Math Stories: Struggles, Triumphs & Benefits

[ScrollPortals]

This is somewhat of a meta topic. I want collect a few personal stories about how you got into and advanced through math. What trials did you face? what kept you going? How did your perspective of the field change as you learned more? Did you know it was beneficial or were you just good at it?
I felt I was good at math once. I did best when I applied it to the games I was programming. Does application help you too? What are some general behavioral methods that can make one more receptive to learning mathematics? Is there any passive methods to help learning comprehension as well? ( like math equations on the wall )

 

[cnh1995]

This is somewhat of a meta topic. I want collect a few personal stories about how you got into and advanced through math. What trials did you face? what kept you going? How did your perspective of the field change as you learned more? Did you know it was beneficial or were you just good at it?
I felt I was good at math once. I did best when I applied it to the games I was programming. Does application help you too? What are some general behavioral methods that can make one more receptive to learning mathematics? Is there any passive methods to help learning comprehension as well? ( like math equations on the wall )

I started enjoying maths from 9th grade. We had algebra and geometry. I was fascinated by various topics like simultaneous equations, quadratic equations and their applications to solve various problems. Geometry was cool too..Especially trigonometry. I enjoyed both and scored really good marks in exams.

But during high school, I had read a really interesting book about scientists' contributions to various fields like physics, chemistry, biology, cosmology, quantum physics etc. There was one fantastic chapter on origin of calculus, its development and its applications. I was so amazed that I tried learning it on my own, but gave up as I realized I didn't have enough prerequisite knowledge.
But when I joined college, I spent a lot of time studying calculus and now I love it even more. It also helped me understand many concepts in physics and engineering systems which made engineering really enjoyable. I consider math as the spine of engineering (it's my opinion).

Does application help you too?

Very much..
Applications of calculus (and trigonometry) blew my mind and made me think "Wow..This is something I MUST know". That was my motivation to study calculus as much as I did.

 

[Mark44]

When I was about 8 years old I came across an algebra book. I was fascinated by exotic symbolism such as $x^2$. I tried to understand what they were doing, but didn't get far. During junior high and high school, I had a math class each year (algebra, geometry, algebra/trig, and calculus), and managed to do well in these courses without ever having to study very hard.

The turning point for me was during a calculus/analytic geometry course I took in college. I found myself working on a problem at 3AM that wasn't even assigned! From that point on, I knew that whatever direction I took, there had to be a lot of mathematics associated with it.

 

[Auto-Didact]

My story is a bit of an unconventional one I guess as it is somewhat a combination of mathematics, science and philosophy, but I will try to be as thorough as possible while only mentioning the other two in passing:

From the age of 3, I started to wonder about the world, in what one today would call philosophical terms, which incidentally I would not acknowledge without any feelings of disgust until my early twenties. From around an age of 12, I became enthralled with algebra and geometry, culminating in analytic geometry. At 14, a few years before learning anything about calculus in high school, I glimpsed what was something very special: by geometrically determining the slope of a tangent in between two points on the curves of $y=x, y=x^2$ and $y=x^3$, I conjectured a curious relationship between them and the curve. This to me at the time was an intuitive proof of something special, I immediately tried telling my teacher at the time but he quickly shot it down, wanting me to work on the problems he asked, not try to prove some conjecture coming from my procrastination; had he responded more positively, I might've probably been a mathematician today. I digress.

Around the age of 16 when we began learning calculus, I immediately remembered my conjecture from a few years back, and I delved deeper and deeper into mathematics then. At this point in time, I convinced myself that the only guaranteed route to absolute certainty in reasoning was through mathematics and conjectured that all of mathematics was a massive logical structure. Before this point, I was great at all 'word and language' subjects but only mediocre at math. Hereafter however I actually changed my way of reasoning about things, always trying to think about things in a way that would allow mathematical reasoning to follow. As a consequence I immediately started to excel more at mathematics, while everything else dropped a grade lower. I gained a stance focusing very strongly on pure mathematics and I developed a strong dislike for all applied math, including trigonometry which seemed trivial to me and especially physics which seemed hopelessly dirty. I became a Platonist, a naive logicist and, practically speaking, a classical purist, luckily never having yet been introduced to any views or products of formalism and yet fully unaware of Gödel's devastating blows to logicism (which I would learn early on a few years later in university).

I kept this classical purist stance up until I was 18, during my final year of high school. It was here when I started actually seeing the mathematical beauty in physical laws, instead of them being arbitrary formulas to learn by heart in order to plug-and-chug. Listening in on a mechanics lecture my older brother was attending, I was introduced to dimensional analysis. From that point on I quickly applied it to all high school physics formulae I knew, only to discover I could discover laws of physics by pure algebraic reasoning. I very quickly discovered the Planck units as well in this manner, and tried to come up with new formula based on my knowledge of some others. I then showed it all to my physics teacher, with whom I had a strained relationship due to my disdain of physics up to that point. He however responded in a very positive fashion and told me that some of these formula described some other physical phenomena and how they could be corrected and had been corrected historically.

From that point on I was hooked on physics and saw in it much more beauty than mathematics could offer. After going to university, I ended up studying physics, some mathematics courses and later on some philosophy as well. During all that time, my initial views on the certainty which only mathematical reasoning could bestow upon one was irreparably demolished, especially after discovering that there were undecidable problems in mathematics and especially upon learning that the continuum hypothesis was independent of two opposing axiomatizations of mathematics. Curiously, I also noticed that both math students and professors were much more rigorous formalists and proof driven than anyone in the physics department, who all agreed that the familiar classical mathematics of the 17th, 18th and 19th century was wonderful, but who were woefully unaware and/or uncaring for much or any of the developments in mathematics thereafter.

It was around this same time that I became a bit familiar with string theory in physics, which I first passionately embraced for its mathematical beauty and I felt and recognised very strongly my earlier purist mathematical stance, dare I say hope, at work in string theory, giving an unshakeable faith that the theory must be true. Eventually however something kept telling me that this was not the correct way forward for physics. Moreover, after learning more deeply about chaos, nonlinear dynamics, fractal geometry and nonstandard forms of logic, I gave up on both string theory and mathematics and never looked back. Instead, I looked forward towards physics and very other interdisciplinairy areas in all of science, where time and time again it seems as if these novel late 20th century mathematical tools, along with some others, are of much more use for accurately describing many currently misunderstood phenomena and discovering unknown phenomena, often much more so than anything that has been offered from conventional mathematics, which tends to have been tried before unsuccessfully.

 

[MarneMath]

I wanted to make a lot of money and discovered that working in finance as a quant was a good way to accomplish such goal. Thus I studied and did well in math. Some detours occurred along the way, but in the end became a quant, hated it, and then bounced from job to job in some statistical related role.

 

[StatGuy2000]

I had an interesting in puzzles and problem-solving as far back as I can remember (around 4 or 5 years old?). From around age 7 up, my mother worked with me on various math books from Japan (which my aunt would send to us) -- math books back then were small and thin, and focused on a few key topics. I really enjoyed these as I saw them as extensions of puzzle solving. Once I grew out of these new books, then I would go to the library and borrow more books on math, and participated in various math competitions held at my junior high and high schools.

From that point onwards, I knew I wanted to major in some field where math was involved. I initially thought of studying engineering, but I didn't feel I had a bent for physical manual labour that the profession involved (I always figured engineers at bottom made things with their hands), so I had instead thought about pursuing some combination of math, physics, or computer science. Eventually, I graduated with a bachelors in math and a masters in statistics.

 

[ikihi]

I was terrible at math in high-school. It was my worst subject. In college something changed after I watched a lot of videos about math on you tube...and I realized I was pretty good at it; just had terrible teachers to explain it before. Now I'm pretty good at it and just got done with Calculus.

 

[newjerseyrunner]

I started programming in QBasic when I was a young kid. I immediately began working on games, so that introduced me to trigonometry. I was an expert in SOHCAHTOA before learning the functions in school. Once I got past simple integrals and derivatives, I found it no longer useful to my normal life, so I stopped paying attention. I would memorize formulas for tests, then immediately drop them from my mind.

I also got back into it later because of Youtube. My math teachers also sucked, they taught the formulas without every telling us what they were used for. I could always recite x = (-b +- (b^2 - 4ac)) / 2a and knew that it was to find the zeros of a quadratic. Nobody ever told me that it was for completing a square. No calc teacher ever gave me a concrete example of what a derivative is. In physics, it's quite easy to understand, but it took me forever to realize that my net income is the first derivative of my bank account with respect to time, and my raises are the second. I find examples like that so much clearer than just an abstract "rate of change" or "slope of the line."

I think I began to enjoy it when I got good enough to visualize it. If I can visualize a transformation from one equation to another, I can better analyze what I want. For example, when deciding how much money I want in my 401k by the time I'm 40, 50, 60... I'm now familiar enough with the equations to give quick estimates for whatever variable I want in there, where most people would be off by a lot due to the exponential nature of finance.

 

[StatGuy2000]

I started programming in QBasic when I was a young kid. I immediately began working on games, so that introduced me to trigonometry. I was an expert in SOHCAHTOA before learning the functions in school. Once I got past simple integrals and derivatives, I found it no longer useful to my normal life, so I stopped paying attention. I would memorize formulas for tests, then immediately drop them from my mind.

I also got back into it later because of Youtube. My math teachers also sucked, they taught the formulas without every telling us what they were used for. I could always recite x = (-b +- (b^2 - 4ac)) / 2a and knew that it was to find the zeros of a quadratic. Nobody ever told me that it was for completing a square. No calc teacher ever gave me a concrete example of what a derivative is. In physics, it's quite easy to understand, but it took me forever to realize that my net income is the first derivative of my bank account with respect to time, and my raises are the second. I find examples like that so much clearer than just an abstract "rate of change" or "slope of the line."

I think I began to enjoy it when I got good enough to visualize it. If I can visualize a transformation from one equation to another, I can better analyze what I want. For example, when deciding how much money I want in my 401k by the time I'm 40, 50, 60... I'm now familiar enough with the equations to give quick estimates for whatever variable I want in there, where most people would be off by a lot due to the exponential nature of finance.

I find this a recurring theme here among posters from the US -- that math teachers taught the formulas without ever telling the students what they were used for. I'm curious why that is -- is it because teachers were not given the flexibility to explain this to the students in their lesson plan? Or is it that many math teachers don't know themselves what these formulas are used for?

 

[Comeback City]

My guess is...

many math teachers don't know themselves what these formulas are used for

And thus I am constantly teaching myself what they mean because I like to know the meaning behind things

 

[QuantumQuest]

This is somewhat of a meta topic. I want collect a few personal stories about how you got into and advanced through math. What trials did you face? what kept you going? How did your perspective of the field change as you learned more? Did you know it was beneficial or were you just good at it?
I felt I was good at math once. I did best when I applied it to the games I was programming. Does application help you too? What are some general behavioral methods that can make one more receptive to learning mathematics? Is there any passive methods to help learning comprehension as well? ( like math equations on the wall )

Back when I was about 12 years old in the first year of Gymnasium (European High School translated, but basically is three years of pre-high school compared to US high school), I had a crash landing right off the bat: my first test in math was under base grade i.e. under 50%. I was so ashamed that I didn't know how to face all this. After a while, I went to a really great tutor that showed me that math is not some fearsome monster but apart from incredibly useful, is also very entertaining. I put my best efforts too and starting the next year, I was among the four to five best students in my school. But the point here is what caused me this trouble in the beginning and this was nothing else but the mindset I had regarding math, from my previous years as a pupil. This was what had to and did change. Also, the same concept held true for the transition from Gymnasium to High school and so on.Since then, I have a great love for math and although my formal studies are not in math, I can say that I have read way more math textbooks and solve problems and exercises than in my main fields of study for which I can't say that they had few reading involved in any case.

Now, to say that math just helped me is an understatement. Through math, I really managed to have a very decent understanding about many fields of study in my formal studies, as well as outside them (Physics is one of them) but equally importantly in my life in general. Math don't ever lie about anything nor allow gray fields for at-will translations. And although our life is full of such gray fields, math is always a good guide to make decisions. So, I think that the application of math is of crucial importance.

As a final point, I think that loving math is what can boost anyone further in this field. Particular methods, strategies and tools can potentially be very helpful in order to learn but will not be much fruitful if someone does not really love the subject.

 

[gmax137]

I find this a recurring theme here among posters from the US

My guess is...

I guess I had better math teachers than whoever you guys are talking about.

 

[StatGuy2000]

I guess I had better math teachers than whoever you guys are talking about.

As did I personally (which further fostered my interests in math which I described earlier in this thread).

 

[newjerseyrunner]

As did I personally (which further fostered my interests in math which I described earlier in this thread).

I had one or two good math teachers, but I honestly think I learned more math from my physics teacher than my math teacher. He actually forced us to use the math, not do equations just for the sake of equations.