A Presidential Trivia Question, how I tried to solve it

       

A friend of mine told me that in the last six months, the last grandchild of one of our former presidents (who had already passed away) died.

I tried to  deduce who it was without checking the web directly. For example, I  looked up when various presidents were born to narrow it down, but try not to search for the answer itself.

I could look this up easily. However, by spending time thinking about it and exploring related questions, I might learn things I  didn’t know before.

Things I care about? Maybe.

I now have a lot of white space, so you can think about the answer yourself and perhaps make a guess, then my reasoning process and the answer.

Before answering, I’ll walk through the reasoning I used for my educated guess.
Assume the president was born in year x.

ADDED LATER: In the original version of this post (and its still there) I would make comments like: 

                           Warren G. Harding- why is the G always mentioned.

A commenter pointed out that middle names and initials are an American thing. This made me wonder why some of them didn't use their middle initial. Hence I have ADDED information about that. I won't bother writing ADDED LATER for those late adds. 

END OF ADDED LATER

Assume the president’s youngest child is born in approximately year x+35.

Assume that child’s youngest child is born in approximately year x+70.

Assume the grandchild lives 80 years, so dies in approximately year x+150.

Then x+150=2025, so x=1875.

Since this is an approximation, I looked at all presidents born between 1850 and 1900. The website I consulted tells us the answer. What would we do without the internet? (Maybe spend more time offline tightening our bounds on the polynomial van der Waerden numbers.)
Here are all the presidents who were born in a year in [1850,1900].

Theodore Roosevelt — born 1858. Formal name: Theodore Roosevelt Jr. No middle name. 

William Howard Taft — born 1857. He seems to have his full name mentioned. Why? 

Woodrow Wilson — born 1856. Formal name: Thomas Woodrow Wilson. So it would be impossible to use a middle initial unless you do what David Dwight Eisenhower did and swith the two names, so then he would be Woodrow T. Wilson. 

Warren G. Harding — born 1865

Calvin Coolidge — born 1872. Formal name: John Calvin Coolidge Jr. Similar to Woodrow Wilson.  Cal's dad was John Calvin Coolidge Sr.  Naming your kid after yourself, including the middle name, coud be a mistake, see here.

Herbert Hoover — born 1874. Formal name: Herbert Clark Hoover. I am surprised he wasn't called Herbert C. Hoover. Maybe Herbert Hoover was better because its alliterative. 

Franklin D. Roosevelt — born 1882

Harry S Truman — born 1884 (There really is no period after the S. Both chatty and Wikipedia get that wrong.)

Dwight D. Eisenhower — born 1890 (born David Dwight Eisenhower; he preferred to be called Dwight).

When I was asked the question, I guessed Harry S. Truman. I was wrong.

In fact, none of the presidents on that list is the one. 

The correct answer is John Tyler, who was born in 1790.

My rule-of-thumb assumptions (35 years to have a child; an 80-year lifespan) were  large underestimates for this case. John Tyler had sixteen children. The third-to-last was Lyon Tyler, born in 1853 — John Tyler was 63 at the time, which is 28 years more than my estimate of 35. Lyon Tyler had six children; the second-to-last was Harrison Tyler, born in 1928 — Lyon was 75, which is 40 years more than my estimate of 35.

(In 1840 William Henry Harrison and John Tyler were elected Prez and Veep. WHH died after giving his inaugural speech in the cold rain, and Tyler became president. Lyon Tyler names his son Harrison. My thought was: Did Lyon name his son after WHH? I asked Google 

Why did Lyon Tyler name his son Harrison? 

The AI Overview said:

Lyon Tyler named his son Harrison because his own mother, Julia Gardiner, was a member of the Harrison family of Virginia, making Harrison a great-grandson of both President John Tyler and William Henry Harrison, the president whom John Tyler succeeded. Naming his son Harrison was a way for Lyon Tyler to honor the family connection to both presidents, particularly the presidential connection. 

Thats not quite right- Harrison is John Tyler's grandson, not great-grandson. 

I didn't know that John Tyler's grandchild was named Harrison.

I didn't know that John Tyler's grandchild was also related to WHH.

)


Harrison Tyler died in 2025 at the age of 96, which is 16 years more than my estimate of 80.

So my point (do my posts need a point?) is that I made an approximation but was still way off. John Tyler is an outlier, which is hard to account for.

Let’s say I assumed 60-year-old fathers and the grandson lives to 90. Then we would have:

x + 210 = 2025
x = 1815

This is an approximation, so I would look at presidents born between 1790 and 1840:

John Tyler: 1790. No middle name. 

James K. Polk: 1790. Why is the K always mentioned?

Zachary Taylor: 1784. No middle name. 

Millard Fillmore: 1800. No middle name. 

James Buchanan: 179. He never had kids. That’s just as well, since his children would have had the stigma of their father being one of the worst presidents of all time by most accounts.

Abraham Lincoln: 1809. Born February 12, 1809 — the same day and year Charles Darwin was born. No middle name. 

Andrew Johnson: 1808. No middle name. 

Ulysses S. Grant: 1822.  Born Hiram Ulysses Grant, but he didn’t like that the initials were H.U.G.

Rutherford B. Hayes: 1822. Why is the B always mentioned?

James Garfield: 1831. James Abram Garfield. I sometimes see the A initial and sometimes not. 

Chester Arthur: 1829. My Darling’s favorite president — really! Formal name Chester Arthur which I have seen written, though not as much as the others. Perhaps I just didn't notice him as much as my Darling did. 

Grover Cleveland: 1837. Formal name: Stephen Grover Clevelant. 

Three points:

1) When I picked 60–60–90, I did not know that John Tyler would actually make it onto the list.

2) He just barely made the list.

3) I would not have picked 60–60–90 unless I had already learned that 35–35–80 was far too small.

The Complexity Argument for Capitalism

We're seeing an attack on capitalism on both ends of the political spectrum with with the election of Democratic Socialist Zhoran Mamdani as mayor of New York, and Donald Trump trying to direct the economy through tariffs, less independency of the Federal Bank and partial government control of companies such as a nearly 10% ownership of Intel and the "golden share" of U.S. Steel.

Now I'm not an economist and there are many arguments for and against socialism and capitalism, especially in their purest forms. I want to focus on the complexity of the economy. Let's start by considering rent control.

It starts with the worthy goal of preventing people from having to leave their apartments because of rising rents due to market demand. So you limit the rent increases and the ability to evict current residents. But this could cause landlords to cut back on improvements, not prioritize service and repairs, or build new properties to increase the supply. So you have to give landlords incentives to do these things, leading to other issues which leads down a rabbit hole. I saw extreme rent control in Berkeley in the 1980s and a lack of available housing forced me to live 13 miles away. 

That's just rent control in a single city. Other attempts to control the economy will lead to unexpected inefficiencies and you can't predict markets enough to catch them.

The 1920 essay Economic Calculation in the Socialist Commonwealth by Ludwig von Mises argued that market prices give critical information for companies and individuals to make decisions. I think of it like a circuit, where the prices are values of intermediate gates so that we can have simple operations at every level leading to a very complex behavior in the aggregate, much like a neural net today. Frederick Hayek went further in his 1945 essay The Use of Knowledge in Society that a center planner couldn't adapt with the speed of change in the markets. 

Could today's neural nets replace the need for these intermediate pricing and adapt quickly? It's really a combination of the two, many companies are using sophisticated machine learning models that lead to more accurate pricing, adding to the efficiency of markets. 

Capitalism has its challenges: Companies can shrink or close, people can lose their jobs and we need good safety nets. Government has a role to protect safety, enforce contracts and provide services and some control where competition doesn't scale, like utilities and pubic transportation. Government also has a role in promoting public goods including education, scientific research and national defense. 

While neither Mamdani or Trump want anything close to complete government control of the economy, I still worry that even their limited influences will hurt innovation and in the longer run hurt the very people these policies are meant to help. 

Did Euclid exist? Is it okay to quote people that did not exist?

 
The following excerpt from Abrahim Ladha's comment on Lance's post about
AI and intro theory caught my attention:


---------------------------
BEGIN EXCERPT

Not just with AI, but in theory and math courses, there have always been Bart Simpson
level questions by students of the form

"Why do I need to know this?

like

Why do I need to know my times tables when the calculator does this for me?

There has never been a good answer because these students already do not have an open mind.
Euclid was asked such a question once and said something like

give him a penny so he may feel like he earned something for what he learned.

END EXCERPT
-----------------------------------

He gives a quote by Euclid.

1) I have heard that Euclid might not have really existed.

2) I have never heard that quote.

I asked Abrahim Ladha if he had a source for the Euclid quote.

I never go a response.

I asked chatty:

        What is the historical evidence that Euclid existed?

and also

        Did Euclid say give him a penny so he may feel like he earned something for what he learned?

The answer to both questions are below. The bottom line is that

1) Euclid might not have existed.

2) The idea underlying the quote is attributed to him. The exact quote is modern rendering. 

Should Abrahim have consulted chatty before making his comment.

1) YES, it's important to make sure your facts are correct.

2) NO, his point is still valid. (That is a slippery slope.)

----------------------------------------
BILL: What is the historical evidence that Euclid existed?

That’s a great question — and a surprisingly tricky one.

Short answer

There is no direct historical evidence that Euclid (often called Euclid of Alexandria) existed
as an individual in the way we can verify the existence of, say, Archimedes. What we “know”
about Euclid comes almost entirely from later sources, not from contemporary records.

The evidence we do have

1)
Type: Ancient testimonies

Source: Proclus, Commentary on the First Book of Euclid’s Elements

Date: ca. 450 CE

Note: Written about 700 years after Euclid’s supposed lifetime. Proclus says Euclid lived
in the time of Ptolemy I (reigned 323–283 BCE) and taught in Alexandria. This is our main source.

2)
Type: Mentions by other ancient authors

Source: Pappus of Alexandria (4th century CE), Diogenes Laërtius (possibly), and others

Date: 200–600 years later

Note: These references repeat information similar to Proclus’s account — that Euclid compiled
the Elements and worked in Alexandria.

3)
Type: Mathematical evidence

Source: The Elements and other works attributed to Euclid (Data, Optics, Phaenomena, etc.)

Date: ca. 300 BCE?

Note: These texts show a unified style and method, suggesting a single organizing mind
(or school). But there is no personal or biographical detail inside them.

4)
Type: Absence of contemporary evidence

Note: There are no letters, inscriptions, or administrative records naming Euclid. No ancient
biography (unlike Archimedes or Apollonius).

Scholarly interpretation

Traditional view: There was a historical Euclid, a mathematician who worked in Alexandria
around 300 BCE and compiled earlier Greek geometry into the Elements.

Skeptical or revisionist view: “Euclid” may have been a collective name for a team or a
school of mathematicians in early Hellenistic Alexandria, much like “Hippocrates” in medicine.

The Elements itself is consistent in style, so even if multiple people contributed, it was
edited or systematized by someone with extraordinary coherence and rigor.

In summary

There is no direct documentary or archaeological proof that Euclid existed as an individual,
only later testimony and internal evidence from the mathematical works. Historically, most
scholars accept that there was a person — or at least a leading mathematician — behind the
name “Euclid,” but his life remains almost entirely unknown.
---------------------

BILL: Did Euclid say

`give him a penny so he may feel like he earned something for what he learned.'

ChatGPT said:

The quote you’re referring to — something like “Give him a penny so he may feel he has learned
something” — is attributed to Euclid, but not in those exact modern words.

It comes from an ancient anecdote recorded by Proclus (a 5th-century commentator on Euclid) in
his Commentary on Euclid’s Elements. The story goes like this:

A student, after learning the first theorem of geometry, asked Euclid,

“What shall I get by learning these things?”

Euclid called his slave and said,

“Give him a penny, since he must make gain out of what he learns.”

In Greek, it’s roughly:

“Δός αὐτῷ ὀβολόν, ἐπειδὴ κερδαίνειν δεῖται ἀπὸ τῶν μαθημάτων.”

So your paraphrase captures the spirit of the anecdote — Euclid was mocking the idea of
studying geometry for material reward — but the exact wording

“give him a penny so he may feel he earned something for what he learned”

is a modern retelling, not a direct quotation.