New perspectives on functional inequalities

No, this blogpost has nothing to do with social stratification and class struggle nor does it address gender or racial inequalities. It is about Mathematics. The occasion? I have finally finished a book, which has been 3 years in the making,  “Functional Inequalities: New Perspectives and New Applications” (Sorry, it’s just the preface, the introduction and the table of contents–publisher oblige!). Why am I talking about it? Because it was hard, taxing and technical and I am so relieved it’s over. What is it about?

Roughly, and at the risk of being hung upside down by fellow mathematical analysts,  it is about the fact that there are all kind of  “energies” that are controlled by “entropy”. The question is which ones are they and how to prove/substantiate such claims.

Now, why did I write it? Well, for at least two reasons. The first is stated in the preface. “This project is rather an attempt at describing how most functional inequalities are not merely the byproduct of ingenious guess work by a few wizards among us, but are often manifestations of certain natural mathematical structures and physical phenomena. Our main goal here is to show how this point of view leads to systematic approaches for, not just proving the most basic functional inequalities, but also for understanding and improving them, and for devising new ones – sometimes at will, and often on demand.”

You do catch my drift, don’t you? Since my student days, I have always been in awe of  the wizardry exhibited by some of  my colleagues; those who could pull magical “mathematical inequalities” out of a hat. How did he/she think of that argument? Then, about ten years ago, I started seeing some things that helped me in the demystification process (and what an important life process demystification is!). Gone was my anguish of fading away into the sunset without discovering one single “new inequality”.  

I bet you are eager to know the second reason. Well, it is because my son wouldn’t have it any other way. He has been waiting for his turn ever since I had dedicated this book to his mother, then this one to his older sister and then this one to his other sister.

I have tried hard to convince him to accept my promise of dedicating to him my next and last book, the one I am supposed to write in my retirement. But then, he knew that this one was probably going to be about my own life story: either a too ordinary tale or a too embarrassing one!

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6 Responses to New perspectives on functional inequalities

  1. Bravo! Congratulations on finishing your book.

  2. Joseph says:

    Great post dad!

  3. Eugene Barsky says:

    Nassif, the library in UBC has all three books –,+N.+(Nassif),+1953. I am looking forward to purchasing your newest one!

  4. Tom Leinster says:

    Echoes of Gian-Carlo Rota in 1964, who began his seminal paper on enumerative combinatorics with this:

    One of the most useful principles of enumeration in discrete probability and combinatorial theory is the celebrated principle of inclusion-exclusion […] When skillfully applied, this principle has yielded the solution to many a combinatorial problem.

    But he noted:

    The lack of a systematic theory is hardly matched by the consummate skill of a few individuals with a natural gift for enumeration.

    And then he introduced a systematic theory, so that we don’t all have to be wizards.

    • Ghoussoub says:

      Thanks Tom. This does sound eerily similar. But when you think about it, it is more common that not in a discipline such as ours, where so many of us “mortals” are trying to understand and expand on the insights of the “greats”.

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