Terry Tao's generals (2012)

Here&#x27;s some interesting backstory on how Terence almost failed this exam: <a href="https:&#x2F;&#x2F;www.ams.org&#x2F;notices&#x2F;202007&#x2F;rnoti-p1007.pdf" rel="nofollow noreferrer">https:&#x2F;&#x2F;www.ams.org&#x2F;notices&#x2F;202007&#x2F;rnoti-p1007.pdf</a>

&gt; <i>Stein then asked me what other boundedness theorems I knew. I couldn&#x27;t think of any concrete ones off hand, but I mumbled about a convolution operator being bounded if its Fourier transform was bounded and had some smoothness condition, but I couldn&#x27;t recall any details</i>.<p>You and me both, buddy!

Thought this Oppenheimer anecdote may amuse the HN contingent.<p>&quot;Oppenheimer obtained his Doctor of Philosophy degree in March 1927 at age 23, supervised by Max Born.[28][29] After the oral exam, James Franck, the professor administering, reportedly said, &quot;I&#x27;m glad that&#x27;s over. He was on the point of questioning me.&quot;[30] &quot;<p>Franck had won the Nobel two years earlier.<p>Sources: [Refs] quoted directly from Wikipedia article<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;J._Robert_Oppenheimer" rel="nofollow noreferrer">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;J._Robert_Oppenheimer</a><p>[30] from Wikipedia: <a href="https:&#x2F;&#x2F;content.time.com&#x2F;time&#x2F;subscriber&#x2F;article&#x2F;0,33009,853367-4,00.html" rel="nofollow noreferrer">https:&#x2F;&#x2F;content.time.com&#x2F;time&#x2F;subscriber&#x2F;article&#x2F;0,33009,853...</a> --&gt; p.4

First of all, nobody ever passed these exams with flying colors unless the examiners wanted that to happen or were having a bad day. Assume that there are three full professors testing you, and they have an average of 20 years each of post-graduate experience. That&#x27;s 60 years of reading -- no way that a 2nd or 3rd year graduate student can keep up. Part of the process is humiliating the students a bit -- they did this for everyone.<p>They also had a language requirement, which was often fulfilled by memorizing the 500 most common words in a foreign language as well as 300-500 common math terms in that language; there was a library of prepared crib sheets for these. It was kind of a running joke in that it tested your ability to translate an article from German&#x2F;Russian&#x2F;French into English sufficiently well to explain it to a bored examiner, but most of the students kind of looked it as a kind of giant &#x27;Wheel of Fortune&#x27; exercise in intelligently guessing between the revealed clues.<p>Second, some of the other graduate students basically went insane studying for this -- one locked himself in a room with a 30 day supply of microwavable meals, and another locked himself in his dorm and (having read MicroSerfs) only ate 2 dimensional food slipped under the door. A lot of this was immature students trying to out-do each other in commitment and probably didn&#x27;t markedly improve pass rates.<p>Tao matured, but mostly because he got older -- there were finally reasonably smart people his age studying with him. He also used to hang out with John Conway a lot, and Conway was going through his own problems; he spent more time with the &#x27;more conventionally normal&#x27; faculty and that probably rubbed off.

There’s a big long list of these in <a href="https:&#x2F;&#x2F;web.math.princeton.edu&#x2F;generals&#x2F;" rel="nofollow noreferrer">https:&#x2F;&#x2F;web.math.princeton.edu&#x2F;generals&#x2F;</a>, not just Tao’s.

This seems a great way for system design interviews.<p>Interviewer: what do you know about transactions?<p>Candidate: Transactions can be serializable.<p>Interviewer: great, tell me the difference between final state serializability and view state serializability and prove that they are the same if neither of them has dead step.<p>Candidate: yada yada yada.<p>Interviewer: Can you tell me how to use such concepts in implementing a production database system? Please come with a few short illustrative examples too.

This is the first time I&#x27;ve read a detailed account of &quot;generals&quot; in a US math PhD. I&#x27;m surprised how broad the topics covered seem. I did my PhD in the UK and the transition to fully fledged PhD candidate after the first couple of years was significantly less traumatic than this seems!

Sorry for asking, but I&#x27;m not familiar with this term. &quot;Generals&quot; means &quot;final exam&quot;? For PhD?

My first distracted thought upon reading this title on HN: cool, Terry Tao is finally getting his own army!<p>Jokes aside, Tao also has a nice write-up in AMS Notices on this experience and how it influenced his career:<p><a href="https:&#x2F;&#x2F;www.ams.org&#x2F;notices&#x2F;202007&#x2F;rnoti-p1007.pdf" rel="nofollow noreferrer">https:&#x2F;&#x2F;www.ams.org&#x2F;notices&#x2F;202007&#x2F;rnoti-p1007.pdf</a>

&gt; What other simple groups do you know. (The monster? But I backed down quickly, saying I knew not how to define it.)<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Monster_group" rel="nofollow noreferrer">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Monster_group</a><p>TT was 21 when he got his PhD, according to wikipedia.

I am dim today. Is this Tao getting rejected for some interview for something?

&gt; they decided to pass me, though they said that my harmonic analysis was far from satisfactory. :(<p>Funny, because he received the Fields medal 1o years later for &quot;his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory&quot;. So either his knowledge wasn&#x27;t that bad or he is a very quick learner. ;)

&gt; Talk about primes in arithmetic progressions<p><i>Turns on super saiyan mode for the first time</i>

I found these questions excellent prompts for chatgpt.<p>I imagine using chatgpt plus these questions would greatly help a grad student study for their comps.

I don&#x27;t know any of those theories and I feel quite ignorant and humbled. Extremely smart.

<a href="https:&#x2F;&#x2F;terrytao.wordpress.com&#x2F;" rel="nofollow noreferrer">https:&#x2F;&#x2F;terrytao.wordpress.com&#x2F;</a>

&gt; primes of the form 4n - 3.<p>I think they mean 4n + 3 unless this is a joke I&#x27;m missing

<i>I did state though that all second derivatives of u would have L^p norms bounded by that of the Laplacian. Kleinermann asked me for an elementary explanation of this, but I couldn&#x27;t think of one.</i><p>I haven&#x27;t the foggiest idea of what an &quot;elementary explanation&quot; of anything during a math graduate degree committee assessment would even sound like.

so has he accomplished anything big&#x2F;groundbreaking other than being a child prodigy and having a high iq?<p>serious question. i only know his name for being smart. not anything specific