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196 Are the Androids Dreaming Yet? Look inside 2 Principia Mathematica 3 Volume Set (v. 1-3) Principia Mathematica Amazon Listing for Principia Mathematica are undervalued. When mathematicians use the letters ‘PM’, they are usually referring to Russell and Whitehead’s Principia Mathematica rather than the afternoon. Hilbert’s Problems In 1900, while Russell and Whitehead were in full flow writing out their rules, David Hilbert was invited to deliver the annual lecture at the International Congress of Mathematicians in Paris. He asked a mathematician friend what subject he should pick for the talk and, in a moment of inspiration, the friend suggested laying out a vision for the future of mathematics. Rather than tell people how wonderful mathematicians were, and why their discipline was the pinnacle of human scientific endeavor, why not try modesty and list all the problems on which they were stumped? Hilbert liked the idea and devoted his talk to all the problems he thought mathematicians would solve in the 20" century. Hilbert’s Problems were simply an intellectual challenge. He offered no prizes. At the turn of the 21“ century, the Clay Institute created the Millennium Prizes for solving the most important modern mathematical problems. Each solution wins a prize of a million dollars! There are 23 numbered Hilbert Problems in all: ten in the original lecture and a further 13 in the written transcript. In 1928, he clarified the 2™ and 10" problems, refining them into three distinct questions: Is mathematics consistent, complete and decidable? Ironically this means that Hilbert’s 23 problems actually number 24! The most important Hilbert questions where these last three. They ask whether Russell and Whitehead would be successful — can you write out all the rules of mathematics and then simply calculate the answer to any problem or derive any proof. This is known as the Decision Problem. Can you mechanically decide any mathematical question without doubt? To explain Hilbert’s Problems, I need to define mathematics properly. HOUSE_OVERSIGHT_015886