Ami Iida

“However, in 1930 (published in 1931), Godel produced his bombshell, which eventually showed that the formalists' dream was unattainable! He demonstrated that there could be no formal system F, whatever, that is both consistent (in a certain 'strong' sense that I shall describe in the next section) and complete-so long as F is taken to be powerful enough to contain a formulation of the statements of ordinary arithmetic together with standard logic. Thus, Godel's theorem would apply to systems F for which arithmetical statements such as Lagrange's theorem and Goldbach's conjecture, as described in 2.3, could be formulated as mathematical statements.”
― Roger Penrose

“In year 1500, there were about 500 million Homo Sapiens in the entire world. Today, there are 7 billion. The total value of goods and services produced by humankind in the year 1500 is estimated at $250 billion, in today's dollars. Nowadays the value of a year of human production is close to $60 trillion. In 1500 humanity consumed about 13 trillion calories of energy per day. Today, we consume 1,500 trillion calories a day. (Take a second look at those figures -- human population has increased fourteen-fold, production 240-fold, and energy consumption 115-fold.)”
― Yuval Noah Harari

“Platonist view of mathematical ideas: that mathematical truths ‘really’ exist, but they do so in an ideal form in some sort of parallel reality, which has always existed and always will.”
― Ian Stewart, Significant Figures: The Lives and Work of Great Mathematicians

“But we must not follow those who advise us…being mortal, [to think] of mortal things, but must, so far as we can, make ourselves immortal, and strain every nerve to live in accordance with the best thing in us; for even if it be small in bulk, much more does it in power and worth surpass everything.”
― Aristotle