It sounds like you're looking for problems in probability theory (rather than statistics). I don't have anything specific for you but you might have better luck searching for problems, puzzles, and examples in probability. For instance:
It has nothing to do with being easier to work with (at least, not in this day and age). The biggest reason is that minimizing sum of squares of residuals gives the maximum likelihood estimator if you assume that the error is iid normal.
If your model is different (y = Ax + b + e where the error e is not normal) then it could be that a different penalty function is more appropriate. In the real world, this is actually very often the case, because the error can be long-tailed. The power of 1 is sometimes used. Also common is the Huber loss function, which coincides with e^2 (residual squared) for small values of e but is linear for larger values. This has the effect of putting less weight on outliers: it is "robust".
In principle, if you knew the distribution of the noise/error, you could calculate the correct penalty function to give the maximum likelihood estimate. More on this (with explicit formulas) in Boyd and Vandenberghe's "Convex Optimization" (freely available on their website), pp. 352-353.
Edit: I remembered another reason. Least squares fits are also popular because they are what is required for ANOVA, a very old and still-popular methodology for breaking down variance into components (this is what people refer to when they say things like "75% of the variance is due to <predictor>"). ANOVA is fundamentally based on the pythagorean theorem, which lives in Euclidean geometry and requires squares. So as I understand it ANOVA demands that you do a least-squares fit, even if it's not really appropriate for the situation.
We have no evidence that the lead in solder makes its way into the body of the person doing the soldering (and we've been at this for quite some time!). The concerns about lead in solder are due to the environmental hazards of electronics waste, and the hazards associated with mining and smelting lead.
As everyone in this thread is sharing links, I'm gonna pitch in, too.
This lecture by Dennis Freeman from MIT 6.003 "Signals and Systems" gives an intuitive explanation of the connections between the four popular Fourier transforms (the Fourier transform, the discrete Fourier transform, the Fourier series, and the discrete-time Fourier transform):
How do you compute the fractional FT? My guess is by interpolating the DFT matrix (via matrix logarithm & exponential) -- is that right, or do you use some other method?
https://math.stackexchange.com/questions/2140493/counterintu...