Building something useful in a circuit design using off-the-shelf ICs and components doesn't require a very deep understanding of the theoretical basis for why it works. There's really no need to be gated by thinking that overly complex mathematics and physics concepts must be fully understood before building. Most electronic parts datasheets have example circuits and layouts that can be followed to get a working design. A lot of progress can be made just by reading the datasheet, learning how to use a tool like fusion 360 electronics, kicad, etc., to connect the parts in a schematic, lay them out on a board, generate a gerber, send it to a china PCB shop like PCBway, get the pcb, assemble/solder the parts onto it, some cases may need some firmware which AI can do a lot now, finally fire it up and see if it works. Very few calculations or theoretical knowledge needed, outside of Ohms law.

> As a hobbyist I found hardware to be quite impenetrable, given the hard mathematics and physics requirements.

IMO there aren't any. It's mostly about reading datasheets, and connecting pins to each other IOC those datasheets.

Maybe the physics and mathematics are more important for analog electronics or designing ASICS?

Do you have any specific projects you'd like to build? Post here and we can talk through it. And/or start by downloading KiCAD and clicking around until you understand the UI.

The programming side is mainly also reading datasheets. Instead of connecting the right pins together, you are writing a certain value to a register, as described in tables.

About a year ago, I found a YouTube channel[0] which consists mostly of a really smart guy (with a proper background in electrical engineering) buying cheap electronics from eBay/Temu/AliExpress/etc, taking them apart and identifying the components, then reverse-engineering them. (Often followed by a discussion of how much better of a product it could be if the manufacturer hadn't cheaped out on a two-cent component.)

I'd previously had a barebones interest in electronics (think: kits with LEDs and buzzers in like 3rd grade), but listening to his discussions and explanations of how these things worked gave me a fairly decent understanding of how some basic electrical principles work.

I also recently watched a video series[1] that explained how microcontrollers (specifically the ATMega328, the one powering the Arduino) work, from a very low level that I've always wondered about. The key part of that series, for me anyway, was getting the chip off of the Arduino PCB and onto a bare breadboard. From there I went and read/skimmed the ATTiny85 datasheet[2] (a very popular "baby brother" chip to the ATMega328) which also helped me understand how these chips do things like PWM on a low level.

I've built one project (a simple PWM dimmer based on a potentiometer) and am working on another (designing a PCB with KiCAD[3] to replace the circuit board for a battery-powered LED lantern, so I can design my own sequencing interface for what happens when you press the singular button), and it has been quite the learning experience, but one I've greatly enjoyed!

[0] https://www.youtube.com/@bigclivedotcom, also at https://odysee.com/@bigclivedotcom:0d

[1] https://www.youtube.com/watch?v=tBq3sO1Z-7o&list=PLNyfXcjhOA...

[2] https://ww1.microchip.com/downloads/en/devicedoc/atmel-2586-...

[3] This comment is long enough already, but KiCAD is a fantastic piece of FOSS software. It's a full schematic/PCB design suite, and there are plenty of tutorials all across the Internet for it.

Just to be clear, I made a working prototype (and put a hyperbole in the title), I have a lot to learn still.

You can learn something practical like "embedded DisplayPort should be impedance controlled to 100 Ohms" without fully understanding the physics behind it.

AI can be very convincing. It told me to put the ESD protection as close the Ethernet connector as possible, so I put it between the port and the magnetics. This worked, but resulted in around 1% packet loss. When I moved it after the magnetics, I got 0% packet loss. This cost me a full revision, but I'd say this is the price to pay for not learning everything by the book.

I was going to say, AI has really enabled my hardware projects recently. I've found incorrect output is less common with the newest models - and they're capable of drawing decent diagrams too which can really help me sanity check some of their ideas. I've also had some success with asking it to cite sources where possible, so I get lots of useful links into robotics forums like chief delphi and similar which also help sure up the math

Or, you could make some mistakes.