If you liked this, you might also be interested in this project by The Caretaker. He has been diagnosed with dementia, and is producing music over several months to try to capture the progression of the disease. I recommend giving it a listen:
Isn't this the point of the gas tax? For every mile you drive, you use more gas. The more gas you use, the more you pay. Tracking which roads people are driving on would also require massive infrastructure investment, and have significant privacy implications.
When this proof has been presented to me in the past, I believe we assume that m is a positive integer. This is mentioned in one of the comments, but I agree that it should be more clear in statement of the theorem.
Even with a mobile app, it may still be worth knowing how to navigate the old fashioned way. I would imagine that books / hand calculations are more resistant to power failure than apps and GPS are.
Unfortunately, I don't live near UCLA (Does anyone know of a similar program in the Boston area?).
However, I have found that it is not too hard to learn advanced math without the help of an instructor. A couple math-inclined co-workers and I have been reading Topology by Munkres. Since it is such a popular textbook, there are plenty of solutions to exercises online. Working with other people makes it easier to ask questions if you are confused, and also helps me stay motivated.
The Awl ran an interesting piece on this [1] which focused more on how disruptive the bagel machine was to the bagel unions. I wonder if people will ever lament the loss of taxis if Uber and its ilk take over.
If you liked this, you may be interested in Dorothy Gambrell's analysis from the other direction. She took the top songs from billboard over the past 100 years, and tried to find out which ones have remainied popular.
“We discovered the tile using using a computer to exhaustively search through a large but finite set of possibilities,” said Casey. “We were of course very excited and a bit surprised to find the new type of pentagon.
I would expect it to take longer than seconds, since there are many ways that these shapes can fit together, and there are many possible edge lengths.
You might be interested in this article [1]. Basically, even if many proofs are incorrect, their results are almost always still true. Also, there have been many large changes in what counts as 'rigorous' over time. I agree with you that computer-checked proofs seem like a logical next step in the rigor of mathematics.
I have read similar perspectives before[1], and I am not sure how I feel about them. On the one hand, much of the industrial pollution /is/ in response to consumer demand and reducing personal consumption has some impact on that. But on the other hand, it seems very clear that by and large the public will never change consumption patterns to be more environmentally friendly ( sometimes because they cannot financially, and often because they do not care ). So it seems systematic changes are necessary.
https://thecaretaker.bandcamp.com/album/everywhere-at-the-en...