For a more practical direction, you should start with Guesstimation if you are not already versed with it. It is an indispensable tool for getting people to think you know some math as well as helping you detect really bad ideas in addition to helping you get playful with mathematics, which is the only way to really master it as a tool.
Also paying a penny for something would be a major inconvenience at this point. I haven't carried coins in ages. If it is adding a penny onto some other bill, no problem. But a separate paying experience of just 1 penny would be quite costly to me.
He dislikes the idea of presenting infinity as a complete thing. And that one objection leads to a lot of different new directions to pursue. His rational trigonometry does trigonometry entirely without transcendental functions. It can involve square roots at times, but it is kept to a minimum. Everything else is entirely rational based. He has several videos that delve into the problems of each of the standard formulations of real numbers. He also argues for a more practical and computational version of the Fundamental Theorem of Algebra.
An interesting demonstration of the difficulty of real number arithmetic, relevant to some other comments here, is multiplying 1/9 by itself. For fractions, it is trivial as it is 1/81 and this can be converted into a repeating decimal, of course. But try multiplying the decimal form of 1/9 by itself. It is all 1's in the multiplication so it should be easy, right? If you write it down, essentially, the n+1th place is generated by summing n 1s. That is, it is .0123456789(10)(11)(12).... where I put in parentheses the sum of that columns digits. So one has to carry and as it goes further out, one is carrying over many digits; when out a trillion places, we are carrying across 12 places, which is larger than the repeating pattern. Just carrying that first 10 leads to .01234567900(11)(12)... And .012345679 is the basic pattern of 1/81 but it is hard to see feeling confident about that if one only had the infinite decimal to work with. The point is that something with a non-repeating pattern such as computing sqrt(2)pie seems difficult enough that it verges on the vacuous. He does point out the difference for his criticism applying to Pure Mathematics rather than Applied Mathematics. Approximations are fine for applications and what Wildberger is really saying is he wants a Pure Mathematics that really supports that explicitly by focusing on rational numbers as much as possible.
For example, he introduces differential calculus with polynomials by considering transforming p(x) to q(x) = p(x+r), collecting powers of x, and then translating back to p(x) = q(x-r) which is just replacing x with x-r. If expanded out, all the r's cancel, but if one leaves them and then truncates the different powers, one gets the different polynomial approximations. While neat in avoiding limts, the real nice thing is applying this technique to algebriac curves. For example, we can view the unit circle as the solution to 0= p(x,y) = x^2 + y^2 - 1. We can do the same trick above computing p(x+r, y+s), expand, and then retranslate and truncate. This can give us the approximations to the unit circle at a given point on the circle. This sidesteps having to compute the derivative of the square root function to get the tangent lines to the unit circle.
An example of an alternate work flow is multiplying two complex numbers on the unit circle. The traditional approach is to say "compute the angles and then add the angles". But the computing of the angles is impossibly hard to do in a precise fashion (approximate is fine, of course). But there is a perfectly fine accurate procedure. Take the points z and w on the unit circle and draw a line through them. Draw a parallel line through 1. The line will intersect the circle at z*w. As a quick example of this, if you multiply a+bi and -a+bi, this becomes -a^2 -b^2 = -1. Geometrically, the line through these two points is horizontal and the horizontal line through 1 intersects at -1. You can see that with angles, but it feels less intuitive to me that that is how it will work out.
Even the set of Natural Numbers being called infinite is something he questions. He used the term "unending" which I like as well. And by understanding that "most" natural numbers cannot be represented in this universe (assuming it is a finite universe), then it leads to questions such as what numbers can be represented? We have islands of simplicity such as 10^10^10^10^10^10^10 + 23. How dense are they in the larger numbers? Can we do anything useful with those islands? These questions are less prompted when we simply think of the natural numbers as this one big set of sameness. But if we demand that being able to do the computations is actually an important requirement, then we can investigate many more interesting ideas. And Wildberger's point is that this should be in the domain of Pure Mathematics with it being taught to future mathematicians instead of it being relegated to Applied Mathematics.
I have seen some of Wildberger's work, yes. My stance isn't as strong as him on some points - I certainly don't reject the reals outright or take issue with them. I think they're fascinating mathematical objects, I just reject choosing this particular mathematical object as what we mean by a "number".
Their guides are indispensable for my occasional dabbling.
Just saved flexbox and grid guides using the SingleFile extension, something I discovered a couple of weeks ago here on HN. HN warns and provides solutions.
Being willing to take advantage of the luck by working hard, taking risks, having a vision as to how to succeed and be useful. It is very much about empowering both yourself and others. The luck part is there to help prevent the "I did this, why didn't you?" crappy privileged perspective, but it needs to be balanced with the drive.
As an example, over a decade ago, I quit a job with no plans of getting another one. Someone I knew told me about an opportunity (luck / connections), and I pursued it. It was hard at first, but now it is almost a turn-key operation. Still requires work, but far less than it did at the beginning. It has netted me a good tidy sum which has been crucial for living the life I want.
Was it luck? Absolutely. Was it my own ability, hard work, and willingness to take that step? Yes. What would have happened had I said no? No idea, but probably less of a good outcome.
Ideally, one tries to frame one's life to be empowering but not arrogant, not trivializing the difficulty of other's paths. Luck is not empowering. Belief that hard work alone can get you to the height is not empowering. Some mixture of these things, that can be empowering. Understanding that the goal is to be useful to others as well as yourself, that's really empowering.
I recommend making sure you are good with Guesstimation to start (The book of that name by Weinstein and Adams). Be sure to create your own questions and attempt to answer them. Watch some TED talks and try to use mathematical skepticism to criticize them. Doing all this should make you comfortable using mathematics as a tool. Once you are in that frame of mind, you can explore and have fun with the other topics as ably listed in the other comments on this page. Think of math as a faithful toolkit to explore the world. Once you start to try to describe the world in mathematical language, the more proper tools of mathematics will make much more sense.
Also, keep in mind that pretending things are lines is really useful. See the secant method.
I've been using literate-programming for a decade now to do my side web projects (using a tool I wrote myself, of course, as tradition dictates in the LP space: https://github.com/jostylr/literate-programming ). I find it really useful as a project management tool in dealing with the chaos of several different languages, build tools, etc. With HTML, I've used markdown for text content, pug for more structural setups, plain HTML for header boilerplate, all weaved into the same output document that is just plain HTML. It also is often useful for splitting css between a main site sheet vs local to a file (e.g., a lot of css styling on the main landing page is different than the other content-based pages of a site, at least back when websites had content).
I've also found it useful when essentially plugging in data or HTML fragments into JavaScript. I can quickly write a trivial dsl that takes in the data in a convenient form and transforms it into a convenient code version. A variant of the transformational technique is when similar code is almost the same, but just needs a little subbing. I can write a single block covering most of the commonality, and then sub in the differences. For example, if writing some arithmetic operator function code, replacing '+' with the other operators.
An aspect I also love about the approach is having two views of the code. The LP view is more of an outline with blocks subbing in, with some transformations going on. The compiled LP version is one where you can see all the code in full context, minimizing the jumping around at that level, something that cannot be achieved with a bunch of functional calls.
Over the last few weeks, I have started to learn Elixir. I have noticed that I feel less drawn to use literate-programming for that language. It feels like it is so well designed that literate-programming is almost redundant for it. I am trying to figure out justifying that statement, but it is still early days for me in that language. But it feels like, for instance, the matching on function parameters so that one can avoid if-else if-...-else constructs cuts down on a lot of boilerplate stuff. Admittedly, JavaScript has a lot less of that as well nowadays with all the new language constructs. Maybe it is just about Elixir being a functional language with the safety and little overhead of calling functions that make it more attractive to use functions as the outlining / reordering mechanism. Also, the pipe operator allows steps of transformations to be done easily and clearly, which is super helpful. And having tests run from the doc code is something to embrace, further making the separate commenting in LP less favorable in the Elixir context.
One huge downside of LP is that it allows the dictates of a given language to be worked around, making it harder for others to follow up with the work. Ideally the text of the LP helps with that, but it still is a barrier. This seems less of a problem in the front-end web world because that is just a mess of competing notions, but in something cohesively designed with sensible standards that the community follows (my impression of Elixir), it would become a much bigger downside to strike out on your own path.
In Firefox (not sure about the others), they do give some info on some errors, such as what might be overriding a rule (other rules or not an appropriate display type or something) or some invalid property or value. Not perfect, but it is not all in the dark.
And the ability to directly manipulate the CSS and see the impacts can make getting the right visuals fairly quick, not to mention the ability to change the view size and directly interact with that in all the different screen sizes.
To get some great gamified practice with some CSS concepts, I recommend https://codepip.com/ The well-regarded Flexbox Froggy and Grid Garden come from that site, but there are a number of other ones. I believe they all have some mini-tutorial aspects to them in addition to using the syntax to accomplish specific goals.
I also recommend two that were already mentioned but I have found them extremely enlightening: CSS-in-depth and CSS-for-JS-devs (I am a programmer first so it speaks to me).
I have also enjoyed the first few episodes of The CSS Podcast though I have not gotten to far into it.
The book Guesstimation leads to a good very rough approximation mindset, both in terms of how one computes as well as understanding the innate roughness of an answer to a question. They may already be comfortable with that approach, but if, not, it is a very useful place to begin though it is more of a preparation for those ideas.
For a more practical direction, you should start with Guesstimation if you are not already versed with it. It is an indispensable tool for getting people to think you know some math as well as helping you detect really bad ideas in addition to helping you get playful with mathematics, which is the only way to really master it as a tool.