chemistry which had been my first love - my parents gave me a high school chemistry textbook when I was 7 and I learned it all and tried to do the experiments at the kitchen table). And I probably spent as much time rowing crew, founding and running clubs to do various outdoor activities and going on expeditions to obscure mountain ranges during my PhD as doing math (which mostly I did in bed and in the bath since it was purely theoretical): another friend who is now a famous professor told me “you need 2 hours of inspiration in 3 years to get a great math PhD”.
I certainly worked hard in the first few years after college, which was the first time I’d ever done an all-nighter. But at least for me that was the first point at which quantity of work mattered as well as quality (since usually there was an unlimited number of extra projects you could take on when you’d finished the first task). So I’m glad I picked a line of work that still fascinates me, though I’ve generally opted for more interesting choices that are more about thinking than hours worked, instead of options that would make the most money but require excessive dedication to specific companies or working in less interesting areas.
And in common with @shawbridge my PhD has counted for a lot in terms of first impressions with potential new clients/employers even though it’s not useful for anything I’d do for them, simply because hard STEM PhDs for famous professors at top universities are of huge signaling benefit.
The ability to visualize abstract multi-dimensional concepts is key to most truly gifted mathematicians, especially in pure math. Books like Gödel, Escher, Bach (Gödel, Escher, Bach - Wikipedia) which link art, music and math are cult reads amongst mathematicians for a reason.
Interesting! I don’t have that ability at all. I hated geometry, ha. I loved trig and calculus. I wish I had known it would have be helpful to visualize things in 3D as a structural engineer. Oh, well. I’ve trained my brain to figure it out.
It’s just the way my brain works, but I’m definitely not gifted at math. I work as a graphic/web designer, though, and that mental shape manipulation is useful there. I can freehand with a fair amount of precision. I place the element and then go back and make sure I did it right, but it’s usually pretty close.
I remember absolutely zilch about Calculus and am lucky I made it through that class in college. For my second math requirement I took “Philosophy of Logic”.
And yes, my mathy brother likes Escher and that sounds like a book he probably read when it came out. Escher was not really my jam, but I found him amusing when I was in my teens. We had some of those big coffee table books I would look at.
To me this rings true. Had I taken a different path when I was younger, my life would have been different. Can’t say it would have been better or worse. Of course you can imagine ways in which it could have been better though no control group (just like with kids) so you just do not know. Pick a path and make the best of it. And don’t ever look back. LIfe’s too short for that (unless things don’t work out and then you need to re-evaluate and learn).
Worked with an attorney who blamed all of his ills in his life on his parents holding him back from kindergarten. At that point, it was 25+ years in his rearview mirror. Another friend who blamed his problems on his parents not sending him to local private academy for high school (where his parents taught). But he did his undergrad at Notre Dame. Just made choices while there that didn’t pan out (though knowing what they were, its a struggle to see how huge success was in the cards). At some point you need to move past excuses.
Geometry isn’t about calculating some length or degree of an angle. Teaching these and other so-called practical uses of geometry is what’s wrong with many HS geometry classes these days. Geometry should be about developing a student’s ability to visualize, to imagine, and to think logically and rigorously. Being a good measure of a student’s mathematical aptitude doesn’t mean that it is loved by all. On the contrary, it’s more likely hated by many for that reason.
Ah, but that’s what I’m talking about — at least the first two of those. Visualization and imagination come easy to my oldest and pretty easy to me. I think my oldest would do well on a spatial intelligence quiz. My younger kid’s brain doesn’t work quite the same way.
I’m sure spatial intelligence is very helpful for mathematicians, but it also helps with other professions and everyday life (I have a good sense of direction). I don’t think that doing well in Geometry means that a HS student should consider majoring and pursuing a career in mathematics, but maybe doing poorly in Geometry means they should give that trajectory another think if that’s what they were planning on.
As a non-math person with two very, very non-math kids, at least two of us thought Geometry was relatively easy.
At times I will look back at critical forks in my road, not because I have any regrets, but just musing what-ifs. Then I circle back to one of my favorite short stories by O. Henry, “Roads of Destiny”.
I was good at geometry, but what interested me about it was the proofs. I loved being able to create a chain of logic to prove something that at first glance seemed unprovable. I was sorry that the version of geometry my kids got had much less of this and it may be part of the reason why computer programming ended up appealing so much to my older kid as the process is similar.
Yes, proofs are integral part of geometry. Any geometry class that doesn’t teach proofs probably isn’t worth taking. Computer Science has a lot of similarities with math. Some CS theory courses are really math courses in different names with heavy use of proofs. Programming is much less theoretical but still highly logical. It’s not a requirement for all programmers, but the best ones can figure out the most optimal algorithm to solve a given problem.
I’ve thought about this a lot. I’m very happy with where I landed in my career, but have often wished I had chosen a different kind of college experience.
I went to a very large state school with a reputation for partying (and no big academic rep to match). I was a “good kid” in high school, so I fell off the deep end with the party scene when I was a freshman and sophomore. None of my friends were all that committed to learning and we didn’t have those wide-ranging intellectual conversations about politics, history, literature, etc. The Greek life was very strong and I joined a sorority during the second semester of my freshman year. I suppose that led me to focus quite a bit on my social life, and it also stoked insecurities about my body and attractiveness in a way that lasted years after college was over.
However, once I found my passion in my major, I learned to hustle. I got great grades and found several internships. I spent a lot less time partying. I studied abroad my junior year–and I got to spend some time reading, going to museums and traveling. It was by far my favorite college experience.
That said, it was the hustle and passion I put into my major, along with those internships, that landed me my first job in my field. And I continued to grow from there, moving to NYC for a decade, moving back to CA with my husband and family, and now working in a role that uses my skills and experience in an interesting way that I find very fulfilling. I traveled internationally quite a bit before the pandemic, and I genuinely enjoy my work and my colleagues.
So – in retrospect, I’m grateful for the experience I had. I’m stronger for it. But if I could go back and choose again, I would have picked a smaller, more personal undergrad experience that reflected my “inner school nerd” and not the big, bright party scene. But then, I don’t know what direction my career might have gone.
@OhiBro, I’ve been out of the hedge fund business for quite a number of years so I’m less clear on how hiring is done. My impression is that a number of quant funds have math tests as a starter to interviews these days, but I think other folks on here would have a better sense of how those firms are doing their hiring.
I assure you that my inability to study mathematical proofs had zero effect on my ability to think logically or problem solve. These are considered by my partners to be two of my greatest skills. It sickens me to think I could have been deprived of my career because I have no math skills. There are many ways to build logic and problem solving skills. Insisting that math is the only way is terrible for people like me.
Imagine if we told people who had a disability that prevented them from participating in sports that they couldn’t go to business school because business school is about working well in teams and nothing builds team building skills like sports. Oy
Oh, man, the STEM obsession. I fought it for a while, then shrugged and said fine, be that way, I’ll be employed till the end of my days doing the work you deliberately stopped training people to do. In recent years I notice it commands a higher and higher salary, too, meaning I can be picky about the projects I work on. You want me to work for you, better make sure those are some socially play-nice projects.
Humanities gonna getcha every time, I’m afraid. We did try to warn people about that.
Way back when, the first time I recall encountering instruction in logic and proofs (at a beginner level) was in high school geometry. But, after that, an emphasis on proofs does not show up again in math until the college sophomore or junior level courses.
The problem people like you face is that non-math logic is math-adjacent, so (in a high school level context) it is sometimes instructed in math courses but not in other courses, and (in education) math is used as a proxy for logical thinking, to the detriment of people like you. At the college level, instruction in non-math logic exists (e.g. philosophy), although it may not be as widely chosen.
Some colleges (e.g. Harvard, as revealed by the admissions lawsuit) appear to overweight the importance of athletic ECs over other ECs (even for those not recruited as athletes). So what you imagine may have real life analogues. In addition, there was a business article some years back about how lacrosse players seemed to be favored for Wall Street hiring.
“At the college level, instruction in non-math logic exists (e.g. philosophy), although it may not be as widely chosen.”
It was chosen by me! My SLAC allowed for the math requirement to be completed taking PHL XXX “Intro to Logic”. I was thrilled to not be in a math class ever again and then wowed by how hard that class was. Probably one of the best choices I ever made and it was done out of sheer will to avoid.
