Preface to Joseph Rotman's Introduction to Algebraic Topology.
JHC Whitehead was the nephew of AN Whitehead.
JHC Whitehead was the nephew of AN Whitehead.
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The same person when asked what version of Python he uses for his "AI/ML" work said 2.11 :)
Original video: https://youtu.be/G6GjnVM_3yM
Original video: https://youtu.be/G6GjnVM_3yM
Hardy-Littlewood Axioms for Collaboration
Axiom 1: It didn't matter whether what they wrote to each other was right or wrong.
Axiom 2: There was no obligation to reply, or even to read, any letter one sent to the other.
Axiom 3: They should not try to think about the same things.
Axiom 4: To avoid any quarrels, all papers would be under joint name, regardless of whether one of them had contributed nothing to the work.
Axiom 1: It didn't matter whether what they wrote to each other was right or wrong.
Axiom 2: There was no obligation to reply, or even to read, any letter one sent to the other.
Axiom 3: They should not try to think about the same things.
Axiom 4: To avoid any quarrels, all papers would be under joint name, regardless of whether one of them had contributed nothing to the work.
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Forwarded from Deputy Sheriff The Viking Programmer
cartesian product ... stuff about computing mostly
Write-only? A simple program translated from C to Forth
The old joke is that Forth is a “write-only language”. in other words, you can write this stuff but you cannot understand it (and hence maintain it). Of course, any endorsement of this …
Poincaré, the greatest mathematician of the recent era, divided all problems into two classes: binary problems and interesting problems. Binary problems are problems which admit of an answer “yes” or “no” (for example, Fermat’s question).
Interesting problems are those for which an answer of “yes” or “no” is insufficient. They require investigation of questions that lead one further. For example, Poincaré was interested in how to change the conditions of a problem (for instance, the boundary conditions of a differential equation), while retaining the existence and uniqueness of its solution, or how the number of solutions varies when we make some other change. Thus he started the theory of bifurcations.
Three years before Hilbert gave his list of problems, Poincaré formulated the basic, in his view, mathematical questions that the nineteenth century would leave for the twentieth. This was the formulation of the mathematical basis for quantum and relativistic physics.
Today, many people think that relativistic physics at the time, in 1897, did not yet exist, since Einstein published his theory of relativity only in 1905. But Poincaré formulated the principle of relativity earlier, in his article of 1895, “On the Measurement of Time”, which Einstein actually used (and which, by the way, he didn’t acknowledge in writing until 1945). In just the same way, Schrödinger, in laying the foundation for quantum mechanics, achieved his success only because he used the mathematical works of his predecessor Hermann Weyl, whom no one mentioned later on, although Schrödinger actually references these works (in his first book).
V.I Arnold, Experimental Mathematics (2010)
Interesting problems are those for which an answer of “yes” or “no” is insufficient. They require investigation of questions that lead one further. For example, Poincaré was interested in how to change the conditions of a problem (for instance, the boundary conditions of a differential equation), while retaining the existence and uniqueness of its solution, or how the number of solutions varies when we make some other change. Thus he started the theory of bifurcations.
Three years before Hilbert gave his list of problems, Poincaré formulated the basic, in his view, mathematical questions that the nineteenth century would leave for the twentieth. This was the formulation of the mathematical basis for quantum and relativistic physics.
Today, many people think that relativistic physics at the time, in 1897, did not yet exist, since Einstein published his theory of relativity only in 1905. But Poincaré formulated the principle of relativity earlier, in his article of 1895, “On the Measurement of Time”, which Einstein actually used (and which, by the way, he didn’t acknowledge in writing until 1945). In just the same way, Schrödinger, in laying the foundation for quantum mechanics, achieved his success only because he used the mathematical works of his predecessor Hermann Weyl, whom no one mentioned later on, although Schrödinger actually references these works (in his first book).
V.I Arnold, Experimental Mathematics (2010)
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We have successfully worked our way through Bourbaki's Elements of History of Mathematics, and the new book we'd be starting with is Hermann Weyl's Symmetry. After Poincare, I think I can only think of Weyl as the only mathematician who had a similar universalist spirit. He not only went into history and philosophy of mathematics and science, he actually used ideas from Brouwer's intuitionism for point-set topology. Similarly, he took a Husserlian phenomenological approach for physics. I can count on my fingers the number of physicists I know who have ever taken a look at Husserl.
Other than Arendt Heyting, Hermann Weyl was the most radical supporter of intuitionism. And before we had great constructivists like Erett Bishop and Abraham Robinson, it was Weyl who developed classical calculus from scratch without touching axiom of choice or proof by contradiction and Cantor's infinite sets. And the inspiration for this radical constructivism in Weyl was due to the philosopher Johann Gottlieb Fichte, the successor to Kant in the tradition of German Idealism!
The Symmetry text is not really rigorous, but it's a good pick after going through the very technical Bourbaki text. The text provides examples from history, physics, and of course mathematics. And since it's a pretty short monograph, we have planned to next read through Haskell Curry's Outlines for a Formalist Philosophy of Mathematics.
Other than Arendt Heyting, Hermann Weyl was the most radical supporter of intuitionism. And before we had great constructivists like Erett Bishop and Abraham Robinson, it was Weyl who developed classical calculus from scratch without touching axiom of choice or proof by contradiction and Cantor's infinite sets. And the inspiration for this radical constructivism in Weyl was due to the philosopher Johann Gottlieb Fichte, the successor to Kant in the tradition of German Idealism!
The Symmetry text is not really rigorous, but it's a good pick after going through the very technical Bourbaki text. The text provides examples from history, physics, and of course mathematics. And since it's a pretty short monograph, we have planned to next read through Haskell Curry's Outlines for a Formalist Philosophy of Mathematics.
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(φ (μ (λ)))
We have successfully worked our way through Bourbaki's Elements of History of Mathematics, and the new book we'd be starting with is Hermann Weyl's Symmetry. After Poincare, I think I can only think of Weyl as the only mathematician who had a similar universalist…
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