
Mathematical Chronology - kercker
http://www-history.mcs.st-andrews.ac.uk/Chronology/full.html
======
laichzeit0
I'm not a mathematician, but I've always been fascinated by two specific
periods in the history of mathematics: Around 1750-1850 where you have Gauss,
Fourier, Poisson, Laplace, Navier, Cauchy, Lagrange, Euler. That's just...
insane.

And then the mathematics that happened around ~1940.. Kolmogorov, Fisher,
Poincaré, Gödel, Von Neumann, Church, Turing...

Just crazy.

~~~
WhitneyLand
I'd love to be able to watch a simple video interview with these guys.
Something like...Dr. Gödel, could we take just a few of your notable insights
and have you walk us through _how the fuck_ you managed to come up with them?

~~~
mrkgnao
As I understand it, a significant portion of the cleverness is in the audacity
of encoding something liar paradox-like into a formal logical framework (and
perhaps also the precision with which logics were specified and differentiated
from one another).

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imh
>1591

>Viète writes In artem analyticam isagoge (Introduction to the analytical
art), using letters as symbols for quantities, both known and unknown. He uses
vowels for the unknowns and consonants for known quantities. Descartes, later,
introduces the use of letters x, y ... at the end of the alphabet for
unknowns.

This may be my favorite point in the history of mathematics. Using
placeholders for things (variables) and efficient notation makes reasoning
easy. It's such an obvious thing now, but I think it's amazing.

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williamblake
There is a network of artificial tunnels in Egypt called the Serapeum of
Saqqara. It contains at least 24 large boxes made from single pieces of solid
granite, allegedly moved there from a very interesting granite quarry several
hundred miles away, then hollowed out to a mirror finish and a precision of a
few ten-thousandths of an inch as tested by a precision machinist with a
precision toolmaker's square who is also an engineer. After observing them,
the engineer went on to ask the largest US companies in such business if they
could make one. Only one responded and the answer was interesting. The place
is real and the boxes, some as much as 90 tons (or the weight of more than
fifty Prius cars) are not going anywhere. It's not in the books, nor is
anything that explains it in the timeline but you can see it in person and
test if for yourself. This place is only one of many that, by their nature and
existence, question the conventional timeline of history

There is also a mathematician that, with some help from others, is doing a
rigorous mathematical review of the conventional timeline of history and
apparently there are some major problems with what has previously been
accepted, written and taught. Does anyone know who I am referring to here?

How many people here are aware of the Serapeum mentioned above? Where does
that level of precision work fit in with the timeline?

~~~
pluteoid
The qualities of the Saqqara boxes are entirely consistent with what we know
about the mathematical and engineering sophistication of ancient Egyptians.
There is nothing well-verified "not in the books" that upends the
"conventional timeline". The only people claiming otherwise are Discovery
Channel nutcase types who want you to believe, without real evidence, often
with fake evidence, and always with fatuous reasoning, that angels and aliens
intervened in ancient human history.

[https://nathandickey.wordpress.com/2014/02/03/demythologizin...](https://nathandickey.wordpress.com/2014/02/03/demythologizing-
the-giant-stone-boxes-of-egypt/)

~~~
williamblake
I'm sorry that I have given you the impression that I or others like myself
who discuss these questions believe in ancient aliens. I realize that this is
a topic of confusion for many "debunkers". I don't accept belief as a valuable
tool the process of discovering the truth, nor do I deem it necessary in the
practice of science. Unbiased observation, free from belief is important.

And denotative language seems to be more effective than connotative language,
at least as far as these kings of arguments are concerned. Logical argument is
better than the disparagement of persons and groups when arguing and making a
point. And staying on topic is also a good thing.

There is a growing discussion regarding belief systems within academia and
various conventional sciences such as archeology. This seems to be a problem
and if it is not cleaned up fairly quickly and replaced with something more
logical, evidence-based, reality-accepting and legitimately scientific, the
term "pseudoscience" will likely be used against those coming from the
conventional side of these topics.

I don't see anything relevant from your link that explains the precision of
the boxes I mentioned above. What do you know about ancient Egyptian
mathematics and engineering that relates to this subject? I have read the
entire page you linked to, so forgive me in advance for missing it.

~~~
kevinwang
Well the linked page says:

It’s also not surprising that they could create a flat surface or angles that
are exactly-ish 90 degrees. The Egyptians boast some of the earliest known
texts on geometry, like the Rhind Papyrus (from around 1650 BCE) and the
Moscow papyrus (from about 1850 BCE). The latter papyrus indicates that the
Egyptians could approximate pi (as 3.16049) and find the volume of a truncated
pyramid. It stands to reason that 500 years later, they would be able to carve
a flat surface and make a corner of exactly-ish 90 degrees.

~~~
posterboy
If you look at marble statues, a square box is hardly amazing in comparison.
"a few ten-thousandths of an inch" \- close to micro meter precision - sounds
almost like exaggeration, but some type of stone might just split in a very
planar way.

~~~
williamblake
Yes, there are some amazing marble statues. Have you seen the one where there
is a fishing net cut from marble? Or the twins from Russia - two identical
statues except for some obvious clumps of hair of hair, as if an image was
taken at different times, in the breeze, and an artist or machine reproduced
the statue from the image. I am assuming that most marble statues are at least
an order of magnitude less precise than the granite box. Granite, by the way,
is composed of different materials, such as, for example, feldspar and quartz.
It doesn't break along a plane. Yes, a micrometer is .0001". Calipers, on the
other hand, often only measure to .001" and would not be able to measure
anything this precise.

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mrkgnao
> 1964

> Hironaka solves a major problem concerning the resolution of singularities
> on an algebraic variety.

Essentially, sometimes the varieties (which are geometric objects like curves,
surfaces, etc.) studied in algebraic geometry are _singular_ : they might have
_singularities_ , like nasty self-crossings or sharp edges. Hironaka's result
lets you take a "bad" variety and "resolve its singularities", giving you a
good ( _nonsingular_ ) variety which you can work with instead.

This is in "characteristic zero", i.e. over fields like the real or complex
numbers. We also have fields of positive characteristic, e.g. the integers
modulo any prime number. Over such fields, I understand that this is a much
harder problem to solve.

The aforesaid Heisuke Hironaka is 86 now.

In March of this year, he published a (purported) proof of resolution of
singularities in positive characteristic.

The /r/math thread has some good explanations.

[https://www.reddit.com/r/math/comments/6aqwbo/hironaka_publi...](https://www.reddit.com/r/math/comments/6aqwbo/hironaka_published_a_proof_of_resolution_of/)

~~~
ice109
>can work with instead

what can you actually do with these "smoother" varieties?

~~~
mrkgnao
They are much closer to the curves and solids we're familiar with from
everyday experience. For example: you have well-defined tangents at every
point for a smooth curve, but a self-intersecting curve doesn't. So many
techniques and a lot of intuition carries over into the abstract algebraic
setting.

More generally, algebraic geometry is a central field of math because it is,
basically, about solving polynomial equations. It's one of the most "well-
connected" fields of mathematics today. Number theory, differential geometry,
complex geometry, even differential equations: all these fields benefit from
their interactions with modern algebraic geometry. (Also biology, I've heard.
Lior Pachter is a name I remember in this connection.)

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jordigh
A guy I knew used to say that this is why computer science is so much easier
to learn than number theory. It's thousands of years of number theory to learn
vs a few dozen years of computer science. On top of that, the recent
historical explosion of computer science is also accompanied by perhaps an
even larger explosion of number theory.

~~~
posterboy
Also, mathematics has to be discovered _and remembered_ , whereas half the
internet seemingly consists only of programming tutorials and documentation.

Edit: In the end there is no difference, however. Both are structural
sciences. I guess you meant the maths in a CS degree.

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drio
This is great. Thank you for sharing.

These days I am working on trying to understand the Fourier transform (1807).
It is great fun. I finally understand the equation and how it works. Pure
beauty. Now I am in the process to use it in practice. I am planning to write
about it and perhaps write some visualizations to help others understand.

This post made me think about a crazy idea I had. I wanted to write periodic
posts to talk about the work of all these great mathematicians. I also wanted
to have a place where people could buy gear (t-shirts). The same way people is
very proud of wearing a sports guy t-shirt (Lebron 23), I'd love to see people
wearing t-shirts with mathematicians names (Fourier 10). It's crazy I know.

~~~
pdm55
An interesting book, written by an interesting group, is "Who is Fourier".
They seem to be mainly undergraduates in Japan who learn and teach each other
new languages. They took on a similar task to explain Fourier Transforms to
each other. Their motivation was to understand the mathematics of languages.

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WhitneyLand
Please anyone, what is best timeline metaphor you know of?

This is great stuff, but I immediately want to interactively browse through
the information. For different parts be able to dive deeper, see high level
views, different categories, taxonomies, links to related topics.

Not trying to reinvent Wikipedia or hypermedia. But specifically to timelines
with a lot of density, it seems there ought to be some nice user interface
that could be leveraged for these scenarios.

~~~
perilunar
I've played with the vis.js timelines a bit and quite like them:
[http://visjs.org/timeline_examples.html](http://visjs.org/timeline_examples.html)

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journeeman
It doesn't seem to mention the works of the Indian mathematicians from Kerala,
India on calculus. I think their work predated that of Newton and Leibniz.

~~~
ralfd
Interesting, but (wiki):

> Their work, completed two centuries before the invention of calculus in
> Europe, provided what is now considered the first example of a power series
> (apart from geometric series).[2] However, they did not formulate a
> systematic theory of differentiation and integration, nor is there any
> direct evidence of their results being transmitted outside Kerala.

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chus9000
Here you have the chronology in an infographic made with an automatic tool
that I'm working on:

[http://history.takethejuice.com/output/MTQ5Njk0MDc1NC1NYXRoZ...](http://history.takethejuice.com/output/MTQ5Njk0MDc1NC1NYXRoZW1hdGljYWwgQ2hyb25vbG9neQ==)

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Herodotus38
Too bad it ends at 2000, though I understand that 17 years ago may still be
too soon to know what should count as history. Does anybody have a suggestion
of what they think will eventually be included in such a timeline covering the
last 20 years if it were made in 2100?

~~~
ihm
I'm surprised Gromov and Thurston's contributions to geometry in the 70s-00s
aren't emphasized more. Some things I think should be on there from my
admittedly limited point of view:

\- 1982/87: Yao and then later Goldreich-Micali-Wigderson prove the
"fundamental theorem of cryptography", which essentially states that any
computational functionality can be achieved "efficiently" and securely. I.e.,
given k parties with one input each and any function F of k inputs and k
outputs, the parties can communicate so that each learns their output of the
function on all the inputs, and nothing else.

\- 2003: Perelman's proof of the geometrization conjecture.

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decasteve
If we consider the topical chronology/lineage stemming from Euclid's Elements,
and how much of our world relies on Mathematics, one could argue that it is
the most influential book ever written.

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samdoidge
Highlight: 'About 1950BC Babylonians solve quadratic equations.'

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partycoder
It would be good to include the setbacks caused by religious intervention.

You can find some of it here in this other timeline:
[http://superstringtheory.com/history/history1.html](http://superstringtheory.com/history/history1.html)

e.g: Hypatia, Galileo, Kepler, Copernicus... and many more.

~~~
fjdlwlv
Galileo's wasn't held back by religious intervention against science.

Even debates about heliocentrism weren't interfering with math.

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iamandoni
> Adleman, Rivest, and Shamir introduce public-key codes, a system for passing
> secret messages using large primes and a key which can be published.

My OCD wishes they would have said Rivest, Shamir, and Adleman like the
algorithm is named after

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tempodox
Fascinating.

Nitpick: It would be even nicer if the images on the main page were annotated
with the person's name. I recognized e.g. Einstein and Turing, but who are all
the others?

~~~
kercker
You can try this link: [http://www-history.mcs.st-
andrews.ac.uk/Miscellaneous/bg_pic...](http://www-history.mcs.st-
andrews.ac.uk/Miscellaneous/bg_picture.html)

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lorddoig
I wish I knew St Andrews was home to a cool mathematics department and the
progenitor of Idris when I was there, filling my body with mind-altering
chemicals.

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mrybczyn
Fantastic, I wish I had read this back in elementary / high school.

Will review with the kids!

Not having this context in mathematics teaching is criminal.

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du_bing
A typo:

1991 Quidong Wang finds infinite series solutions to the n-body problem (with
minor exceptions).

The name is Qiudong Wang.

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h3ctic
Wondering how much from the last 100 years has been left out

~~~
swampers
Probably a huge amount given that ~50% of the mathematicians* who have ever
been alive are alive today.

Source: Pure Mathematics Hons BSc, St Andrews - I took the St Andrews "History
of Mathematics" course this site's information is used in.

*For a given value of 'mathematician'. And 'alive', I guess.

~~~
mbrd
Nice to see another St Andrews person on HN - I took that course too! I only
wrote two essays during my four year degree, one for this class! (I wrote
about Alexander Aitken, a gifted mental arithmetician)

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macawfish
No mention of William Clifford?

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metakermit
Pro tip – Cmd/Ctrl+F for "independently". Research redundancy :)

