Supplemental: Reclusive genius passes away!


Math is still quite hard:
The headline shouted at us from yesterday’s Washington Post:

Reclusive genius a ‘giant’ of math

In an 1100-word piece, Matt Schudel reported the death, at age 86, of Alexander Grothendieck, “whose brilliant mind electrified the world of mathematics in the 1950s and 1960s, earning him the equivalent of the Nobel Prize in his field.”

We’d never heard of Grothendieck! Hungrily, we fell upon the Post report, hoping to learn what his brilliant mind had done.

Basically, Schudel wasn’t saying. He started by telling us this:
SCHUDEL (11/16/14): Mr. Grothendieck (pronounced GROHT-en-deek) emerged from a life of exile during World War II to become one of the most important mathematical thinkers of the 20th century. His contributions to mathematics were often likened to those of Albert Einstein in physics.

His nominal specialty was algebraic geometry, which combines elements of both mathematical disciplines, but Mr. Grothendieck used his remarkable capacity for abstract thinking to make advances across the entire spectrum of mathematics.

He developed unifying concepts that could be applied to a variety of avenues of mathematical thought, including number theory, category theory, functional analysis and topology.

In 1966, Mr. Grothendieck was awarded the Fields Medal, considered the world’s highest honor in mathematics. Two of his major publications, “Elements of Algebraic Geometry” and “Fundamentals of Algebraic Geometry,” are so essential to mathematicians that they are known simply by their initials in French, EGA and FGA.

“He was one of the giants of mathematics, who transformed mathematics entirely with his work,”
Cedric Villani, who won the Fields Medal in 2010, told Agence France-Presse.
We were still a bit unclear. In what way did Grothendieck transform mathematics entirely?

Schudel soldiered on:
SCHUDEL (continuing directly): As a student, Mr. Grothendieck once recalled, he was taught how to calculate the volume of a sphere and other geometric shapes, but he sought a deeper understanding: the definition of volume itself.

When he embarked on his career, he didn’t concentrate on solving age-old puzzles so much as on developing new, simplified approaches to mathematical investigation. Other scholars came to apply Mr. Grothendieck’s theoretical frameworks to such fields as computer programming, software development, satellite communications, classification systems and the study of biological data.

His ideas were instrumental in solving one of the enduring conundrums of mathematics, Fermat’s Last Theorem. In 1637, Pierre de Fermat jotted a mathematical notation in the margin of a book, but its proof had baffled the world’s greatest mathematical minds for more than three centuries.

Finally, in 1995, British mathematician Andrew Wiles published a proof of the theorem. He arrived at his solution using the principles of algebraic geometry, the field that Mr. Grothendieck had redefined to its foundations.
He sought a deeper understanding—the definition of volume itself? We don’t understand that either.

As we said, Schudel devoted 1100 words to his obituary. When we were done, we had no real idea what Grothendieck had actually done, mathematically speaking.

Luckily, Sunday’s New York Times also featured a long obituary. Instantly, Weber and Rehmeyer tackled the problem:
WEBER AND REHMEYER (11/16/14): Algebraic geometry is a field of pure mathematics that studies the relationships between equations and geometric spaces. Mr. Grothendieck was able to answer concrete questions about these relationships by finding universal mathematical principles that could shed unexpected light on them. Applications of his work are evident in fields as diverse as genetics, cryptography and robotics.

“He had an extremely powerful, almost otherworldly ability of abstraction that allowed him to see problems in a highly general context, and he used this ability with exquisite precision,” Allyn Jackson wrote in a 2004 biographical essay about Mr. Grothendieck for Notices of the AMS, a journal of the American Mathematical Society. “Indeed, the trend toward increased generality and abstraction, which can be seen across the whole field since the middle of the 20th century, is due in no small part to Grothendieck’s influence.”
We don’t understand that either. Math remains very hard.


  1. Why on earth should Somerby or anyone else expect to understand a complex field without any training in it? The obituaries both convey the sense that this man made major contributions to mathematics and I think that is sufficient, without expecting that 1100 words also explain what those contributions were beyond their importance.

    We are at a point where the amount of knowledge accumulated by our culture exceeds what someone can acquire casually or through four years of college. People therefore specialize, but even spending an additional 4-10 years to acquire a doctorate, someone cannot know everything there is to be truly expert in a broad subfield. So we devote a career to a subspecialty and become pretty competent in it, although new knowledge is still being added faster than we can keep up with it.

    So why on earth does Somerby think a reporter should be able to understand complex mathematics well enough to explain it to readers who have also not put in the time to begin to understand the impact of this man's accomplishments, much less the substance of his work?

    Is Somerby implying that his obituary shouldn't have tried to tell anyone why this guy was important? Do we only publish rock star's deaths? What if someone doesn't listen to modern music and has never heard anything by that rock star, and yet is being told he revolutionized some musical genre? Is it the writer's fault if the reader hasn't listened to music sufficiently to know what is being discussed?

    I just don't understand why this post appear or what it is trying to say. Math isn't hard. It just takes effort and time to understand it, just as it takes effort and time to understand anything these days. You don't get understanding without the effort -- no matter what your native intelligence.

    1. So you expect absolutely no effort from journalists to understand and attempt to enlighten?

    2. I agree with Anon at 3:09. My guess is that the writers (a) probably couldn't understand math well enough to describe what Grothendieck had done, and (b) in any event couldn't describe it in lay terms that would have made sense. I like some of Bob's criticisms about writing that makes it appear that we're learning something when we're really learning nothing, but I don't think that these obituary writers can be criticized for not trying to explain concepts that almost certainly aren't going to be explained in a small newspaper column.

  2. We remember being impressed, many years ago, when Bob derided people who claimed "A Brief History Of Time" was a coherent, easy-to-read, book. We consider ourselves fairly intelligent and educated, and had no fucking idea what that book was supposed to be explaining to us, easy or not. However, here, we consider Bob to be way off base. It is not the job of an obituary writer to provide a math lesson to his or her readers. The obituary writer is supposed to summarize the person's life, capturing, in brief form, who they were and what they were about. These obituaries do that adequately. Somehow, we suspect if the obituary writers were capable of even understanding the deceased person's work, let alone explaining ti to people, they would not be writing obituaries.

  3. If it makes Bob feel any better, I spent five years in graduate school studying advanced mathematics, and I don't understand Grothendieck's contributions either. Now, a statement of Fermat's theorem is pretty easy to understand. It says there are no positive integers a, b, c, and n, such that a^n + b^n = c^n, where n is greater than 2.

    1. Really, David? You sure it wasn't your wife, or your third cousin twice removed who studied advanced mathematics?

    2. You realize that statistics is not advanced mathematics, right?

    3. Right you are David in Cal. Easy to understand. I copied ti right out of the NY Times obit myself.

      That said, the obituary also described imprecisely Mr. Grothendieck’s contribution to proving a set of hypotheses posed by André Weil. Mr. Grothendieck proved two of the four hypotheses and developed a new proof of a third; his former student Pierre Deligne proved the fourth. Mr. Grothendieck and Mr. Deligne were not working together.

    4. "I spent five years in graduate school ...."

      Usually takes 2 or 3 years. That explains a lot.

    5. No, it doesn't. I know almost no mathematicians who got a PhD in 2-3 years. Five is about par. You don't know what you are talking about. (It might take about that time to get a Masters, but hardly anybody gets a Masters degree in mathematics.)

  4. I shall now go back to the obituaries of Albert Einstein and Neils Bohr for a complete understanding of relativity theory and quantum mechanics

  5. OMB (No need to Memorialize the OTB)

    The immortal word of BOB will live forever on the Intenet created by a college disciple. There is no need to worry about an obituary to explain his many contributions to the study of journalism, East Coast Irish Catholicism, beachfront home aquisition and decor, developmental delays in writing skills among Ivy League graduates, and cranial wiring diagrams for anchor persons.

    However, his contributions to mathematics were ginormous. His Very Rough Rule of Thumb, which he was able to apply to any standardized test to debunk persistent plutocrat flogging of ratty teachers and call attention ignored black children, was never understood by even the best experts in educational statistics.

    Even BOB, who wrote about it constantly, could never express it in terms his legion of follower could cogently regurgitate in blog commentary. Fortunately it relied on the number 10, making it easier for those who did not understand it to think they truly did.

    His analysis missed.

    1. It was nice while you were gone. Did you get a weekend pass to visit your empathy-fatigued relatives?

    2. We noticed how many stifled commenters filled Bob's box with long discussions on weighty topics. We shall try it again some time. However warp speed travel in a small craft with deadrat and David in Cal can be tiresome.

    3. 1132: it was nice your Mom let you out of the playpen for a little while. Now it's nap time.

    4. It's a relativistic effect. Much like an object becoming more massive as it accelerates, you become more tiresome the harder you try to be clever. From the frame of reference of your reader of course. From your own frame of reference, I'm sure you find that you're always the smartest kid in the room.

    5. Shorter deadrat: Nanny, nanny boo boo.


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