*(Quanta Magazine)*

When a German retiree proved a famous long-standing mathematical conjecture, the response was underwhelming.

Continue reading “A Long-Sought Proof, Found and Almost Lost | Quanta Magazine”

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# Category: Mathematics

## A Long-Sought Proof, Found and Almost Lost | Quanta Magazine

A Long-Sought Proof, Found and Almost Lost by *(Quanta Magazine)*

## 🔖 What is good mathematics? | Terry Tao

What is good mathematics? by *(arxiv.org)*
## Some thoughts after reading

## Checkin UCLA Mathematical Sciences Building

UCLA Mathematical Sciences Building

## Why some infinities are bigger than others | Aeon Essays

Why some infinities are bigger than others by *(Aeon Essays)*

## 🔖 Confessions of the Pricing Man: How Price Affects Everything by Hermann Simon

Confessions of the Pricing Man: How Price Affects Everything by *(Springer, 2015)*
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## 🔖 Linear Operator Theory in Engineering and Science

Linear Operator Theory in Engineering and Science by *(Springer, 2nd printing 2000 edition (October 4, 2013))*
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## Checkin Mathematical Sciences Building, UCLA

Mathematical Sciences Building, UCLA

## 👓 A Conversation with @LPachter (BS ’94) | Caltech

A Conversation with Lior Pachter (BS '94) *(The California Institute of Technology)*
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## Checkin Mathematical Sciences Building, UCLA

Mathematical Sciences Building, UCLA

## Checkin UCLA Store (Ackerman Union)

UCLA Store (Ackerman Union)

## JUMP Math, a teaching method that’s proving there’s no such thing as a bad math student | Quartz

A mathematician has created a teaching method that’s proving there’s no such thing as a bad math student by *(Quartz)*
## Checkin Mathematical Sciences Building, UCLA

Mathematical Sciences Building, UCLA

## 🔖 IPAM Workshop on Gauge Theory and Categorification, March 6-10

IPAM Workshop on Gauge Theory and Categorification *(Institute of Pure and Applied Mathematics at UCLA - March 6-10, 2017)*

## Entropy | Special Issue: Maximum Entropy and Bayesian Methods

Entropy | Special Issue : Maximum Entropy and Bayesian Methods *(mdpi.com)*
## The Map of Mathematics: Animation Shows How All the Different Fields in Math Fit Together | Open Culture

Musings of a Modern Day Cyberneticist

When a German retiree proved a famous long-standing mathematical conjecture, the response was underwhelming.

Continue reading “A Long-Sought Proof, Found and Almost Lost | Quanta Magazine”

Syndicated copies to:Some personal thoughts and opinions on what ``good quality mathematics'' is, and whether one should try to define this term rigorously. As a case study, the story of Szemer\'edi's theorem is presented.

This looks like a cool little paper.

Update 3/17/17

And indeed it was. The opening has lovely long (though possibly incomplete) list of aspects of good mathematics toward which mathematicians should strive. The second section contains an interesting example which looks at the history of a theorem and it’s effect on several different areas. To me most of the value is in thinking about the first several pages. I highly recommend this to all young budding mathematicians.

In particular, as a society, we need to be careful of early students in elementary and high school as well as college as the pedagogy of mathematics at these lower levels tends to weed out potential mathematicians of many of these stripes. Students often get discouraged from pursuing mathematics because it’s “too hard” often because they don’t have the right resources or support. These students, may in fact be those who add to the well-roundedness of the subject which help to push it forward.

I believe that this diverse and multifaceted nature of “good mathematics” is very healthy for mathematics as a whole, as it it allows us to pursue many different approaches to the subject, and exploit many different types of mathematical talent, towards our common goal of greater mathematical progress and understanding. While each one of the above attributes is generally accepted to be a desirable trait to have in mathematics, it can become detrimental to a field to pursue only one or two of them at the expense of all the others.

As I look at his list of scenarios, it also reminds me of how areas within the humanities can become quickly stymied. The trouble in some of those areas of study is that they’re not as rigorously underpinned, as systematic, or as brutally clear as mathematics can be, so the fact that they’ve become stuck may not be noticed until a dreadfully much later date. These facts also make it much easier and clearer in some of these fields to notice the true stars.

As a reminder for later, I’ll include these scenarios about research fields:

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- A field which becomes increasingly ornate and baroque, in which individual

results are generalised and refined for their own sake, but the subject as a

whole drifts aimlessly without any definite direction or sense of progress;- A field which becomes filled with many astounding conjectures, but with no

hope of rigorous progress on any of them;- A field which now consists primarily of using ad hoc methods to solve a collection

of unrelated problems, which have no unifying theme, connections, or purpose;- A field which has become overly dry and theoretical, continually recasting and

unifying previous results in increasingly technical formal frameworks, but not

generating any exciting new breakthroughs as a consequence; or- A field which reveres classical results, and continually presents shorter, simpler,

and more elegant proofs of these results, but which does not generate any truly

original and new results beyond the classical literature.

I’ll bet I had a better Pi Day than you did today. I got to sit through three hours of a fascinating lecture on complex analysis covering Bernoulli numbers, Reimann’s Zeta Function, the Gamma Function, Euler’s Function, the duplication formula, the symmetrical form of the zeta functional equation, and Reimann’s Hypothesis. All replete with references to pi! Take that nerds!

Los Angeles, California, United States of America

Syndicated copies to:Georg Cantor showed that some infinities are bigger than others. Did he assault mathematical wisdom or corroborate it?

Continue reading “Why some infinities are bigger than others | Aeon Essays”

Syndicated copies to:The world’s foremost expert on pricing strategy shows how this mysterious process works and how to maximize value through pricing to company and customer.

In all walks of life, we constantly make decisions about whether something is worth our money or our time, or try to convince others to part with their money or their time. Price is the place where value and money meet. From the global release of the latest electronic gadget to the bewildering gyrations of oil futures to markdowns at the bargain store, price is the most powerful and pervasive economic force in our day-to-day lives and one of the least understood.

The recipe for successful pricing often sounds like an exotic cocktail, with equal parts psychology, economics, strategy, tools and incentives stirred up together, usually with just enough math to sour the taste. That leads managers to water down the drink with hunches and rules of thumb, or leave out the parts with which they don’t feel comfortable. While this makes for a sweeter drink, it often lacks the punch to have an impact on the customer or on the business.

It doesn’t have to be that way, though, as Hermann Simon illustrates through dozens of stories collected over four decades in the trenches and behind the scenes. A world-renowned speaker on pricing and a trusted advisor to Fortune 500 executives, Simon’s lifelong journey has taken him from rural farmers’ markets, to a distinguished academic career, to a long second career as an entrepreneur and management consultant to companies large and small throughout the world. Along the way, he has learned from Nobel Prize winners and leading management gurus, and helped countless managers and executives use pricing as a way to create new markets, grow their businesses and gain a sustained competitive advantage. He also learned some tough personal lessons about value, how people perceive it, and how people profit from it.

In this engaging and practical narrative, Simon leaves nothing out of the pricing cocktail, but still makes it go down smoothly and leaves you wanting to learn more and do more―as a consumer or as a business person. You will never look at pricing the same way again.

A unique introduction to the theory of linear operators on Hilbert space. The author presents the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented.

Complex Analysis II

Los Angeles, California, United States of America

Syndicated copies to:Pachter, a computational biologist, returns to CalTech to study the role and function of RNA.

Pachter, a computational biologist and Caltech alumnus, returns to the Institute to study the role and function of RNA.

*Lior Pachter (BS ’94) is Caltech’s new Bren Professor of Computational Biology. Recently, he was elected a fellow of the International Society for Computational Biology, one of the highest honors in the field. We sat down with him to discuss the emerging field of applying computational methods to biology problems, the transition from mathematics to biology, and his return to Pasadena.* Continue reading “👓 A Conversation with @LPachter (BS ’94) | Caltech”

Complex Analysis part II

Los Angeles, California, United States of America

Syndicated copies to:This looks like fun: *Signals and Boundaries: Building Blocks for Complex Adaptive Systems* by John H. Holland

Ackerman Union, Los Angeles, California, United States of America

Syndicated copies to:"Mathematicians have big egos, so they haven’t told anyone that math is easy.”

It’s true what they say, “Complex Analysis IS for lovers.” #theoremoncanonicalproducts #HappyValentinesDay

Los Angeles, California, United States of America

Syndicated copies to:The equations of gauge theory lie at the heart of our understanding of particle physics. The Standard Model, which describes the electromagnetic, weak, and strong forces, is based on the Yang-Mills equations. Starting with the work of Donaldson in the 1980s, gauge theory has also been successfully applied in other areas of pure mathematics, such as low dimensional topology, symplectic geometry, and algebraic geometry.

More recently, Witten proposed a gauge-theoretic interpretation of Khovanov homology, a knot invariant whose origins lie in representation theory. Khovanov homology is a “categorification” of the celebrated Jones polynomial, in the sense that its Euler characteristic recovers this polynomial. At the moment, Khovanov homology is only defined for knots in the three-sphere, but Witten’s proposal holds the promise of generalizations to other three-manifolds, and perhaps of producing new invariants of four-manifolds.

This workshop will bring together researchers from several different fields (theoretical physics, mathematical gauge theory, topology, analysis / PDE, representation theory, symplectic geometry, and algebraic geometry), and thus help facilitate connections between these areas. The common focus will be to understand Khovanov homology and related invariants through the lens of gauge theory.

This workshop will include a poster session; a request for posters will be sent to registered participants in advance of the workshop.

Edward Witten will be giving two public lectures as part of the Green Family Lecture series:

March 6, 2017

*From Gauge Theory to Khovanov Homology Via Floer Theory*

The goal of the lecture is to describe a gauge theory approach to Khovanov homology of knots, in particular, to motivate the relevant gauge theory equations in a way that does not require too much physics background. I will give a gauge theory perspective on the construction of singly-graded Khovanov homology by Abouzaid and Smith.

March 8, 2017

*An Introduction to the SYK Model*

The Sachdev-Ye model was originally a model of quantum spin liquids that was introduced in the mid-1990′s. In recent years, it has been reinterpreted by Kitaev as a model of quantum chaos and black holes. This lecture will be primarily a gentle introduction to the SYK model, though I will also describe a few more recent results.

Open for submission now

Deadline for manuscript submissions: 31 August 2017

A special issue of *Entropy* (ISSN 1099-4300).
## Special Issue Editor

## Special Issue Information

Deadline for manuscript submissions: **31 August 2017**

Dear Colleagues,

Whereas Bayesian inference has now achieved mainstream acceptance and is widely used throughout the sciences, associated ideas such as the principle of maximum entropy (implicit in the work of Gibbs, and developed further by Ed Jaynes and others) have not. There are strong arguments that the principle (and variations, such as maximum relative entropy) is of fundamental importance, but the literature also contains many misguided attempts at applying it, leading to much confusion.

This Special Issue will focus on Bayesian inference and MaxEnt. Some open questions that spring to mind are: Which proposed ways of using entropy (and its maximisation) in inference are legitimate, which are not, and why? Where can we obtain constraints on probability assignments, the input needed by the MaxEnt procedure?

More generally, papers exploring any interesting connections between probabilistic inference and information theory will be considered. Papers presenting high quality applications, or discussing computational methods in these areas, are also welcome.

Dr. Brendon J. Brewer

*Guest Editor*

**Submission**

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are refereed through a peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. *Entropy* is an international peer-reviewed Open Access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1500 CHF (Swiss Francs).

No papers have been published in this special issue yet.

Source: Entropy | Special Issue : Maximum Entropy and Bayesian Methods