Skip to main content
25 votes
Accepted

What was the first electronic computer?

The literature is ambiguous because the question is ambiguous. The characteristics of these early machines are well known, but one can set the criteria for being "electronic computer" according to ...
Conifold's user avatar
  • 77k
18 votes
Accepted

How did the shift from constructed mathematical objects to modern mathematics occur?

TL;DR It is important to distinguish different senses of "constructiveness", the technical one, as in constructivism, and the one of approach to mathematics as primarily problem-solving. ...
Conifold's user avatar
  • 77k
12 votes
Accepted

Does Blum's speedup theorem have any conceptual predecessors?

The resemblance is not superficial. There is a precise relation between computer programs and formal proofs known as the Curry–Howard correspondence that took shape in 1960s. And Gödel's results on ...
Conifold's user avatar
  • 77k
11 votes
Accepted

What did Delaunay invent Delaunay triangulations for before computers were developed?

Delaunay (Gallicized version of Russian Delone) did not invent them, they were used long before 1934. Delaunay triangulations, or more generally tesselations, are dual to Voronoi diagrams, the ...
Conifold's user avatar
  • 77k
10 votes

How did the shift from constructed mathematical objects to modern mathematics occur?

This change apparently occurred in the middle of 19th century. Let me cite Carl Ludwig Siegel about it: It is completely clear to me which conditions caused the gradual decadence of mathematics, from ...
Alexandre Eremenko's user avatar
10 votes

Day-to-day tasks of human computers, à la Hidden Figures movie

If you are interested in descriptions of “everyday life” of human computers, here is an excerpt from Stan Ulam’s autobiography, Adventures of a Mathematician (University of California Press, 1991) ...
Margaret Friedland's user avatar
10 votes

What is so mysterious about Archimedes' approximation of $\sqrt 3$?

There's a very simple geometrical response that provides a rounded solution which might reflect on this problem at http://www.gjbath.com/SQR3.htm. It's so much easier seeing it! This involves ...
Geoff Bath's user avatar
10 votes

What is so mysterious about Archimedes' approximation of $\sqrt 3$?

Archimedes might, of course, have used a better method. (He also produces the approximation $\frac{1351}{780}$, for which the foregoing is not obviously practical...) I disagree on the foregoing not ...
Peter Taylor's user avatar
8 votes

What was the first electronic computer?

Why does being decimal disqualify ENIAC? Decimal electronic stored-program computers used to be a thing, for example the commercially successful IBM 1401. It was a matter of "binary for scientific ...
user12328's user avatar
8 votes

How did Napier come to invent logarithms?

Multiplication is a lot of work; in numerical computing it is considered evil and many tricks are used to avoid it. So Napier created the table of logarithms. (Briggs worked with Napier to make the ...
richard1941's user avatar
7 votes
Accepted

Was Charles Sanders Peirce aware of Charles Babbage's difference engine?

Not only was Peirce aware of the difference engine, he was also aware of the analytic engine, that was never built, of Jevons's 1870 machine, and was later personally involved with designing its ...
Conifold's user avatar
  • 77k
6 votes
Accepted

Has Penrose ever acknowledged criticism of the Penrose-Lucas argument?

Penrose responded to various commentaries made regarding his 1994 book "Shadows of the Mind" in his Beyond the Doubting of a Shadow. I never spent much time reading over this since my ...
Mark Yasuda's user avatar
  • 1,548
6 votes

What is so mysterious about Archimedes' approximation of $\sqrt 3$?

Some information can be found here 1 Using the secant method on the parabola $y = x^2$, a new estimate $x_{n+m}$ for $\sqrt{3}$ can be obtained from $x_n$ and $x_m$ as $$x_{n+m} = \frac{3 + x_n x_m}{...
Ignacio Rodriguez's user avatar
6 votes

How did Napier come to invent logarithms?

John Napier (1550-1617) published his table of logarithms Mirifici Logarithmorum Canonis Descriptio in 1614 after some twenty years of work and described his method of construction in Mirifici ...
Michael E2's user avatar
  • 1,881
6 votes
Accepted

What is the most number of digits of a mathematical transcendental constant that have been required for a real computation?

Lamb discusses the issue in How Much Pi Do You Need?: "I asked a NASA scientist how many digits of pi the agency uses for its calculations. Susan Gomez, manager of the International Space ...
Conifold's user avatar
  • 77k
6 votes
Accepted

Why were early electronic computers mutually incompatible?

There is a heap of answers to this question, and they cover a wide range of aspects of the early computer industry. As has been pointed out, the very first machines were hand built lab experiments. It ...
mikb's user avatar
  • 216
5 votes

Why were early electronic computers mutually incompatible?

First machines were one-off affairs, custom built (often for a very narrow purpose). There just weren't enough of those around to make standarization of anything surrounding them worthwhile. Thomas ...
vonbrand's user avatar
  • 565
5 votes
Accepted

Tools of the trade: were early scientists and mathematicians really "writing with feathers using light from burning animal fat?"

Quick Internet search says that feather quills were mainly used in 600-1800 AD. After that people gradually switched to steel. First true mathematicians (Babylonians) wrote on clay tablets. In the ...
Alexandre Eremenko's user avatar
4 votes

Why were early electronic computers mutually incompatible?

This changed in 1964 when IBM introduced System/360, a scalable computing system. It's obvious now that we have scalable computing systems that we can have scalable computing systems. Before then, ...
user12665's user avatar
4 votes

Day-to-day tasks of human computers, à la Hidden Figures movie

The first memo, on orbit determination, that Katherine Johnson did with a co-worker is The Determination of Azimuth Angle at Burnout for Placing a Satellite over a Selected Earth Position 1960. T.H. ...
nealmcb's user avatar
  • 221
4 votes

What was the first electronic computer?

My personal marker is stored program control, ie, the program is stored in the computer memory. Early machines like the original ENIAC, Colossus, Zuse's Z-machines, were all programmed by changing the ...
mikb's user avatar
  • 216
3 votes
Accepted

Who is Wanner from Rosenrock-Wanner (ROW) methods?

According to Wikipedia, it is the Austrian mathematician Gerhard Wanner.
José Carlos Santos's user avatar
2 votes

What is the most number of digits of a mathematical transcendental constant that have been required for a real computation?

In cryptography, designs often have "constants": effectively parameters which can use an arbitrary number (or an arbitrary number which doesn't have any simple patterns) but which must use the same ...
Peter Taylor's user avatar
1 vote

Newton as the first one to establish numerical analysis as a new field of study

Cardano's formula is useless if you want to really solve the cubic equation. In our culture we say that "solving an equation" means writing its solution in some closed form using a certain ...
Alexei Kopylov's user avatar
1 vote

What/When was the first radio nav system capable of triangulating your position?

Radio navigation was used on a large scale during the "Battle of Britain" in WWII, to direct the fighter planes to the enemy bomber formations. Of course, they experimented much earlier than that, ...
Alexandre Eremenko's user avatar
1 vote

What is so mysterious about Archimedes' approximation of $\sqrt 3$?

We don't know how Archimedes compute square root of 3 not because there is no known method, but because there are several methods that Archimedes could use, and we don't know which one he actually ...
Alexei Kopylov's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible