<story><title>π in Other Universes</title><url>https://azeemba.com/posts/pi-in-other-universes.html</url></story><parent_chain><item><author>IanCal</author><text>&amp;gt; Mathematics can be seen as a logic game. You start with a set of assumptions and you come up with all the logical conclusions you can from that. Then, if someone else finds a situation that fits those assumptions, they can benefit from the pre-discovered logical conclusions. This means that if some conclusions require fewer assumptions, then those conclusions are more generally applicable&lt;p&gt;This is a really, &lt;i&gt;really&lt;/i&gt; nice expression of something my mind&amp;#x27;s been hovering around for a while.</text></item></parent_chain><comment><author>tetha</author><text>This is also a part of why I am somewhat fascinated by the idea and the state of Lean4 and mathlib in Lean4. People put more and more formally verified proofs into mathlib, which in turn makes formally proving further theorems in mathlib easier.&lt;p&gt;If you start with nothing (like in the numbers game), simple proofs are a lot of ... just effort, because you have specify a lot of rewrites and overall work. In mathlib, however, systems like simp (the simplification system) or linarith (&amp;quot;There is a solution by linear arithmetic&amp;quot;) seem to do a lot of heavy, repetitive lifting by now.&lt;p&gt;It&amp;#x27;s a really interesting snowball effect. Sadly, everything I understand is most likely already in there, so I doubt I could contribute meaningfully, haha.</text></comment>
<story><title>π in Other Universes</title><url>https://azeemba.com/posts/pi-in-other-universes.html</url></story><parent_chain><item><author>IanCal</author><text>&amp;gt; Mathematics can be seen as a logic game. You start with a set of assumptions and you come up with all the logical conclusions you can from that. Then, if someone else finds a situation that fits those assumptions, they can benefit from the pre-discovered logical conclusions. This means that if some conclusions require fewer assumptions, then those conclusions are more generally applicable&lt;p&gt;This is a really, &lt;i&gt;really&lt;/i&gt; nice expression of something my mind&amp;#x27;s been hovering around for a while.</text></item></parent_chain><comment><author>lachlan_gray</author><text>It blows my mind to think of mathematics&amp;#x2F;logic almost like a huge cellular automaton. “axioms” don’t necessarily correspond to “truth”, to me they’re arbitrary constraints that can give rise to complexity. And sometimes the resulting systems can be useful</text></comment>