➡️ Learn real Calculus, starting from scratch (pre-calculus) to advanced level! Click here and join Mastering Calculus: https://www.temciencia.com.br Gödel's Incompleteness Theorems are two of the most beautiful and profound contributions in the history of mathematics. In his famous theorems, Gödel showed that mathematics had a serious flaw. In this video, we will talk about how mathematics really works, and how Gödel destroyed Hilbert's dream of a unified theory from a finite group of axioms, from which all mathematical theorems should be derived, resulting in a complete and consistent system. Recommended reading Incompleteness: The Proof and Paradox of Kurt Gödel (Rebecca Goldstein) https://amzn.to/3LPZeUV When Einstein Walked with Gödel (Jim Holt) https://amzn.to/3TPVm8w affiliate links: when you buy, a small percentage is donated to the channel without any price increase for you Related video: ???? What is NON-EUCLIDEAN GEOMETRY? - History of Geometry • What is NON-EUCLIDEAN GEOMETRY? - H... Become a member and help me continue producing this type of content: https://www.youtube.com/temciencia/join ============================================= Script, presentation and editing: Daniel Nunes My Instagram: / tem.ciencia ===================================== WATCH ALSO: ???? THE LEGENDARY CIRCLE SQUARE Problem • THE LEGENDARY CIRCLE SQUARE Problem ... ???? THE ARROW OF TIME: Why don't you remember the future? • TIME'S ARROW: Why Don't You ... ???? The (TRUE) ORIGIN of COMPLEX NUMBERS • The (TRUE) ORIGIN of COMPLEX NUMBERS ... ???? JOSEPHUS' PROBLEM (and its incredible story) • JOSEPHUS' PROBLEM (and its incredible ... ???? A BRIEF HISTORY of MEASURE and INTEGRATION • A BRIEF HISTORY of MEASURE and INTEGRATION ... ???? POINCARÉ CONJECTURE: a 1 MILLION DOLLAR problem • POINCARÉ CONJECTURE: a 1 MILLION DOLLAR problem ... ???? ARISTOTLE'S WHEEL PARADOX • ARISTOTLE'S WHEEL PARADOX ???? ARE YOU RATIONAL? (Allais' Paradox and Prospect Theory) • ARE YOU RATIONAL? (Allais' Paradox... ???? THE BIRTHDAY PARADOX • THE BIRTHDAY PARADOX (how do you ... ???? PRISONERS' DILEMMA and NASH'S EQUILIBRIUM • PRISONERS' DILEMMA and NASH'S EQUILIBRIUM... ???? ST. PETERSBURG PARADOX: HOW MUCH IS INFINITE MONEY WORTH? • ST. PETERSBURG PARADOX: HOW MUCH IS INFINITE MONEY WORTH? ???? Mathematics and Sports Betting: HOW TO BREAK THE BANK? • Mathematics and Sports Betting: HOW TO... ???? THE (almost) IMPOSSIBLE PROBLEM 3 Houses Problem • THE (almost) IMPOSSIBLE PROBLEM Probl... ???? WHY (scientifically) THERE IS NO SCIENTIFIC PROOF • WHY (scientifically) THERE IS NO SCIENTIFIC PROOF ... ???? Was MATHEMATICS DISCOVERED or INVENTED? • Was MATHEMATICS DISCOVERED or INVENTED... ???? WHAT IS IT LIKE TO DO A DOCTORATE IN MATHEMATICS AT IMPA • WHAT IS IT LIKE TO DO A DOCTORATE IN MATHEMATICS... ???? HOW IS THE ENEM SCORE REALLY CALCULATED? • TRI: the MATHEMATICS behind the ENEM SCORE... ???? PageRank: HOW GOOGLE's Mathematical ALGORITHM works • PageRank: HOW GOOGLE's Mathematical ALGORITHM w... ???? A GAME that NOBODY CAN WIN. Here's why. • A GAME that NOBODY CAN WIN. ... ???? WHY DO YOU have LESS FRIENDS than your friends? • WHY DO YOU have LESS FRIENDS than your ... ???? THE ILLUSION of MAJORITY • THE ILLUSION of MAJORITY ???? THE HARDEST QUESTION IN THE HISTORY OF GOOGLE • THE HARDEST QUESTION IN THE HISTORY OF... ???? WHAT is MATHEMATICS FOR? When will you actually use it? • WHAT is MATHEMATICS FOR? When will you... ???? WOULD YOU PASS AN INTERVIEW with AMAZON? AND MICROSOFT? • WOULD YOU PASS an AMAZON INTERVIEW? ???? THE PROBLEM with VOLUME FORMULAS that INTRIGUED GAUSS • The BIG PROBLEM with VOLUME FORMULAS... ???? WHY are there only 5 PLATO SOLIDS in 3D? • WHY are there only 5 PLATO SOLIDS in 3D? ???? What is NON-EUCLIDEAN GEOMETRY? - History of Geometry • What is NON-EUCLIDEAN GEOMETRY? - H... ???? THE RING PARADOX • THE RING PARADOX ???? The SECRET Mathematics of things • Where is the Advanced Mathematics in n... ???? HOW was PI CALCULATED (with a matchbox)? • HOW TO CALCULATE PI by throwing MATCH... ???? 3 PARADOXES OF INFINITY • 3 PARADOXES OF INFINITY ???? Hilbert's INFINITY Hotel: How to Count Infinity? • Hilbert's INFINITY Hotel: a PARADOX...