We already know that, in one sense, Archimedes used methods that would now be recognised as a form of integration - specifically the method of exhaustion (originally developed by Eudoxus, C4th BC), where a series of inscribed and exscribed polygons is use to find successively better approximations to the area under curves (or using polyhedra for volumes).
The inverse, differentiation, came much later (generally attributed to Fermat or Barrow, early - mid C17th). The two ideas were then related and developed into a unified theory calculus independently by Newton and Leibniz. The grudge developed because both wanted to claim to have been the first to 'invent' it - evidence now indicates that Newton did the work first, but Leibniz pulished first.
What we now term calculus uses methods based primarily on Newton's theory and notation based on Leibniz's work.
Also, so far, no examples of transgenic engineering (transfering genes from one species to another) or even invidual directed gene transfer in humans has been shown to be feasible, let alone desirable.
But rememeber genetically modified foods? For example a fish gene is used in GM strawberries to enable them to produce an anti-freeze to survive frosts.
Extending this to humans shouldn't need much of a leap in technology.
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The inverse, differentiation, came much later (generally attributed to Fermat or Barrow, early - mid C17th). The two ideas were then related and developed into a unified theory calculus independently by Newton and Leibniz. The grudge developed because both wanted to claim to have been the first to 'invent' it - evidence now indicates that Newton did the work first, but Leibniz pulished first.
What we now term calculus uses methods based primarily on Newton's theory and notation based on Leibniz's work.
Extending this to humans shouldn't need much of a leap in technology.