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If it requires a supernova to create elements with a higher atomic element than Fe, Iron, how on Earth (pun intended) do we create elements that are much further up in the Periodic Table of Elements?

Well if you're asking how we create elements heavier than iron on Earth, then the answer of course is that we don't, not in any significant amounts at least.Now tiny amounts of exotic superheavy elements have been created in particle accelerators: the typical way to do this is to take a fairly heavy nucleus like Californium-249, and to hit it as softly as possible, but still above the Coulomb barrier, with a smaller nucleus like Carbon-12.This creates a soft landing as it were, and helps maximize the probability that the two nuclei fuse completely, without losing too many small pieces.Now in a supernova, what happens is that there is a huge flux of neutrons, and the heavy nuclei are built up, starting from the iron group elements, by successive neutron absorptions that happen very, very rapidly.The neutron flux is so high, that nuclei are pushed all the way to the neutron drip line before they have a chance to beta decay, so you get a mixture of highly unstable neutron rich isotopes that quickly decay back to the valley of stability by boiling off neutrons, once the neutron flux dies away. They also then undergo natural beta decays. This process is called the r-process and it probably accounts for the vast majority of the elements that are heavier than iron.The supernova explosion itself disperses the elements into interstellar space. The sun and planets were formed, it is thought, from the debris of such an explosion.There is also a slower process that occurs when the neutron flux is far, far lower, that moves by successive neutron absorption, mostly along the valley of stability, starting from iron.This is called the s-process, and it may act in superheavy high metallicity stars. Some people believe this may contribute some of the heavy elements - but this process can't go beyond lead, where there is a cycle that halts the process. So it couldn't explain the existence of the actinides on its own.But the general answer is that heavy elements are built up by successive neutron absorptions starting from seed nuclei in the iron group.This can only happen inside a star, or possibly in very rare events like neutron star mergers.

How do I keep math and physics proofs in my mind?

Many have written on this topic. The great Paul Halmos wrote an essay on the subject which I’m sure you’ll be able to find. I think he named the essay “the ‘elements’ of mathematics” with an extra quote on ‘elements’ (as in the periodic table of elements.) Halmos claims that geometric series 1+r+r^2+… = 1/(1-r) is the ‘Hydrogen’ proof (I forget which one is the Oxygen, etc.)What you ask perhaps belongs to the philosophical discipline of epistemology - what does it mean to know something and how knowledge manifests itself in ones perception and cognition (for example, to be able to think through a related problem.)As to your question, it’s not necessary to ‘memorize’ proofs. However, there are ‘themes’ of sort, those that keep repeating and those are certainly worth committing to memory. This is not unlike committing spelling to memory. It’s probably not necessary to remember how to spell the word idiosyncrasy but the spelling of necessary is necessary to remember (pun intended.)The next question should be ‘what’s a theme?’ - this is something you have to answer for yourself; but for illustration purpose, approximations of differentiable functions by a linear transformation (a matrix) is a theme of multivariate calculus, as is basic manipulations of the Zeta function is a theme in number theory.On the flip side, an example of a non-theme, (well, in my view anyway) is the proof of Radon-Nikodym theorem on the representation of measures as integrals. It’s a fundamental result no doubt, but I never felt that the proof belongs to what I could considered as a theme (or one which I find interesting, or inspiring, that sort of stuff.) But as an old Jewish saying goes “one person’s sardine is another’s filet mignon.” I’ll stop here.

Why is chemistry so tough?

Depending on who you ask this to, you may get different answers.Yea… I’m not entirely sure why this question was added (be it for validation or just for fun). Anyways, different people find different subjects hard, for example I hate physics but don’t find the chemistry element of science too hard (get the pun :D). I know people who are the exact opposite.Oh well, chemistry is a complicated subject (for sure, there’s a lot more to it that just memorising the periodic table) but the toughest subject, maybe not.

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