Yes, irrational numbers were a great discovery (including how they were discovered) and the systematic treatment of math in The Elements was a better example of

Yes, irrational numbers were a great discovery (including how they were discovered) and the systematic treatment of math in The Elements was a better example of the advancement in approaches to knowledge and thinking. And yes, if the Pythagoreans actually thought that this was a formula for irrational numbers, that would indeed to quite impressive.