Problem solving is a top-notch skill. All of us face problems, in work, in life and every day happening. Jokingly mathematicians identify the following stages of a problem solving:
- Identifying the problem (includes preparation, collecting information, identifying challenges and risks) .
- Attacking the problem (use existing tools, techniques to derive new method). Get vigorous, consciously.
- The problem attacking becomes an unconscious activity from a conscious one, then the problem starts attacking you.
- Either problem is consumed or the attacker is consumed by problem.
Especially at stage 4, one will be thinking only about the problem. While driving, eating, teaching and even in sleep. Archimedes resolved the problem when he was bathing. Isaac Singer, the american inventor of sewing machines was supposed to found solution for the problem of finding where to put hole in needle so that it is easy to stitch, in dream, he dreamt of someone chasing him with strange spear with a hole in the spear head. These are examples of sub conscious mind solving problems.
What happens when you are preoccupied with a problem, little too much, okay, way too much? Either you solve the problem successfully or you loose your mind over it and end up ruining your life.
Problem with problems
Mathematics is full of stories like this. And today we will see such stories.
I happened to read about a documentary about mathematicians on BBC and had chance to watch it. “Dangerous Knowledge” is a one-off documentary about four brilliant mathematicians – Georg Cantor, Ludwig Boltzman, Alan Turing and Kurt Godel. After seeing it what struck my mind was, though study of mathematics is seen purely as an intellectual activity with communication with other mathematicians, over the years has become more and more intense on being becoming an personal activity, challenging individual knowledge more than ever. Lets see some strange personalities in mathematical world.
Georg Cantor: (1845 – 1918)
Georg Cantor is known for his deep theories in set theory. His theory includes, importance of one-to-one correspondence, transfinite numbers and infinity of infinities. When he first said that there could be different sizes to infinities, it was totally counter intuitive and created enough uproar (yet to be settled). Henry Poincare declared Cantor’s ideas as a dangerous disease which corrupts the young mind. Leopold Kronecker, Hermann Weyl and few other mathematicians joined in tarnishing Georg Cantor’s mathematical reputation. Cantor also strained his professional relationship with Mittag Leffler and Richard Dedekind. All through this Cantor never worried but only about the mathematical theories he was producing. He was so much occupied by ‘Continuum Hypothesis‘.
Cantor tried proving continuum hypothesis all through his life. Couple of times he claimed wrongly that he was able to prove only to withdraw the claim later. Cantor was so occupied with the continuum hypothesis problem, that he knew that could not solve it easily. Through his mid-career he considered abending mathematical career and pursuing a career in philosophy. He was also admitted to mental sanatorium couple of times for five or more years. When ever he tried fixing continuum hypothesis he had nervous break down and would lose his mental health.
He suffered from depression and nervous breakdown. Cantor declared the theory of transfinite number was given to him by god (another mathematician who attributed his knowledge to god was Srinivasa Ramanujan). Cantor died in a mental asylum in 1918.
David Hilbert during one of his famous speech said:
No one shall expel us from the Paradise that Cantor has created.
Continuum hypothesis is still not proved.
Kurt Godel: (1906 – 1978)
Kurt Godel‘s life too is linked with continuum hypothesis. Godel was a German. He proved one of Hilbert’s mathematical question. Albeit in a negative assertion, he proved that there will be in-complete systems. This is known as incompleteness theorems.
Godel published many papers in logic, set theory and theology. During his hearing for US citizenship, when asked whether there is possibility of dictator ship in US, he answered a strange but possible loop-hole, thus putting his appeal in jeopardy. Albert Einstein was a great friend to Godel. During his last days came to Princeton University only to have a walk with him in campus. Godel tried solving Continuum hypothesis. He did make advancement by proving that adding certain axioms wont prove / disprove the hypothesis.
However, though being a perfect logician, Godel always suspected someone would kill him by poisoning. He always wanted his wife to eat the food before he would eat. Godel is also an introvert. He would restrain from touching people and body contacts. After his wife passing out, Godel never had a proper food. He concentrated on solving the open problems more vigor only to worsen his health. He was admitted to hospital several times for malnutrition. When he passed out in his 70s, the doctor observed Godel died of malnutrition and starving.
Here is a mathematician, a perfect logician, a wealthy person, tried to solve problems late till his age dying of starving.
John Nash: (1928 *)
John Nash is a genius mathematician. He perhaps would have affected our worldly understanding more than anyone else would have. Starting from complex systems, evolutionary biology, market economics to sociology, he had a far more impact. Nash also awarded Nobel prize.
John Nash too had his part of mental paranoia. His story is explained in Hollywood movie – ‘A Beautiful Mind’. He was admitted in hospital for treatment and remained there for close to 12 years. Nash said he started seeing delusional characters, an agency, in which all of them wore a red tie and chasing him.
Nash’s story is that of a successful one with lot of struggle. After his return from hospital for treatment for paranoid schizophrenia. He did further advancement of game theory, economics and market study. He published close to 25 papers after returning from mental asylum.
There are some strange habits among mathematicians:
Andrew Whiles, who proved Fermat’s last theorem, did all the math hiding in attic. He would never tell to his wife of what he was doing and hide in attic for close to 8 years.
Srinivasa Ramanujan declared few equations / proofs were given to him by his family goddess ‘Namakal’.