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Terence Tao
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Attended Princeton University
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Terence Tao

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Died on the taxi ride back from his Abel prize ceremony.  I met him a few times whilst a graduate student at Princeton, but never talked with him at the time; maybe I should have taken the opportunity while I could.
 
Oh dear. What a terrible piece of news.
Mathematician John Nash, subject of film A Beautiful Mind, dies in a New Jersey taxi crash with his wife, US media reports say
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Such a sad event and moment in the field of Mathematics and Science.  He has been, and always will be, an inspiration to those who aspire to a different level of thinking!  R.I.P. to you and your wife Dr Nash, may GOD keep you!
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One of the curious phenomena in political activism (as famously lampooned in the scene linked below from Monty Python's "Life of Brian") is that political activists often reserve their greatest criticism for their natural allies, rather than their natural enemies.  As the linked sketch suggests, this behaviour appears to be quite irrational.  However, it is possible to justify this behaviour as being rational over the short-term, even if it fails to be rational in the long-term.

Here is a simple model to illustrate this.  Suppose there is a political issue X, on which one can take just one of two positions: pro-X and anti-X.  (In the example below, X would be "Judean independence".)  For sake of this discussion, we assume that there are no intermediate or neutral options available. Given a rational actor A, how would A choose which of these two positions to take?  One can postulate a payoff function P( A, p ) which specifies the payoff (or "utility") that A would obtain from taking position p, thus P( A, pro-X ) is the payoff A would get from declaring to be pro-X, and P( A, anti-X ) would be the payoff A would get from declaring to be anti-X.  A rational actor A would then take the position that offered the larger payoff.  For instance, for the Roman authorities in the example below, P( A, anti-X ) would presumably be considerably larger than P( A, pro-X ) (as long as the level of unrest was manageable), whereas for rebels P( A, pro-X ) would presumably be larger than P( A, anti-X ) (as long as the level of suppression by the authorities was not too great).

Now, suppose there were several actors A for which the payoffs P( A, pro-X ), P( A, anti-X ) were close to equal.  A pro-X activist could then attempt to tip the balance for these actors to join the pro-X camp, by actively criticising (or boycotting, etc.) those actors who decided to choose anti-X, thus effectively lowering the payoff P( A, anti-X ) for such actors to the point where it would be rational for A to choose pro-X instead.  On the other hand, for actors A for which P( A, anti-X ) was significantly larger than P( A, pro-X ), such criticism would be substantially less effective, as it would usually not be enough to tip the balance in one's favour.  Hence, the rational use of resources (in the short term) for a pro-X activist is to focus one's attacks on "moderates" that already have significant pro-X sympathies, rather than "natural enemies" that are strongly in the anti-X camp.

However, despite this strategy being rational in the short-term, it is detrimental in the long-term, because it creates a disincentive for strongly anti-X actors to moderate their anti-X position.  One can come up with many examples in real life in which an anti-X actor tentatively introduces a somewhat pro-X policy, but then comes under attack, not just from anti-X activists, but also from pro-X activists for not going far enough.  Perversely, the long-term effect of pro-X activism is then to encourage anti-X actors to simply remain anti-X and not attempt any pro-X initiatives whatsoever, so that pro-X activists do not even bother to attempt influencing them via boycotts or other negative actions.  Another unintended consequence is that long-term-oriented pro-X activist groups may begin to criticise more short-term oriented pro-X groups for sabotaging their long-term cause.

The moral here is that in order for activism to be successful in the long term, it has to pressure "unpersuadable" actors at least as strongly as "persuadable ones", lest one create perverse incentives.
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+Terence Tao It all boils down to this: if you're (for example) a Shia Muslim, the jump from Shia to Sunni is much easier than the jump from Islam to Christianity. So from the Shia's perspective, the Sunni is a much bigger threat to the size of his group (i.e. his power) than the Christians, especially since there are more Sunnis around than Christians.
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The Abel prize is awarded jointly to John Nash and Louis Nirenberg for their respective contributions to PDE.  (It is not the first time the Abel has been awarded for disjoint contributions to a single field; it was also awarded jointly to Thompson and Tits in 2008.)
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Looking forward to going to the arrangements.
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According to the usual stereotypes, Germans have a reputation for (a) efficiency, (b) respect for authority, and (c) not much of a sense of humour.
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“German humour is no laughing matter.”


Except in this case, very much so. I haven't laughed so hard in a long time.
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Videos of the maths, physics, and life science symposia on Nov 10 connected with the 2015 Breakthrough prize.
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Isn't Colbert the only one with number 0? Wouldn't the Colbert number be 1?
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Suppose one has a number of debts, at various amounts and interest rates (e.g. $2000 of credit card debt at 20% interest, a $20000 car loan at 10% interest, etc.).  Suppose one also has some dependable stream of disposable income (e.g. $1000 a month) dedicated to the purpose of paying off these debts.  If the objective is to become debt-free as quickly as possible, what is the optimal strategy to do so?

There are two standard strategies for this, usually called the "snowball" and "avalanche" strategies.  The snowball strategy is to attack the smallest debt first, regardless of interest rate, then move on to the next smallest once the first debt is paid off, and so forth.  The avalanche strategy, by contrast, attacks the highest interest rate debt first, regardless of size, then the next highest after the first debt is paid off, and so forth.  The conventional wisdom is that the avalanche strategy is mathematically superior, but that the snowball strategy can be psychologically easier to maintain due to the motivation provided by quickly eliminating some of the smaller debts.

Under ideal hypotheses (in particular, under the assumption of no minimal payments, no transaction costs or other fees, continuously compounded interest at a fixed, predetermined rate, and under the assumption of no unforeseen fluctuation in the amount of disposable income available each unit time to pay off debt, and one has no risk of abandoning one's repayment strategy due to lack of motivation or other psychological factors), one can indeed show without too much trouble that the avalanche method is the mathematically optimal strategy.  (This is easiest to see by slicing up all the debts to be of equal size, e.g. viewing a $20000 car loan as being mathematically equivalent to ten $2000 loans at the same interest rate.)  But it was an interesting puzzle to work out whether this was still the case in the presence of minimum payment requirements on each debt.  A typical such requirement would consist of either a fixed amount, or some percentage of the outstanding debt, whichever is greater (e.g. a credit card may have a minimum payment of the greater of $25, or 1% of the outstanding debt).  One can then argue that by attacking a smaller debt first, it can free up a minimum payment that can then be applied to other debts, even if the smaller debt is lower interest than other debts.  Because a minimum payment requirement is only removed when the entire debt is paid off, it is no longer the case that a single large loan is mathematically equivalent to several small loans, rendering the preceding argument for the optimality of the avalanche method invalid.

Anyway, the puzzle is this: assuming otherwise ideal circumstances (no transaction costs, etc.), is it mathematically possible to have a combination of debts with minimum payment requirements of the form described above, such that the avalanche strategy is no longer optimal, being beaten by some other strategy such as the snowball strategy?  In other words, is the perceived benefit of freeing up a minimum payment purely psychological, or can it actually have real value?
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No Definitelly not. It is not mathematically possible to have a combination of debts that beat the avalanche strategy.

Intuitivelly is easy to see that each debt is like a bleeding wound, being the interest rate the "amount of bleeding" per debt/wound. It this case it is clear that the better approach is to stop first what is bleeding more and let the less bleeding debts for later. This strategy is the one that minimizes the amount of lost blood/money due to debt payment.
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A variant of the blue-eyed islander puzzle.  (The story, by the way, eventually reveals the solution, so one may wish to stop reading before then if one wants to try one's hand at it first.)
A Singaporean logic problem for teenagers has stumped the world, but is that really what's expected of local students?
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+Tom Delano I can't speak for Terence but a typical math professor would solve this in essentially the time it takes to read it.  Less than a minute.
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Sometimes it is better to describe a set by its elements, rather than by its constraints.
The Los Angeles parking sign revolution has been a long time coming. Last October, the LA City Council voted to try out new, less tell-y/more show-y markers somewhere in...
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How simple yet elusive until now! Maybe we could answer some fundamental management principles if we were to probe deeper.
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Very sad today to hear that Terry Pratchett, who was one of my favourite authors as a child, died today.  I loved his Discworld series (and recently got my son hooked on it too).   In fact, about two decades ago, I even went so far as helping to reconstruct (with a fellow graduate student at the time, Andrew Millard) the rules for a fictional card game that had appeared in his books; we later heard from him that he approved of our reconstruction of the game (which he had never completely formalised himself), which was a huge honour for us.  
Author of more than 70 books, who had early-onset Alzheimer’s disease, dies at his home, his publishers have announced
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There's a new documentary about Yitang Zhang and his work on bounded gaps between primes (with a small mention of the related Polymath project also), a project partly supported by MSRI and the Simons Foundation.  A trailer can be found on the linked page.

I just watched the DVD (which I received a courtesy copy of, as I was interviewed briefly for this documentary, amongst many other mathematicians and friends of Yitang).  It was a nice balance between the mathematics and the personal story (actually, I was impressed by the amount of detail about Yitang's proof that was described accurately and accessibly, with the use of computer animations a nice touch).
In April 2013, a lecturer at the University of New Hampshire submitted a paper to the Annals of Mathematics. Within weeks word spread-- a little-known mathematician, with no permanent job, working in complete isolation had made an important breakthrough towards solving the Twin Prime Conjecture.
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Being rather far from the more algebraic areas of mathematics, I myself have not had too much interaction with Grothendieck's work (though I once had occasion to delve into SGA IV for a research project), but certainly he was one of the most influential mathematicians of the 20th century.  (Incidentally, while he is of course best known for his revolutionary impact in algebraic geometry and related areas, his early work in analysis, particularly on what is now known as Grothendieck's inequality, is still of major interest in high dimensional geometry and certain areas of theoretical computer science.)
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There are men whose greatness is such that they can not be forgotten even against their will.
Grothendieck is one of these.  He was an ingenious mathematician, considered one of the finest minds of the twentieth century (and, in my opinion, of all ages). The life of Alexander was not easy ... as well as his nature.

He is one of my favorite mathematicians because he was able to create Mathematics!
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  • Princeton University
    Mathematics, 1992 - 1996
  • Flinders University
    Mathematics, 1989 - 1992
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  • UCLA
    Mathematician, present
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