Could geniuses of the past catch up in a few months?

Question

A historical college is facing closure, due their failing job placement, inflated grades and rumors that its nothing but a diploma mill.

The last chance for the new president to persuade to the education board that it could turn the ship around, plus get donations from the alumni is good showing on the upcoming math competition.

Since the homegrown talent is lacking, the president asks for help from his aunt who dabbles in voodoo. She promises to embody the spirits of great minds from the past, into the bodies of selected math team.

The only rule is they have to be dead for more then a century, the longer the better. And they wouldn't know anything they didn't know when they died, beside understanding of English. This is for story telling purposes.

Could geniuses of the past catch up in a few months?

My assumption is that he should bring people that are not that far in the past such as Euler, Gauss, Riemann, Descartes, Newton etc.

Older titans such as Euclid, Pythagoras, Fibonacci are too far behind from the modern knowledge.

I want something plausible, but my story is more on the funny side. I plan many funny sketches with 3rd rate math professor trying to teach modern knowledge to some of the greatest minds of the mankind.

Addendum

The geniuses will live and study in the university with the math professor which is their team coach fully at their disposal. The professor will adapt to their needs and knowledge. Meaning chalk and black board, not email and video lessons. Until & unless some of them want to learn in the new way. It's in interest of the math professor's and his colleagues to help them succeed, otherwise both the university and their jobs are lost.

The university buildings date centuries ago, and its not too different from what they've seen in the past.

Though the buildings have been upgraded with modern amenities such as electricity, running water, air conditioning, internet & computers.

So yes there would be culture shock, but hopefully it won't last too long.

Answer 1

Since it has been covered in other answers, I will give an answer that ignores linguistic deficiencies and culture shock, and focus on solely the mathematics.

Mathematics exploded in the 20th century:

Here is a graph of some of the modern areas of mathematics (my apologies for the crummy graphic but I couldn't find a better picture). You can find the source of the graphic as well as a good description of mathematics through the centuries at this website.

In the United States, a typical undergraduate degree in Mathematics would present you with core courses in most of the above disciplines, with the exception of a few of the 'applied mathematics' branches (Mathematical Physics, Fluid Dynamics, Financial Mathematics, and Cryptography) being electives.

The problem you will face is that most of the these disciplines did not exist a century ago; or more accurately, they existed only as anecdotes in other disciplines. Topology is an excellent example. There are theorems in topology that date back to Euler (see the seven bridges of Konisberg ) but the discipline itself (it's theorems, jargon, pedagogy and indeed whole concept) is entirely modern. A list of disciplines which would be largely unrecognizable to a mathematician a century ago would look like:

• Game Theory
• Cryptography
• Information Theory / Theory of Computation
• Category Theory
• Topology
• Abstract Algebra
• Chaos Theory

A list of disciplines that would be vaguely recognizable to some degree, or were cutting edge a century ago include:

• Differential Geometry
• Fractal Geometry
• Set Theory
• Optimization
• Probability Theory
• Numerical Analysis

A list of 'traditional' mathematics that would be recognizable to mathematicians going back at least 300 years would be:

• Geometry
• Trigonometry
• Number Theory
• Calculus
• Differential Equations
• Combinatorics
• Graph Theory

That's a lot. A typical undergraduate or graduate student might take two (possibly three) mathematics courses in a four month (120 day) semester; that is around 48 days per discipline. Let's lay out a curriculum that spends 60% of it's time on topics from the first list, 30% from topics in the second list, and 10% from topics in the final list. If we assume we spent three months (90 days) prepping our antique mathematician, that means:

• 7.7 days per discipline in the first list, (6 times normal student speed)
• 4.5 days per discipline in the second list, (10 times normal student speed)
• 1.3 days for each discipline in the last list. (37 times normal student speed)

The Answer

I would conclude from those figures that the process of bringing an antique mathematician 'up to speed' at the level of an undergraduate degree in only 90 days is likely hopeless. The main reason why it takes a typical student around 120 days to finish a single introductory course to a discipline is the 'absorption rate' of new concepts; the main reason why students who 'cram' for exams typically fail them.

An alternative

If however, the competition were to be narrowed to a single discipline, then the chances of the president's scheme working greatly increases. Furthermore, I believe that gives your story more drama to work with. Is there a competing college? Do they have an 'expert in discipline X'? If so, what better way to trounce them than revive one of the disciplines founders, get him or her up to speed, and win the competition? If you go this route, here are some recommendations based on disciplines:

• Georg Cantor (1845-1918): invented set theory and the concept of cardinal sets. Would do well with fractals.
• Henry Poincaire (1854-1912): foundational work in topology and chaos theory.
• Carl Friedrich Gauss (1777-1855): foundational work in statistics, number theory, and differential geometry
• Leonard Euler (1707 - 1783): foundational work in number theory and graph theory.

Answer 2

A Few Months isn't Even Enough to get Over Culture Shock

I've traveled and lived internationally quite a lot. It takes 3 to 4 months in a new place just to get over culture shock and the local way of doing things. Culture shock tends to follow a pretty distinct pattern:

Honeymoon: everything is so new and delightfully different! Its so exciting and challenging and odd!

Resentment: EVERYTHING is so OFF! Nothing is working how it should! You know better ways to do things and nobody listens, you are so sick of the silly idiosyncrasies and quirky weirdness in how everyone around you does things. You're sick of being the eternal outsider and just want to go home. Everything is a huge chore and at the end of the day just simple things like getting groceries or going to the bank leave you feeling frustrated and exhausted.

Acceptance: You still miss home and hate the outsider status you still seem to carry around. You still really want to go home and think all the different sometimes inefficient ways things are done really suck, but you've accepted them and take it in stride.

Integration: You have finally been around enough to not be considered the weird foreigner, you understand more about the culture and why they do things the way they do and it doesn't bother you anymore. You still get homesick sometimes but have integrated well enough that your new locale is starting to feel more like a second home and less like a self imposed exile.

I've lived in Germany, France, Poland, Kuwait, USA, Jordan, and England. No matter how many times I've moved its always a few months just to quit feeling like blowing my stack over how inefficient Middle Eastern banking is, or how in Europe, package companies NEVER seem to deliver on time, or how Germans seem to need to cut down half a forest for the papers needed to perform a seemingly trivial task, etc etc. My point being, these guys would be even more isolated from their surroundings since even in their home countries they are no longer part of the culture.

Culture shock is going to provide a truly spectacular distraction from their studies them to overcome. I would give them about 6 months to perform this task without appearing like somebody who is simply plagiarizing the work of past greats.

Answer 3

I think so

The Progress of Knowledge is Slow

Quaternions, invented by Hamilton in 1843, is still cutting edge math for graphics.

Eulers matrix transformations are still used in orbital mechanics.

Matrix mathematics is still the foundation of quantum mechanics.

Riemann manifolds are the foundation of general relativity.

Newton's physics is still applicable for all cases but very small sizes and very high energies. Calculus is still the math for business.

Descartes was a contemporary of Newton, and his ideas challenged Newton's for some time. Descartes might have trouble learning more owing to being unwilling to cede the argument.