Can Mathematics Be Proved Consistent Gdels Shorthand Notes & Lectures On Incompl - Jan von Plato

Kurt Gdel (1906-1978) Shook The Mathematical World In 1931 By A Result That Has Become An Icon Of 20th Century Science: The Search For Rigour In Proving Mathematical Theorems Had Led To The Formalization Of Mathematical Proofs, To The Extent That Such Proving Could Be Reduced To The Application Of A Few Mechanical Rules. Gdel Showed That Whenever The Part Of Mathematics Under Formalization Contains Elementary Arithmetic, There Will Be Arithmetical Statements That Should Be Formally Provable But Arent. The Result Is Known As Gdels First Incompleteness Theorem, So Called Because There Is A Second Incompleteness Result, Embodied In His Answer To The Question Can Mathematics Be Proved Consistent?