#mathematic #physic #science #knowledge #philosophy #empiricism #rationalism - **Poincare** is exploring both **mathematics** but also, the metaphysics of it, how do we do it, how do we acquire knowledge in **mathematics** vs in physics and other sciences - Critical of [[Mathematic]] research as people does not seem to distinguish advances origin, whether it is **empirical**, **hypothesis** or "mathematical" (I do not fully grasp what he said regarding that last point #todo) - In his books (Science & co) he goes from [[Philosophy]] to [[Logic]] to [[Mathematic]] to [[Physic]] <a href="https://www.goodreads.com/book/show/1016008.Science_and_Method" style="float: left; padding-right: 20px"><img border="0" alt="Science and Method" src="https://i.gr-assets.com/images/S/compressed.photo.goodreads.com/books/1344605547l/1016008._SX98_.jpg" /></a><a href="https://www.goodreads.com/book/show/1016008.Science_and_Method">Science and Method</a> by <a href="https://www.goodreads.com/author/show/5558801.Henri_Poincar_">Henri Poincaré</a><br/> My rating: <a href="https://www.goodreads.com/review/show/4109787751">5 of 5 stars</a><br /><br /> Human hardware is extremely limited, and we must be aware of this in order to expand our scientific knowledge above our current high levels of complexity.<br /><br />How do we make mathematical invention and then innovation?<br />The first mathematics were discovered through pure intuition, that is from our knowledge imprinted in our genes, that has been learned by nature when our ancestors needed to count if there is one or two mammoths.<br />But now, we must use empiricism to expand our mathematical knowledge, though, it is unlikely that our hardware is able to unlock the chest containing the future of knowledge, and only artificial intelligence can give us the key.<br /><br />How do we make physical invention and then innovation?<br />Physical invention seems to have always been using more empiricism than mathematics, somehow.<br /><br />Can we know the truth?<br />No, under our very limited hardware, everything lies in the law of probabilities.<br /><br />Is there such a thing as absolute space, or everything is relative?<br />It seems that we are pretty sure now that the world is relative.<br /><br />Can we expand mathematics through pure logic?<br />Bertrand Russell has tried hard to prove this, without success according to Poincare?<br /><br />Poincare goes from philosophy, to logic, to mathematic, to physic, to other sciences. <br/><br/> <a href="https://www.goodreads.com/review/list/103091881-louis-beaumont">View all my reviews</a>