Timeline for What is fairly new theorem one can teach (and prove) to an undergraduate student?
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| Mar 23, 2014 at 21:39 | comment | added | Brian Rushton | @MattF. The question is about new theorems, not difficult new theorems. A lot of interesting facts about fractals are listed as theorems in the resource. (And difficulty is not correlated to importance in general; look at the isomorphism theorems in algebra). | |
| Mar 23, 2014 at 21:32 | comment | added | user173 | "The boundary of the Mandelbrot set has dimension 2." That result of Shishikura looks recent and stated in a way understandable to undergrads. Apparently it was easily conjectured once computers became available. But the proof doesn't look easy or accessible to undergrads....so I still don't see an answer to the original question here, though I'm enjoying the search. | |
| Mar 23, 2014 at 20:03 | comment | added | Brian Rushton | @MattF. That's interesting! The relationship with computers was just a parenthetical, incorrect statement. The theorems on the Mandelbrot set in the reference have been proven in the last 50 years (I believe), and that is the main thrust of my answer. | |
| Mar 23, 2014 at 19:33 | comment | added | user173 | The word "fractal" is only 40 years old (1975), but there is a whole volume of Classics On Fractals, with 19 papers from the century before that (1872-1967). Many of them prove theorems about the dimensionality of various sets. Meanwhile, computers are great for establishing "this function on this input does not converge after 50 iterations", but that by itself is not worth calling a theorem. Which of the theorems in your reference would you say was easily proved with the aid of a computer, but not posed and proved beforehand? | |
| Mar 23, 2014 at 16:50 | history | edited | Brian Rushton | CC BY-SA 3.0 |
added 2 characters in body
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| Mar 23, 2014 at 15:36 | history | answered | Brian Rushton | CC BY-SA 3.0 |