A prize for a theorem

Pierre de Fermat was born in 1601 in Beaumont-de-Lomagne in southwestern France. He was not even a mathematician; he was a civil servant who devoted himself to mathematics as a hobby. He was regarded as one of the most gifted self-taught mathematicians who ever lived.

I think that this quotation from The girl who played with fire by Stieg Larson, the second novel from the series Millennium, was the perfect introduction to a post about the Fermat's Last Theorem and Andrew Wiles, who proofed it in 1993. And he awarded the Abel Prize just some days ago.

Simply a joke?

Pierre de Fermat by Bernarda Bryson

Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos ejusdem nominis fas est dividere: cujus rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.⁽¹⁾

This is what Pierre de Fermat wrote in the margin of Arithmetica by Diofanto and it establish the impossibility to find solutions in the field of natural numbers for the diophantine equation⁽²⁾ that generalizes the Pythagorean theorem: \[a^n + b^n = c^n\] Following the Pythagorean theorem, for $n = 2$ the Fermat's equation has solutions in the field of natural numbers, called Pythagorean triples. For $n$ greater than 2 the story, instead, becomes more complicated, so that the same Fermat, while writing what follows, never provided a full demonstration, but only for the special case of $n = 4$:

I have discovered a truly marvelous proof of this theorem, which can't be contained in the too narrow page margin.

Ludolph van Ceulen: in searching of pi

One of the most important mathematicians for $\pi$, was Ludolph van Ceulen, German mathematician born 28 January 1540 in Hildesheim. His father, Johannes Van Ceulen, was a small trader who could not afford advanced education for a son who showed some interest in mathematics. The main difficulty for Ludolph studies was the Latin, the language in which they were written the basic texts as well as the more recent ones in mathematics and science at the time. And Latin was a subject to be advanced studies.
Another fundamental challenge was the particular historical period in which Ludolph lived. At that time, in fact, life for Protestants was rather complicated: the Spanish Inquisition was, in fact, powerful enough to extend his long hands even in Germany. The Van Ceulen's, as Protestants, were forced, like many in the same conditions, to migrate to the most welcoming Netherlands of Prince William of Orange.
On the other hand Ludolph himself was a traveler: immediately after his father's death became a little travel first in the region of Livonia (Latvia and Estonia in our age), then to Antwerp to visit his brother Gert and then to Delft in the Netherlands where he settled for a time, since there was born one of his five daughter on May 4th, 1578.
His wife, Mariken Jansen, died in 1590, but Ludolph remarriage on June 17th of that year with Adriana Simondochter, widow of Bartholomew Cloot, accounting and math teacher, with whom he had generated eight children, for a total of 13 mouths to feed. The two families, Cloot and Van Ceulen, were in a close relations of friendship, so it's pretty obvious to imagine that the marriage between Ludolph and Adriana was the best solution to avoid losing a strong relationship.

The tabulating machine

Herman Hollerith, an American inventor, was born on the 29th February 1860. His most famous invention was the electromechanical tabulation of data:

At the urging of John Shaw Billings, Hollerith developed a mechanism using electrical connections to trigger a counter, recording information. A key idea was that data could be encoded by the locations of holes in a card. Hollerith determined that data punched in specified locations on a card, in the now-familiar rows and columns, could be counted or sorted mechanically. A description of this system, An Electric Tabulating System (1889), was submitted by Hollerith to Columbia University as his doctoral thesis, and is reprinted in Randell's book.

In the patent of his invention, we can read:

The herein-described method of compiling statistics, which consists in recording separate statistical items pertaining to the individual by holes or combinations of holes punched in sheets of electrically non-conducting material, and bearing a specific relation to each other and to a standard, and then counting or tallying such statistical items separately or in combination by means of mechanical counters operated by electro-magnets the circuits through which are controlled by the perforated sheets, substantially as and for the purpose set forth.

In 1896 Hollerith founded The Tabulating Machine Company, that in 1911, with four others company, became the Computing-Tabulating-Recording Company, renamed International Business Machines (IBM) in 1924.

Save research in Italy

About three weeks ago, Nature published a letter by Giorgio Parisi and signed by 69 italian scientists about the state of the research in Italy. This is the text:

We call for the European Union to push governments into keeping their research funding above subsistence level. This will ensure that scientists from across Europe can compete for Horizon 2020 research funding, not just those from the United Kingdom, Germany and Scandinavia.
Europe's research money is divided between the European Commission and national governments. The commission funds large, transnational collaborative networks in mostly applied areas of research, and the governments support small-scale, bottom-up science and their own strategic research programmes.
Some member states are not keeping their part of the bargain. Italy, for example, seriously neglects its research base. The Italian National Research Council has not overseen basic research for decades, being itself starved of resources. University funding has dwindled to a bare minimum. The ministerial initiative known as PRIN (Research Projects of National Interest) has been defunct since 2012, apart from a few limited programmes for young researchers.
This year's PRIN allocation of a euro92-million (US$100-million) funding call to cover all research areas is too little, too late. Compare this with the annual French National Research Agency's allocation of up to euro1 billion, or with Italy's euro900-million annual contribution to the EU Seventh Framework Programme that ran in 2007–13. That resulted in a net annual loss of euro300 million for Italian science.
To prevent distorted development in research among EU countries, national policies must be coherent and guarantee a balanced use of resources.

You can sign the petition on change.org.

"We are hearing the universe"

When we describe a geometric space, we need to define a metric, or in other words a way to measure distances: in particular in general relativity we use the tensor metric, $g_{\mu \nu}$. Supposing the existence of gravitational waves, it is possible to calculate their effect on the radiation coming from some cosmic objects like a binary or a couple of merging black holes.

On September 14, 2015, within the first two days of Advanced LIGO's operation, the researchers detected a signal so strong that it could be seen by eye. The most intense portion of the signal lasted for about 0.2 s and was observed in both detectors, with a combined signal-to-noise ratio of 24. Fittingly, this first gravitational wave signal, dubbed GW150914, arrived less than two months before the 100-year anniversary of the publication of Einstein's general relativity theory.⁽¹⁾

A bit of math behind Ant-Man

cc @sarofsky

I write also for Lo Spazio Bianco (The White Space), a web-zine about comics. Thanks to Carlo Coratelli, that contacted Sarofsky Corp., we can realize an interview with Erin Sarofsky, President, Owner and Executive Creative Director of the company. They realized some titles for Marvel Studios movies, in oparticular Ant-Man, and I proposed two questions about this movie. The questions, with Erin's answers, are the following, but you can read the complete interview here:

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We loved the opening animation in Ant-Man. It seems it's inspired by the Power[s] of Ten of the Eames. Is it really like that?
Ab-So-Lutely! We were very inspired by the Eames film. Luckily though, our universe is the Marvel Universe... so being 100% accurate was not necessary.
About Ant-Man, we also loved the work with the mathematical modeling you used to produce the animation and we think it would be quite interesting to elaborate about the actual realization method. How does it work?
We actually worked in reverse. We planned our moves and then did the math after the fact. We used the surface of the grass as our zero; anything above that is positive and anything below is negative.
Andy Zazzera, CG Director on the job, and our wicked smart math guy did all the estimations. (Again, nothing is exact because our world is fake... but the math is legit).

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For a while I was tempted to quest something of more detailed about the math developing, but I thought that it could not so interesting for our regular readers. However, I'm convinced that it is not for Field of Science's readers!

One hundred years

Creativity is the residue of time wasted

This interesting quotation by Albert Einstein linked him with Henri Poincaré not only with the contribution of French math to special relativity, but also for the utility of the creative leisure. Indeed Poincaré told that, after some fruitless attempts to sole a particularly difficult mathematical problem, he decided to go away for a geological excursion, in this way stimulating conditions to resolve the problem!
But the most important reason in order to write something about Einstein is the general relativity birthday, that was presented by Einstein on the 25th november 1915 at the Prussian Accademy of Sciences.