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(34)
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######### Topic INDEX #########
Mathematics
28 Articles
Latest
######### Card Article Topic MAIN c #########
Trading Volatility
Emanuel Derman
[short_description]
The Black–Scholes equation takes the idea of Brownian motion from physics and uses it to explain volatility in stock options markets. Emanuel Derman reviews its impact on options traders.
######### Card Article Topic MAIN c #########
A Crisis of Identification
David Michael Roberts
[short_description]
Almost a decade after claiming a proof of the abc conjecture, Shinichi Mochizuki’s work is stil debated. David Michael Roberts examines efforts by Peter Scholze and Jacob Stix to resolve the impasse.
######### Card Article Topic MAIN c #########
Woit’s Way
Andrew Jordan
[short_description]
Peter Woit’s book
Quantum Theory, Groups and Representations
is based on a series of lectures that he gave at Columbia University. Woit is a fine teacher. Andrew Jordan finds much to admire.
######### Card Article Topic MAIN c #########
Big, Little, Nothing, Everything
Alexander Kharazishvili
[short_description]
No finite set is bigger than everything, and so every finite set is smaller than something. If one object is added to a small finite set, it gets bigger, but stays small. Could that be right?
######### Card Article Topic MAIN c #########
Matrix Madness
Daniel Kleitman
[short_description]
Infinitesimally-small probabilities and synapse firings. Daniel Kleitman offers some mathematical objections to Nick Bostrom’s well-known paper, “Are You Living in a Computer Simulation?”
######### Card Article Topic MAIN c #########
Fukugen
Ivan Fesenko
[short_description]
Inter-Universal Teichmüller theory applies mono-anabelian algorithms to algebraic fundamental groups in one universe to obtain descriptions of objects constructed from those groups in another
######### Card Article Topic MAIN c #########
Cantor’s Diagonalization Method
Alexander Kharazishvili
[short_description]
Mathematician Alexander Kharazishvili explores how powerful the celebrated diagonal method is for general and descriptive set theory, recursion theory, and Gödel’s incompleteness theorem.
######### Card Article Topic MAIN c #########
Touched by the Goddess
Krishnaswami Alladi
[short_description]
A recent film starring Dev Patel depicts Srinivasa Ramanujan’s mathematical achievements and tragically early death at 32. Number theorist Krishnaswami Alladi reviews
The Man Who Knew Infinity
.
######### Card Article Topic MAIN c #########
Doing Mathematics Differently
Gregory Chaitin
[short_description]
Spattering drops of ink, Leibniz intuited that a theory as complex as the data it is supposed to explain is useless. Gregory Chaitin finds the same thing using algorithmic information theory.
######### Card Article Topic MAIN c #########
Categories: From Zero to Infinity
Pierre Schapira
[short_description]
Set theory, category theory, and topology. Pierre Schapira explores the concept of identity within category theory, and what it means for the properties to be satisfied only up to homotopy.
######### Card Article Topic MAIN c #########
Strangely Convergent Sequences
Alexander Kharazishvili
[short_description]
Math can be considered an interplay between finite and infinite collections and between discrete and continuous structures. Alexander Kharazishvili looks at convergent and divergent sequences.
######### Card Article Topic MAIN c #########
An Algorithmic God
Gregory Chaitin
[short_description]
Can we think of DNA as a programming language and evolution as programming without a programmer? Gregory Chaitin proposes a new research program, applying software models to biology.
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