TITLE: Examples of creative experiments by mathematicians in modern days
QUESTION [41 upvotes]: I'm reading Random Circles on a Sphere and the authors did the following to empirically check their results:

To make a partial test of the accuracy of the above approximations an experiment was carried out using table tennis balls. These had a mean diameter of 37.2 mm. with a standard deviation around this mean of 0.02mm. One hundred holes of diameter 29.9mm. were punched in an aluminium sheet forming one side of a flat box. The balls were held firmly against the holes by a foam rubber pad, and sprayed with a duco paint. After drying they were removed and replaced at random by hand. Forty sprayings were done in each of three sets of 100 balls. The number of balls not completely covered after N sprayings are shown in Table 2, and fit the theoretical curve rather more closely than the roughness of the approximations used would lead one to expect. The angle α was about 53.43° as used in the calculations.

What are other examples of mathematicians turning into carpenters to test theories in modern days (post 60s)?

REPLY [32 votes]: I was amused by the work of Scott Aaronson on soap bubbles and Steiner trees. Given $n$ points $p_1$, $p_2$, ..., $p_n$ in $\mathbb{R}^2$, the Steiner tree through these points is the connected planar graph of shortest length containing these points. Computing the topology of the Steiner tree, given the coordinates of the points, is NP-hard.
On the other hand, if two parallel glass plates are separated by rods in positions $p_1$, $p_2$, ..., $p_n$ and dipped into a bucket of soapy water, the shape of the resulting soap film is a local minimum for this problem. Which lead to the question: How close is the local minimum, formed by whatever complicated PDE governs soap film, to the NP-hard global minimum?
Aaronson decided to try the experiment, and reported on his results in Section 3 of "NP-complete problems and physical reality". The answer was not very close: The stable shape of the soap film was often not even a tree!

REPLY [19 votes]: Psychologist Frank Rosenblatt built the first neural networks in 1957/8. Today it is trivial to build a neural network using software, but Rosenblatt built a neural network using analogue hardware.
The perceptron could tell the difference between triangles, circles and and squares, or between different letters of the alphabet. Most critically, it could get better at doing so as it was given feedback on whether it was correct or incorrect about previous predictions. In this sense, it could 'learn'.
A hardware implementation of a neural network
The input to the perceptron was an array of 20 x 20 grid of light sensitive resistors

And the weights/bias values of the primitive neural network were stored in racks of cylindrical objects each consisting of an electrical motor and potentiometer (rotary resistor).