It's a shame he went to all the trouble of avoiding conventional education (for the wrong reasons), but then still ended up going down an <i>execution</i> rather than <i>concept</i> focused route. As soon as you start memorizing operations and treating math more like a narrow grind only approached through arbitrary problems solved primarily through computation or use of rote application of poorly understood technique, you lose the ability to understand math as anything other than a human attempting to be a computer.<p>The author expresses his misintuition of variables - there are plenty of simple examples and thought exercises which can inform the intuition. Later he expresses getting mixed up dealing with fractions - this is a clear demonstration that a fundamental understanding of fractions was skipped in order to grind out solutions. Modern math education is spectacularly guilty of going too far too fast.<p>Fundamental understanding gives exponential results yet most courses try and get the axioms and basics out of the way as fast as possible, working through basic proofs or derivations is cute sideshow, if anything. If the fundamentals are well understood, the applications feel trivial, intuitive, beautiful, clever - when the fundamentals are taken for granted, one word describes the relationship to the rest of the material: arbitrary.
I personally found that learning math was far easier as an adult. Like the author, I sucked in grade school. I learned multiple foreign languages. I did well in the sciences. History and geography were simple. Math? It was the one thing that escaped me. As an adult, after various misadventures, entering into college everything was different. My mind was more disciplined, my teacher was far better, and I was more humble. It was easy then.
Despite that — or, maybe, because — my father was a math academic, I did poorly in school with math beyond basic arithmetic. When I was about 25 years old, a friend gave me three algebra textbooks written by an ex-military pilot, John Saxon. In a marathon session lasting about two weeks, I went through all three books from end-to-end and really learned algebra. For whatever reasons, the Saxon books worked really well for me — better than any other learning I have ever gotten from a textbook. Yes, I was really motivated but I attribute a lot of my success learning algebra to those books. Learning that opened a lot of doors since then, mostly because my confidence in taking on matters technical was so much improved.
I’ve been tempted to pick up an adjunct section of algebra at a local community college and invert the usual style of teaching and <i>start</i> with word problems. A lot of people have an intuitive sense of how to figure out, say, how to scale a recipe but when it gets turned into symbolic math it becomes a challenge for them. I’d kind of like to take advantage of that and start from the word problem and then move to how to turn that into symbols so that instead of thinking <i>y</i> = 1.4<i>x</i>-2.8 we'd say think in terms of you pay $1.40 for each donut but the first two are free. If all the <i>x</i>² and <i>x</i>³ have particular meanings, you’re less like to think that <i>x</i>²+<i>x</i>³ = <i>x</i>⁵ but recognize that you can’t simplify the expression until you know what <i>x</i> is.
"Sometimes I dreamed that there were numbers falling from the sky into chasms I couldn’t see the bottom of."<p>Reminds me of the night terrors I had when I was younger. I remember often having dreams that involve the unknowable, unseeable or in some other way were impossible for my finite mind to comprehend. In the worst of those nightmares I was left shaken with fear — feeling as though I had peered from just over the precipice of sanity itself.
My friends dad in his late 60's wanted to learn math and used the No Bullshit math and physics from <a href="https://minireference.com/" rel="nofollow">https://minireference.com/</a> and loved it. Their Linear Algebra is quite good too.
I have to sit on my hands and not help my son with his math homework. The way they have taught him to do math is great - he can solve just about anything in his head - but I can’t help him without introducing him to the old slow way I learned of doing everything.
Brain games do little for the older mind. You are much better off lowering blood pressure and walking. But, if you insist, read [1].
[1]: <a href="https://www.nia.nih.gov/health/cognitive-health-and-older-adults" rel="nofollow">https://www.nia.nih.gov/health/cognitive-health-and-older-ad...</a>
No, but once you have learnt some algebra you'll be in a position to learn other things - electrical physics for example, or audio engineering. These subjects, and many others, use the language of algebra, because algebraic explanations are very compact and easy to follow.
My grandpa used to enjoy doing Euclid's Elements compass and straightedge constructions and understanding proofs.<p>He also enjoyed reproducing geometric proofs of certain equations.<p>What's funny is he hated math as a student but for some reason or other got turned onto Euclid in old age.<p>He then tried to get my dad to read Euclid but that didn't take.<p>Then I came across the book as teen and took an interest so Grandpa and I bonded over that.
So that's how a packer thinks! I'm a mapper[1], and it's always been a mystery to me as to how packers got that way.<p>When I was an IT Admin, I worked with woman who VERY competent at her job, but always needed help using the computer, for even basic tasks, even with a list instructions. It took time before it dawned on me she was a packer, and my instructions weren't specific enough.<p>I started making <i>exact</i> instructions for her, accounting for any possible variance in each step. (As you would in a program) Once I did that, she was thrilled, and we got along very well after that.<p>An example of things that can throw off a packer... in Windows Explorer, drag a file from one window to another... depending on context, there are 3 possible outcomes (move, copy, shortcut creation)... that confuses the heck out of people, especially packers.<p><pre><code> https://wiki.c2.com/?MappersVsPackers</code></pre>
Probably not. Knowing more stuff doesn't make you "smarter". Nor would mastering kinds of math that many people find challenging prove you are more intelligent. Clearly many intelligent people are not great at math or don't know algebra.<p>But exercising your curiosity and practicing the art of learning will always increase your mental fitness and the ability to <i>apply</i> your intelligence better. It's always good to keep in shape - mentally too.<p>I don't think it matters much what the subject is. It doesn't have to be algebra, as long as it captures your interest. Algebra is very challenging because it requires thinking in abstract concepts, so it's a great subject. It will indirectly lead to deeper understanding in many other fields too, including computer science.<p>Intelligent people are often curious and desire to learn new things, so No I don't think learning algebra makes you smarter - but I think the desire to is a possible symptom of this kind of curiousity.
Scientists can't agree to what extent human intelligence is inherited vs. acquired, and so asking if doing some activity x will result in an increase in personal smartness y will result in a wide variety of answers. (sort of a differential equation isn't it? Change in intelligence over time as a function of doing algebraic manipulations every day).<p>There are some plausible benefits - it's likely to help with internal mental organization, for example. However, some thought should be given to how to set to work, in particular avoiding bad habits that eventually thwart future progress (this can happen in say, learning to play a musical instrument).<p>Learning algebra (or any other field) conceptually is like constructing a connected map of various islands, although from reading this article it isn't clear whether that was accomplished. There's no mention of concepts like associativity, distribution, commutation, how this applies to the order of operations when you start mixing up + * - /, and the rather strange but also fundamental notion of identity. For example:<p><a href="https://byjus.com/maths/commutative-property/" rel="nofollow">https://byjus.com/maths/commutative-property/</a><p>This is a bit sad because understanding these concepts opens the doors to fun higher math. Matrix multiplication is generally non-commutative, and this property makes it useful for quantum mechanics calculations. Symmetry operations - rotations and reflections and so on - are not generally commutative, but are associative. This is all very important in things like protein crystallography. A solid grasp of these ideas also allows for the introduction of the concept of groups as a way of looking at algebra. Here's a great series on that whole business:<p><a href="https://www.socratica.com/lesson/groups-motivation-for-definition" rel="nofollow">https://www.socratica.com/lesson/groups-motivation-for-defin...</a><p>A good rule is to spend at least as much time understanding fundamental concepts and abstractions as on working out the results of specific explicit examples.
One of my retirement goals is to redo my math degree - turns out it's really easy to get hooked up with online tutors, and I figure it's totally worth paying $20-$40 an hour to work through a textbook.
The title sounds like a non-question.<p>I posit that learning anything (even fengshui or astrology), at any age, will make you smarter, as long as you bring a pair of critical eyes with you. Besides learning about the actual “thing” (which you can still fail at the end of the day), you can always introspect to figure out why/how you failed and what your limits are, and then you’ll maybe find closure in saying “I’ve tried. It didn’t work out. There was no 'wasted potential' - the potential was never there to begin with. And I’m a wiser person now.”
This quote reminded me of learning chess as an adult as well:<p>> In the paper Acquiring Skill at Mental Calculation in Adulthood, Neil Charness and Jamie Campbell say that middle-aged people perform as older ones do, but if they practise, they perform more as younger people do. If speed is valued more than accuracy, the decline in ability is obvious. If accuracy is valued more than speed, the decline is less obvious and maybe not even very pronounced.
In my opinion, nothing can make you smarter. Learning rationalist techniques may make you better at thinking through problems, learning memory techniques like Memory Palace may improve your memory, using learning techniques like Spaced Repetition may help you learn and retain large amounts of information with the minimum necessary effort, but nothing can make you smarter.
Math is so much easier when your using it to model something that is real. I remember in Physics 1 in college when the professor was going over how a baseball hits a bat and how it is modeled with all of its nth order derivatives. Everything clicked! Not to say theoretical math isn't fun though!
The author also wrote this excellent article:<p><a href="https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty" rel="nofollow">https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty</a>
Probably yes, since past research indicates that learning delays cognitive decay.<p>Even more, there is research pointing that continuous learning will prolong your lifespan. Best indication is a study on how university professors tend to live longer.
Despite the title, I don't think the article is about algebra "making you smarter", but more whether you can learn it successfully and if by pursuing such an endeavor you can hamper age-induced cognitive decline.
My litmus test of someone being intelligent or not--among other such tests--is what they say about Shakespeare. This might anger the Brits, but Shakespeare is garbage--and the guy says: "I read .... most of Shakespeare."<p>One famous guy lambasting Shakespeare (Tolstoy) was only marginally smarter, because according to his "Confessions", he read it many times over (incl. in English) and STILL could not find any artistic value in it. I could not have put up with that--for me, it was the first few pages that I knew this was a waste of time. You don't need to drink the whole festering junk of a decayed meal to know it is not edible.<p>He also claims he wants to test the limits of his intelligence by tackling Mathematics once again--implying wrongly, as it were, that math education is fine and it is our brains that are incapable of learning. Not so fast: how am I less intelligent if the bozo teaching me does not know how to teach maths?<p>Citing Carl Jung does not help either, though he namesdrops to mitigate the shame of not being able to do maths...Jung was not as bright as is commonly believed as well. He once claimed that UFO's were all imaginary-- a sweeping generalization by someone claiming to be scientist-- whereas I for sure know that UFO's are real for I have seen one and to prove that I wasn't seeing things, I had a camcorder ready which recorded the space-ship going vertically up very slowly. I have lost the video though but it certainly happened 20 years ago and I still remember it.<p>EDIT: I see I have touched quite a few nerves.