The difference is that math is the only field of study of things that are 100% true about the universe. It's the most pure knowledge that humanity has, so it's normal people recognize it. You can read 100 philosophy books and maybe you will learn a few things that are correct among all the rambling, but everything you learn from the basics of math proof by proof all the way "up", you can be assured everything is true. There's something special about this field of knowledge that nothing else has.

In a sense even this is not true, as in any sufficiently complex (which turns out to be quite simple) formal system you can create proofs that are true and untrue at the same time creating a contradiction. In other words, mathematics works by setting up useful axioms and following up on the logical consequences, but they usually can be used to create contradictory proofs even if useful in many problems.

I recommend learning about Gödel’s incompleteness theorem behind it all.

For a pop science book that explains it nicely I recommend ”I am a strange loop”. The wiki intro is also quite good

https://en.m.wikipedia.org/wiki/G%C3%B6del%27s_incompletenes...

Math is not about the universe, it would be true even if the universe didn’t exist at all.

There must be a word for everything, so just replace with whatever you want instead, if universe triggers you.

It is, however, about turtles.

Wait a minute, the universe as we know it, is a model of a universe, the way we humans understand it today.

That model is flawed, this is in fact the basis of science.

The latest scientific finding is considered true until... a more advanced model proves that there are cases where it is not true. A thrown object on earth follows a parabole? ... no it follows a straight line, the space around it is bent by a force that is known as the gravitational field.

What about math itself, no universe considered?

Math itself follows axioms which cannot be proven. Since we found no contradictions in the maths built upon those axioms, we consider those axioms to be true. You can think however of axioms on which you can build equations that are true and untrue at the same time.

My point being, whether we like it or not, the Truth with a capital T does not exist or at least cannot be proven.

Cannot be proven, physically. Mathematical truths prove themselves with their application to physical motion, e.g. Fourier Transformation, such extension of logical principles unto physical body sensations in contact with an external world is great evidence for myself that mathematical reasoning self-reliance in its ordering is great.

Well, we let kids believe they’re just not good at math, and tell them that’s ok I’m sure you’re good at other things, and they believe it, and wish we’d stop doing that.

There’s a world of difference between that and beating yourself up for not being in the top 0.01% of performance.

To coast through a serious program (physics, engineering physics, pure math, etc…) at a major university while barely doing any work and also simultaneously getting high marks takes a lot more than 0.01% performance.

More like 0.001%, at the very least, with some extra luck needed too.

We have not acknowledged an approach that teaches the majority math properly. Find approaches that do and also have some problems that resonate to children in an age appropriate way set for their environment.

Worse still, we lead kids to believe that 'doing math' is performing computations. And so even many kids that can calculate passably grow up thinking that 'math' is boring and they hate it.

Pretty early after kids learn about numbers and computations, they learn about sets, units, lengths, surfaces, weights etc.

Where i live, mathematical formulas are already thought to 7-8 year olds. Also real world questions are asked for which they need to find a solution, and where they need to explain how they found it.

> grow up thinking that 'math' is boring

How can it be thought in a less boring way, i do not immediately see it.

> real world questions are asked for which they need to find a solution, and where they need to explain how they found it.

This could be fun if the questions are predictable enough, but typically in my own early education 'word problems' just ended up being computation problems with the single extra step of translating the question into one of a very small handful of known formulas.

> mathematical formulas are already taught to 7-8 year olds

That's great, but applying memorized formulas is still just computation.

> How can it be thought in a less boring way, i do not immediately see it.

Mathematics is the work mathematicians do. That work is fundamentally creative: it's about exploring, defining, and constructing abstract structures and conducted through writing. Mathematics as it's taught before college is typically presented almost exclusively as a mere instrument in service of engineering or the empirical sciences. This is like teaching physics purely as a parade of unexplained facts about past results and never giving students a chance to conduct experiments!

There should be way less emphasis on the notion of a single track of linear progress from arithmetic to calculus. Formulas should be derived by students rather than just presented to them for memorization. Formal logic should be introduced about as early as arithmetic; first-order logic certainly isn't any more complicated than addition and multiplication. Teachers should prove the principles they expect students to rely on. Mathematical topics which do not require great facility with engineering computations (e.g., calculus, linear algebra, trigonometry), like propositional logic, discrete math, and basic geometry, should be used as opportunities to get students reading and writing proofs for themselves in multiple mathematical contexts as early as possible.

The more students have a sense of the foundations of what they're learning, the more meaningful it can be to them. The more deeply they understand their formulae, the less memorization is required. And the sooner they engage with proofs, the sooner they have a chance to engage with mathematical as a creative and collaborative process.

While they are not studying maths, they can grow and improve themselves in other ways, not?

> There are many things to learn and ways to grow as a person, why beat ourselves up for not being very good at this or that particular thing?

I'd say that this takes a lot of work to unlearn, be it social media or whatever else seems to teach us to compare ourselves against others. Even though there are people way more brilliant than me out there (maybe they're naturally gifted, maybe they have a better work ethic, or different circumstances), it is definitely possible to be happy for their success, rather than lean into being jealous or what have you.

Of course, they will often achieve more than I will and will lead better lives as a result of that, but that's also something to accept and take in stride, rather than for example believing that I'm some temporarily embarrassed soon-to-be millionaire who's one good idea away from a lavish lifestyle. Not that it should discourage me from being curious about new ideas, even if writing my own particle simulation quite quickly ran into the n-body problem and also the issues with floating point numbers when the particles get close and the forces between them great.

What made you believe you were in the 99.999th percentile when going into university? (As opposed to something more realistic like the 99th percentile)

Unless you were literally outsmarting your teachers every day at age 16, it seems difficult to successfully fool yourself in this way.

There are a lot of things that one can be in the absolute top of, and overall academic achievement need not be one of them.

Speaking personally, when these articles come out, there are always a lot of comments about "I didn't really try super hard in high school, but college was a huge wakeup call for me and I had to learn to learn."

That wasn't me at all. I somewhat lazily skated through high school, and got a mix of 4s and 5s on AP exams. I did the exact same thing in college, with no change to my work/learning ethic, and lazily skated my way to finishing my 4-year molecular bio degree in 3 years, with a GPA of like 3.5 or so. Then I went to grad school, did more of the same for two years, and won an award for having the 2nd best masters thesis produced by the university that year.

Then I got a great job in my field doing cancer research, did that for 5 years, then jumped careers entirely and now work in robotics.

But you know what? I feel like I'm constantly surrounded by people smarter than me. I'm not some brilliant person, I'm just some dude that when presented with some problem, things just seem to make sense for a path forwards, and maybe my special thing is that I just always go explore that path and learn that either I was right or why I was wrong and that just pays dividends. When I see people around me who work hard at things, who study and memorize and read papers, they impress the heck out of me, because I really struggle to do the same thing. And when I do, I really struggle to absorb any information; if something doesn't make sense to me, it's like it just passes out of my head. I have to do/build/try it to make it make sense a lot of the time, or at least have things framed in a way that just intuitively makes sense for me.

Anyway, my point is that maybe I was the top 99.99% of something, because, clearly I was/am pretty good at some things that apparently most "gifted" people struggle with. But I never got a 4.0, I never aced all my classes, and I never really cared to as long as I felt I was getting what I needed to out of the classes. I did the work I needed to do to gain the information and skills I felt I was there for, and as long as the number assigned to me by the professor for doing so was at least an 80, I was happy.

> What made you believe you were in the 99.999th percentile when going into university?

Oh, nothing at all. I'm just a case of suddenly discovering in university that you also need good work ethic and that showing up alone is no longer enough (as a sibling comment points out) and you can't always cram all of the topics for exams in your head in a single night before the exam. In my case, calculus introducing new concepts (for which I didn't have a practical use, so it was even more confusing) and probability theory get less intuitive was that wake-up call. Well, that alongside an ASM course with a toolchain that I couldn't easily get working on my computer, or working with Prolog in similar circumstances, or understanding that I've underestimated how long making a 2D simulation project in C++ for extra credit would take, if I need to have collision detection and some physics for a soccer example.

That said, in my Master's studies, once I got to specialize in the things that were of more interest to me, I ended up graduating with a 10/10 evaluation for the thesis and 9.87/10 weighted average grade across the subjects. That's not like a super big achievement from a small regional university, but definitely goes to show that learning some things was easier for me than others. I probably need to venture outside of my comfort zone occasionally though and not just do the things that are comfortable.