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"The Rutherford planetary model" was not exactly... anything, it was a vague umbrella term. The inspection of Rutherford's 1911 paper shows that Rutherford did not propose even one of the three OP versions. What he did propose, that there is a positively charged nucleus, does not distinguish among them. He did assume that the electron cloud was ...
5
Heat equation was first formulated by Fourier in a manuscript presented to Institut de France in 1807, followed by his book Theorie de la Propagation de la Chaleur dans les Solides the same year, see Narasimhan, Fourier’s heat conduction equation: History, influence, and connections. "Diffusion phenomena" were not studied until much later, when ...
4
The first and most famous example was the book of Archimedes which is usually called The Method (more complete title is The Method of mechanical theorems), where he uses
mechanics (statics) to compute volumes of various bodies. Unfortunately, this book was lost and found again only in the beginning of 20th century.
Meanwhile what he did there was ...
1
The first mathematician who did this accurately and with all detail was Joseph Fourier. Though he had predecessors. (One can almost never answer the question "who did this first", so on my opinion, it is not even worth asking. "Nothing is new under the Moon", as Ecclesiastes wrote). Fourier wrote a very influential book
titled
"...
1
Dyson proposed that a good understanding of quasicrystals would help solving the Riemann hypothesis.
My suggestion is the following. Let us pretend that we do not know
that the Riemann Hypothesis is true. Let us tackle the problem from
the other end. Let us try to obtain a complete enumeration and
classification of one-dimensional quasicrystals. That is to ...
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