Logical difficulties in modern mathematics | njwildberger: tangential thoughts

Modern mathematics is enormously complicated and sophisticated. It takes some courage, and perhaps some foolishness, to dare to suggest that behind the fancy theories lie serious logical gaps, and indeed error. But this is the unfortunate reality. Around the corner, however, is a new and more beautiful mathematics, a more honest mathematics, in which everything makes complete sense! It is my job to give people glimpses of this better, more logical alternative, and to empower young people especially to not be afraid to question the status-quo and the dubious thinking that currently holds sway over the subject. My MathFoundations series of videos will investigate these problems in a systematic way; let me here at least briefly outline some of the problems, so you can get an initial idea, and so that perhaps some of you will start to think more seriously about these important issues. I will be saying a lot more about these topics in future posts. The notion of rigour in mathematics is a d

Modern mathematics is enormously complicated and sophisticated. It takes some courage, and perhaps some foolishness, to dare to suggest that behind the fancy theories lie serious logical gaps, and indeed error. But this is the unfortunate reality. Around the corner, however, is a new and more beautiful mathematics, a more honest mathematics, in which everything makes complete sense! It is my job to give people glimpses of this better, more logical alternative, and to empower young people especially to not be afraid to question the status-quo and the dubious thinking that currently holds sway o

saved by

• Lucas

related reading

• There’s more to mathematics than rigour and proofs | What's newterrytao.wordpress.com
• Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)plato.stanford.edu
• Napkin.pdfvenhance.github.io
• What do we mean by "the foundations of mathematics"?lawrencecpaulson.github.io
• The fall of the theorem economydavidbessis.substack.com
• Inconsistent Mathematics (Stanford Encyclopedia of Philosophy)plato.stanford.edu
• Formalism in the Philosophy of Mathematics (Stanford Encyclopedia of Philosophy)plato.stanford.edu
• Von Neumann: "The Mathematician" - MacTutor History of Mathematicsmathshistory.st-andrews.ac.uk
• Dedekind’s Contributions to the Foundations of Mathematics (Stanford Encyclopedia of Philosophy)plato.stanford.edu
• The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematicswolframscience.com
• More than argument, logic is the very structure of realityaeon.co
• How Many Numbers Exist? Infinity Proof Moves Math Closer to an Answer. | Quanta Magazinequantamagazine.org